Sec 2 G1 Maths Tutor Bukit Timah

Reader note: These are original hypothetical monetary exercises, not current financial products, offers, rates, legal terms or recommendations about borrowing. A classroom cost comparison covers only the stated amounts. Real contracts require up-to-date written terms and individual consideration. School scope, actual tutor classes and fees must be verified directly.

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

Day one: add one deposit to a multiplied number of monthly payments.
Day two: compare a plan’s full total against a supplied cash price.
Day three: find the unknown monthly payment from the complete sum.
Day four: compare two made-up terms, including one stated once-only fee.
Day five: explain why ‘lowest monthly payment’ and ‘lowest full cost’ do not mean the same thing.

Parents can use invented amounts rather than real family payment records. Ask ‘How often is that amount paid?’ and ‘Does the advertisement-like number cover the complete schedule?’ Those two questions expose the important mathematical distinctions without turning a tuition exercise into a real purchase decision.

Frequently asked questions

How do I find total paid?

Add the deposit once, every scheduled periodic payment and any other separately stated amount under the specified terms.

Is a lower monthly payment always cheaper?

No. The number of payments, deposit and fees can alter the full total.

How do I find an unknown monthly payment?

Subtract once-only charges from the complete stated total and divide by the number of equal payments.

Does overpaying the cash price tell us APR?

No. Annualised financing rates require more detailed cash-flow and financing assumptions.

Are these genuine offers or personal advice?

No. Every plan in this guide is fictional and used only for mathematical literacy.

Are instalments mentioned in G1 Mathematics?

The 2027 K110 graduating syllabus names instalments as a possible household-finance context. Current year-level teaching depends on the school.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

Day one: add one deposit to a multiplied number of monthly payments.
Day two: compare a plan’s full total against a supplied cash price.
Day three: find the unknown monthly payment from the complete sum.
Day four: compare two made-up terms, including one stated once-only fee.
Day five: explain why ‘lowest monthly payment’ and ‘lowest full cost’ do not mean the same thing.

Frequently asked questions

How do I find total paid?

Add the deposit once, every scheduled periodic payment and any other separately stated amount under the specified terms.

Is a lower monthly payment always cheaper?

No. The number of payments, deposit and fees can alter the full total.

How do I find an unknown monthly payment?

Subtract once-only charges from the complete stated total and divide by the number of equal payments.

Does overpaying the cash price tell us APR?

No. Annualised financing rates require more detailed cash-flow and financing assumptions.

Are these genuine offers or personal advice?

No. Every plan in this guide is fictional and used only for mathematical literacy.

Are instalments mentioned in G1 Mathematics?

The 2027 K110 graduating syllabus names instalments as a possible household-finance context. Current year-level teaching depends on the school.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

10 minutes: identify deposit, per-period charge, number of periods and any one-time fee.
20 minutes: build a payment schedule as blocks and a one-variable equation.
25 minutes: solve full totals and reverse questions individually.
15 minutes: compare two fictional complete schedules.
10 minutes: spot one missing term or unjustified inference.
10 minutes: reverse-check the total and choose a short delayed retest.

Five manageable parent practice sessions

Day one: add one deposit to a multiplied number of monthly payments.
Day two: compare a plan’s full total against a supplied cash price.
Day three: find the unknown monthly payment from the complete sum.
Day four: compare two made-up terms, including one stated once-only fee.
Day five: explain why ‘lowest monthly payment’ and ‘lowest full cost’ do not mean the same thing.

Frequently asked questions

How do I find total paid?

Add the deposit once, every scheduled periodic payment and any other separately stated amount under the specified terms.

Is a lower monthly payment always cheaper?

No. The number of payments, deposit and fees can alter the full total.

How do I find an unknown monthly payment?

Subtract once-only charges from the complete stated total and divide by the number of equal payments.

Does overpaying the cash price tell us APR?

No. Annualised financing rates require more detailed cash-flow and financing assumptions.

Are these genuine offers or personal advice?

No. Every plan in this guide is fictional and used only for mathematical literacy.

Are instalments mentioned in G1 Mathematics?

The 2027 K110 graduating syllabus names instalments as a possible household-finance context. Current year-level teaching depends on the school.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

10 minutes: identify deposit, per-period charge, number of periods and any one-time fee.
20 minutes: build a payment schedule as blocks and a one-variable equation.
25 minutes: solve full totals and reverse questions individually.
15 minutes: compare two fictional complete schedules.
10 minutes: spot one missing term or unjustified inference.
10 minutes: reverse-check the total and choose a short delayed retest.

Five manageable parent practice sessions

Day one: add one deposit to a multiplied number of monthly payments.
Day two: compare a plan’s full total against a supplied cash price.
Day three: find the unknown monthly payment from the complete sum.
Day four: compare two made-up terms, including one stated once-only fee.
Day five: explain why ‘lowest monthly payment’ and ‘lowest full cost’ do not mean the same thing.

Frequently asked questions

How do I find total paid?

Add the deposit once, every scheduled periodic payment and any other separately stated amount under the specified terms.

Is a lower monthly payment always cheaper?

No. The number of payments, deposit and fees can alter the full total.

How do I find an unknown monthly payment?

Subtract once-only charges from the complete stated total and divide by the number of equal payments.

Does overpaying the cash price tell us APR?

No. Annualised financing rates require more detailed cash-flow and financing assumptions.

Are these genuine offers or personal advice?

No. Every plan in this guide is fictional and used only for mathematical literacy.

Are instalments mentioned in G1 Mathematics?

The 2027 K110 graduating syllabus names instalments as a possible household-finance context. Current year-level teaching depends on the school.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

A sixty-second full-cost comparison
Once-only versus repeated amounts
What a total cannot tell you
Complete a deposit-plus-payments total
Compare cash price with full instalment cost
Recover the unknown monthly payment
Recover the unknown number of months
Compare two different payment plans
Make a household budget arithmetic check
Identify missing or misleading plan terms
A three-pupil tutorial
Questions and answers
Official references

Which option has the lower full total?

Ask a pupil to compare fictional A at $30 per month for 24 months and fictional B at $50 per month for twelve months, with no deposits. A totals $720 and B totals $600; B is $120 lower despite its larger monthly amount. If B then adds an up-front deposit of $150, its full total becomes $750 and A becomes lower by $30. A good learner updates the equation to reflect the new fact rather than remembering the first plan’s answer.

A deposit has a different time role from a monthly fee

Use a one-off deposit block followed by n equal monthly payment blocks. The model is T=D+mn+F when a one-off administration fee F is explicitly supplied. Every symbol should be named, including whether a dollar amount is an up-front deposit, a payment each month or a charge counted only once. The rate’s unit is dollars per payment, while n is the count of payments. That dimensional distinction helps correct faulty multiplication.

Lower total and easier cash flow are different questions

Two plans can have the same full total but different up-front and monthly needs. A simple price difference also does not define an effective annual interest rate, nor does a positive residual in a fictional monthly budget prove affordability. Real arrangements need current written payment schedules and terms; these school examples can teach arithmetic without making financial recommendations.

282 original instalment cost and comparison clinics

The examples use fictional plans, deposits, durations, fees and budgets. Each focuses on one mathematical decision, a complete worked calculation, an early error to avoid and a changed-payment test. Use a few cases appropriate to current school scope rather than copying the entire bank. Real offers and personal financial circumstances are not being evaluated.

Complete a deposit-plus-payments total

For complete a deposit-plus-payments total, list every monetary amount and its frequency before calculating. Use the total to check an unknown monthly payment or payment count by reversing operations. Be clear that comparing two complete arithmetic totals is not the same as recommending a real financial commitment. If the question omits a fee or schedule, don’t invent it.

1. One deposit and 3 repeated payments · 1

Question: An imaginary purchase requires a $40.00 deposit paid once and 3 monthly payments of $30.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 3 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 3×$30.00=$90.00. Adding the deposit once gives $130.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Common first error: Multiplying the deposit by 3 treats it as an extra monthly payment. Adding only one monthly charge neglects 2 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $130.00−$40.00=$90.00, which exactly equals 3 payments of $30.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $30.00 were added without changing the deposit, the new full cost would be $160.00. The deposit should not be repeated.

2. One deposit and 4 repeated payments · 2

Question: An imaginary purchase requires a $180.00 deposit paid once and 4 monthly payments of $140.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 4 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 4×$140.00=$560.00. Adding the deposit once gives $740.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Common first error: Multiplying the deposit by 4 treats it as an extra monthly payment. Adding only one monthly charge neglects 3 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $740.00−$180.00=$560.00, which exactly equals 4 payments of $140.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $140.00 were added without changing the deposit, the new full cost would be $880.00. The deposit should not be repeated.

3. One deposit and 6 repeated payments · 3

Question: An imaginary purchase requires a $320.00 deposit paid once and 6 monthly payments of $250.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 6 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 6×$250.00=$1,500.00. Adding the deposit once gives $1,820.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Common first error: Multiplying the deposit by 6 treats it as an extra monthly payment. Adding only one monthly charge neglects 5 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $1,820.00−$320.00=$1,500.00, which exactly equals 6 payments of $250.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $250.00 were added without changing the deposit, the new full cost would be $2,070.00. The deposit should not be repeated.

4. One deposit and 8 repeated payments · 4

Question: An imaginary purchase requires a $460.00 deposit paid once and 8 monthly payments of $360.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 8 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 8×$360.00=$2,880.00. Adding the deposit once gives $3,340.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Common first error: Multiplying the deposit by 8 treats it as an extra monthly payment. Adding only one monthly charge neglects 7 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $3,340.00−$460.00=$2,880.00, which exactly equals 8 payments of $360.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $360.00 were added without changing the deposit, the new full cost would be $3,700.00. The deposit should not be repeated.

5. One deposit and 10 repeated payments · 5

Question: An imaginary purchase requires a $600.00 deposit paid once and 10 monthly payments of $120.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 10 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 10×$120.00=$1,200.00. Adding the deposit once gives $1,800.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Common first error: Multiplying the deposit by 10 treats it as an extra monthly payment. Adding only one monthly charge neglects 9 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $1,800.00−$600.00=$1,200.00, which exactly equals 10 payments of $120.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $120.00 were added without changing the deposit, the new full cost would be $1,920.00. The deposit should not be repeated.

6. One deposit and 12 repeated payments · 6

Question: An imaginary purchase requires a $140.00 deposit paid once and 12 monthly payments of $230.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 12 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 12×$230.00=$2,760.00. Adding the deposit once gives $2,900.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Common first error: Multiplying the deposit by 12 treats it as an extra monthly payment. Adding only one monthly charge neglects 11 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $2,900.00−$140.00=$2,760.00, which exactly equals 12 payments of $230.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $230.00 were added without changing the deposit, the new full cost would be $3,130.00. The deposit should not be repeated.

7. One deposit and 15 repeated payments · 7

Question: An imaginary purchase requires a $280.00 deposit paid once and 15 monthly payments of $340.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 15 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 15×$340.00=$5,100.00. Adding the deposit once gives $5,380.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Common first error: Multiplying the deposit by 15 treats it as an extra monthly payment. Adding only one monthly charge neglects 14 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $5,380.00−$280.00=$5,100.00, which exactly equals 15 payments of $340.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $340.00 were added without changing the deposit, the new full cost would be $5,720.00. The deposit should not be repeated.

8. One deposit and 18 repeated payments · 8

Question: An imaginary purchase requires a $420.00 deposit paid once and 18 monthly payments of $100.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 18 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 18×$100.00=$1,800.00. Adding the deposit once gives $2,220.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Common first error: Multiplying the deposit by 18 treats it as an extra monthly payment. Adding only one monthly charge neglects 17 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $2,220.00−$420.00=$1,800.00, which exactly equals 18 payments of $100.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $100.00 were added without changing the deposit, the new full cost would be $2,320.00. The deposit should not be repeated.

9. One deposit and 24 repeated payments · 9

Question: An imaginary purchase requires a $560.00 deposit paid once and 24 monthly payments of $210.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Interpret the payments: A deposit is an up-front one-time amount. A monthly fee repeats 24 times. The full total follows deposit + monthly charge × number of months, not a comparison between the deposit and one single instalment.

Worked answer: The repeated subtotal is 24×$210.00=$5,040.00. Adding the deposit once gives $5,600.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Common first error: Multiplying the deposit by 24 treats it as an extra monthly payment. Adding only one monthly charge neglects 23 months. Identify the payment’s frequency before choosing the operation.

Reverse-check: Subtract the up-front deposit from total: $5,600.00−$560.00=$5,040.00, which exactly equals 24 payments of $210.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $210.00 were added without changing the deposit, the new full cost would be $5,810.00. The deposit should not be repeated.

10. One deposit and 3 repeated payments · 10

Question: An imaginary purchase requires a $100.00 deposit paid once and 3 monthly payments of $320.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 3×$320.00=$960.00. Adding the deposit once gives $1,060.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,060.00−$100.00=$960.00, which exactly equals 3 payments of $320.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $320.00 were added without changing the deposit, the new full cost would be $1,380.00. The deposit should not be repeated.

11. One deposit and 4 repeated payments · 11

Question: An imaginary purchase requires a $240.00 deposit paid once and 4 monthly payments of $80.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 4×$80.00=$320.00. Adding the deposit once gives $560.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $560.00−$240.00=$320.00, which exactly equals 4 payments of $80.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $80.00 were added without changing the deposit, the new full cost would be $640.00. The deposit should not be repeated.

12. One deposit and 6 repeated payments · 12

Question: An imaginary purchase requires a $380.00 deposit paid once and 6 monthly payments of $190.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 6×$190.00=$1,140.00. Adding the deposit once gives $1,520.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,520.00−$380.00=$1,140.00, which exactly equals 6 payments of $190.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $190.00 were added without changing the deposit, the new full cost would be $1,710.00. The deposit should not be repeated.

13. One deposit and 8 repeated payments · 13

Question: An imaginary purchase requires a $520.00 deposit paid once and 8 monthly payments of $300.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 8×$300.00=$2,400.00. Adding the deposit once gives $2,920.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,920.00−$520.00=$2,400.00, which exactly equals 8 payments of $300.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $300.00 were added without changing the deposit, the new full cost would be $3,220.00. The deposit should not be repeated.

14. One deposit and 10 repeated payments · 14

Question: An imaginary purchase requires a $60.00 deposit paid once and 10 monthly payments of $60.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 10×$60.00=$600.00. Adding the deposit once gives $660.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $660.00−$60.00=$600.00, which exactly equals 10 payments of $60.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $60.00 were added without changing the deposit, the new full cost would be $720.00. The deposit should not be repeated.

15. One deposit and 12 repeated payments · 15

Question: An imaginary purchase requires a $200.00 deposit paid once and 12 monthly payments of $170.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 12×$170.00=$2,040.00. Adding the deposit once gives $2,240.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,240.00−$200.00=$2,040.00, which exactly equals 12 payments of $170.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $170.00 were added without changing the deposit, the new full cost would be $2,410.00. The deposit should not be repeated.

16. One deposit and 15 repeated payments · 16

Question: An imaginary purchase requires a $340.00 deposit paid once and 15 monthly payments of $280.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 15×$280.00=$4,200.00. Adding the deposit once gives $4,540.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $4,540.00−$340.00=$4,200.00, which exactly equals 15 payments of $280.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $280.00 were added without changing the deposit, the new full cost would be $4,820.00. The deposit should not be repeated.

17. One deposit and 18 repeated payments · 17

Question: An imaginary purchase requires a $480.00 deposit paid once and 18 monthly payments of $40.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 18×$40.00=$720.00. Adding the deposit once gives $1,200.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,200.00−$480.00=$720.00, which exactly equals 18 payments of $40.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $40.00 were added without changing the deposit, the new full cost would be $1,240.00. The deposit should not be repeated.

18. One deposit and 24 repeated payments · 18

Question: An imaginary purchase requires a $620.00 deposit paid once and 24 monthly payments of $150.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 24×$150.00=$3,600.00. Adding the deposit once gives $4,220.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $4,220.00−$620.00=$3,600.00, which exactly equals 24 payments of $150.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $150.00 were added without changing the deposit, the new full cost would be $4,370.00. The deposit should not be repeated.

19. One deposit and 3 repeated payments · 19

Question: An imaginary purchase requires a $160.00 deposit paid once and 3 monthly payments of $260.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 3×$260.00=$780.00. Adding the deposit once gives $940.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $940.00−$160.00=$780.00, which exactly equals 3 payments of $260.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $260.00 were added without changing the deposit, the new full cost would be $1,200.00. The deposit should not be repeated.

20. One deposit and 4 repeated payments · 20

Question: An imaginary purchase requires a $300.00 deposit paid once and 4 monthly payments of $370.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 4×$370.00=$1,480.00. Adding the deposit once gives $1,780.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,780.00−$300.00=$1,480.00, which exactly equals 4 payments of $370.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $370.00 were added without changing the deposit, the new full cost would be $2,150.00. The deposit should not be repeated.

21. One deposit and 6 repeated payments · 21

Question: An imaginary purchase requires a $440.00 deposit paid once and 6 monthly payments of $130.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 6×$130.00=$780.00. Adding the deposit once gives $1,220.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,220.00−$440.00=$780.00, which exactly equals 6 payments of $130.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $130.00 were added without changing the deposit, the new full cost would be $1,350.00. The deposit should not be repeated.

22. One deposit and 8 repeated payments · 22

Question: An imaginary purchase requires a $580.00 deposit paid once and 8 monthly payments of $240.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 8×$240.00=$1,920.00. Adding the deposit once gives $2,500.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,500.00−$580.00=$1,920.00, which exactly equals 8 payments of $240.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $240.00 were added without changing the deposit, the new full cost would be $2,740.00. The deposit should not be repeated.

23. One deposit and 10 repeated payments · 23

Question: An imaginary purchase requires a $120.00 deposit paid once and 10 monthly payments of $350.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 10×$350.00=$3,500.00. Adding the deposit once gives $3,620.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,620.00−$120.00=$3,500.00, which exactly equals 10 payments of $350.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $350.00 were added without changing the deposit, the new full cost would be $3,970.00. The deposit should not be repeated.

24. One deposit and 12 repeated payments · 24

Question: An imaginary purchase requires a $260.00 deposit paid once and 12 monthly payments of $110.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 12×$110.00=$1,320.00. Adding the deposit once gives $1,580.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,580.00−$260.00=$1,320.00, which exactly equals 12 payments of $110.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $110.00 were added without changing the deposit, the new full cost would be $1,690.00. The deposit should not be repeated.

25. One deposit and 15 repeated payments · 25

Question: An imaginary purchase requires a $400.00 deposit paid once and 15 monthly payments of $220.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 15×$220.00=$3,300.00. Adding the deposit once gives $3,700.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,700.00−$400.00=$3,300.00, which exactly equals 15 payments of $220.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $220.00 were added without changing the deposit, the new full cost would be $3,920.00. The deposit should not be repeated.

26. One deposit and 18 repeated payments · 26

Question: An imaginary purchase requires a $540.00 deposit paid once and 18 monthly payments of $330.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 18×$330.00=$5,940.00. Adding the deposit once gives $6,480.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $6,480.00−$540.00=$5,940.00, which exactly equals 18 payments of $330.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $330.00 were added without changing the deposit, the new full cost would be $6,810.00. The deposit should not be repeated.

27. One deposit and 24 repeated payments · 27

Question: An imaginary purchase requires a $80.00 deposit paid once and 24 monthly payments of $90.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 24×$90.00=$2,160.00. Adding the deposit once gives $2,240.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,240.00−$80.00=$2,160.00, which exactly equals 24 payments of $90.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $90.00 were added without changing the deposit, the new full cost would be $2,330.00. The deposit should not be repeated.

28. One deposit and 3 repeated payments · 28

Question: An imaginary purchase requires a $220.00 deposit paid once and 3 monthly payments of $200.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 3×$200.00=$600.00. Adding the deposit once gives $820.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $820.00−$220.00=$600.00, which exactly equals 3 payments of $200.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $200.00 were added without changing the deposit, the new full cost would be $1,020.00. The deposit should not be repeated.

29. One deposit and 4 repeated payments · 29

Question: An imaginary purchase requires a $360.00 deposit paid once and 4 monthly payments of $310.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 4×$310.00=$1,240.00. Adding the deposit once gives $1,600.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,600.00−$360.00=$1,240.00, which exactly equals 4 payments of $310.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $310.00 were added without changing the deposit, the new full cost would be $1,910.00. The deposit should not be repeated.

30. One deposit and 6 repeated payments · 30

Question: An imaginary purchase requires a $500.00 deposit paid once and 6 monthly payments of $70.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 6×$70.00=$420.00. Adding the deposit once gives $920.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $920.00−$500.00=$420.00, which exactly equals 6 payments of $70.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $70.00 were added without changing the deposit, the new full cost would be $990.00. The deposit should not be repeated.

31. One deposit and 8 repeated payments · 31

Question: An imaginary purchase requires a $40.00 deposit paid once and 8 monthly payments of $180.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 8×$180.00=$1,440.00. Adding the deposit once gives $1,480.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,480.00−$40.00=$1,440.00, which exactly equals 8 payments of $180.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $180.00 were added without changing the deposit, the new full cost would be $1,660.00. The deposit should not be repeated.

32. One deposit and 10 repeated payments · 32

Question: An imaginary purchase requires a $180.00 deposit paid once and 10 monthly payments of $290.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 10×$290.00=$2,900.00. Adding the deposit once gives $3,080.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,080.00−$180.00=$2,900.00, which exactly equals 10 payments of $290.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $290.00 were added without changing the deposit, the new full cost would be $3,370.00. The deposit should not be repeated.

33. One deposit and 12 repeated payments · 33

Question: An imaginary purchase requires a $320.00 deposit paid once and 12 monthly payments of $50.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 12×$50.00=$600.00. Adding the deposit once gives $920.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $920.00−$320.00=$600.00, which exactly equals 12 payments of $50.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $50.00 were added without changing the deposit, the new full cost would be $970.00. The deposit should not be repeated.

34. One deposit and 15 repeated payments · 34

Question: An imaginary purchase requires a $460.00 deposit paid once and 15 monthly payments of $160.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 15×$160.00=$2,400.00. Adding the deposit once gives $2,860.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,860.00−$460.00=$2,400.00, which exactly equals 15 payments of $160.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $160.00 were added without changing the deposit, the new full cost would be $3,020.00. The deposit should not be repeated.

35. One deposit and 18 repeated payments · 35

Question: An imaginary purchase requires a $600.00 deposit paid once and 18 monthly payments of $270.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 18×$270.00=$4,860.00. Adding the deposit once gives $5,460.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $5,460.00−$600.00=$4,860.00, which exactly equals 18 payments of $270.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $270.00 were added without changing the deposit, the new full cost would be $5,730.00. The deposit should not be repeated.

36. One deposit and 24 repeated payments · 36

Question: An imaginary purchase requires a $140.00 deposit paid once and 24 monthly payments of $30.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 24×$30.00=$720.00. Adding the deposit once gives $860.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $860.00−$140.00=$720.00, which exactly equals 24 payments of $30.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $30.00 were added without changing the deposit, the new full cost would be $890.00. The deposit should not be repeated.

37. One deposit and 3 repeated payments · 37

Question: An imaginary purchase requires a $280.00 deposit paid once and 3 monthly payments of $140.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 3×$140.00=$420.00. Adding the deposit once gives $700.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $700.00−$280.00=$420.00, which exactly equals 3 payments of $140.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $140.00 were added without changing the deposit, the new full cost would be $840.00. The deposit should not be repeated.

38. One deposit and 4 repeated payments · 38

Question: An imaginary purchase requires a $420.00 deposit paid once and 4 monthly payments of $250.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 4×$250.00=$1,000.00. Adding the deposit once gives $1,420.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,420.00−$420.00=$1,000.00, which exactly equals 4 payments of $250.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $250.00 were added without changing the deposit, the new full cost would be $1,670.00. The deposit should not be repeated.

39. One deposit and 6 repeated payments · 39

Question: An imaginary purchase requires a $560.00 deposit paid once and 6 monthly payments of $360.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 6×$360.00=$2,160.00. Adding the deposit once gives $2,720.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,720.00−$560.00=$2,160.00, which exactly equals 6 payments of $360.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $360.00 were added without changing the deposit, the new full cost would be $3,080.00. The deposit should not be repeated.

40. One deposit and 8 repeated payments · 40

Question: An imaginary purchase requires a $100.00 deposit paid once and 8 monthly payments of $120.00. The problem explicitly states there are no other fees. What is the complete amount paid?

Worked answer: The repeated subtotal is 8×$120.00=$960.00. Adding the deposit once gives $1,060.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,060.00−$100.00=$960.00, which exactly equals 8 payments of $120.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $120.00 were added without changing the deposit, the new full cost would be $1,180.00. The deposit should not be repeated.

Compare cash price with full instalment cost

For compare cash price with full instalment cost, list every monetary amount and its frequency before calculating. Use the total to check an unknown monthly payment or payment count by reversing operations. Be clear that comparing two complete arithmetic totals is not the same as recommending a real financial commitment. If the question omits a fee or schedule, don’t invent it.

41. Cash price versus complete plan · 1

Question: An imaginary item has a cash price of $1,200.00. A fictional alternative has a deposit $40.00 plus 4 payments of $277.50; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Interpret the payments: A comparison should use complete totals for the same stated item, currency and conditions. The smaller monthly amount is not necessarily the cheaper entire schedule. The deposit counts once and the payment repeats 4 times.

Worked answer: The full plan total is $40.00+4×$277.50=$1,150.00. The difference total minus cash is −$50.00; under these hypothetical figures, the plan costs $50.00 less than cash.

Common first error: A student who compares one monthly payment $277.50 with the entire cash price $1,200.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,150.00−$1,200.00=−$50.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,170.00, so the cash comparison changes by twenty dollars.

42. Cash price versus complete plan · 2

Question: An imaginary item has a cash price of $1,900.00. A fictional alternative has a deposit $100.00 plus 6 payments of $350.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $100.00+6×$350.00=$2,200.00. The difference total minus cash is +$300.00; under these hypothetical figures, the plan costs $300.00 more than cash.

Common first error: A student who compares one monthly payment $350.00 with the entire cash price $1,900.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,200.00−$1,900.00=+$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,220.00, so the cash comparison changes by twenty dollars.

43. Cash price versus complete plan · 3

Question: An imaginary item has a cash price of $2,600.00. A fictional alternative has a deposit $160.00 plus 8 payments of $373.75; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $160.00+8×$373.75=$3,150.00. The difference total minus cash is +$550.00; under these hypothetical figures, the plan costs $550.00 more than cash.

Common first error: A student who compares one monthly payment $373.75 with the entire cash price $2,600.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,150.00−$2,600.00=+$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,170.00, so the cash comparison changes by twenty dollars.

44. Cash price versus complete plan · 4

Question: An imaginary item has a cash price of $3,300.00. A fictional alternative has a deposit $220.00 plus 10 payments of $333.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $220.00+10×$333.00=$3,550.00. The difference total minus cash is +$250.00; under these hypothetical figures, the plan costs $250.00 more than cash.

Common first error: A student who compares one monthly payment $333.00 with the entire cash price $3,300.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,550.00−$3,300.00=+$250.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,570.00, so the cash comparison changes by twenty dollars.

45. Cash price versus complete plan · 5

Question: An imaginary item has a cash price of $1,700.00. A fictional alternative has a deposit $280.00 plus 12 payments of $160.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $280.00+12×$160.00=$2,200.00. The difference total minus cash is +$500.00; under these hypothetical figures, the plan costs $500.00 more than cash.

Common first error: A student who compares one monthly payment $160.00 with the entire cash price $1,700.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,200.00−$1,700.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,220.00, so the cash comparison changes by twenty dollars.

46. Cash price versus complete plan · 6

Question: An imaginary item has a cash price of $2,400.00. A fictional alternative has a deposit $340.00 plus 15 payments of $150.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $340.00+15×$150.67=$2,600.05. The difference total minus cash is +$200.05; under these hypothetical figures, the plan costs $200.05 more than cash.

Common first error: A student who compares one monthly payment $150.67 with the entire cash price $2,400.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,600.05−$2,400.00=+$200.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,620.05, so the cash comparison changes by twenty dollars.

47. Cash price versus complete plan · 7

Question: An imaginary item has a cash price of $3,100.00. A fictional alternative has a deposit $80.00 plus 18 payments of $142.78; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $80.00+18×$142.78=$2,650.04. The difference total minus cash is −$449.96; under these hypothetical figures, the plan costs $449.96 less than cash.

Common first error: A student who compares one monthly payment $142.78 with the entire cash price $3,100.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,650.04−$3,100.00=−$449.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,670.04, so the cash comparison changes by twenty dollars.

48. Cash price versus complete plan · 8

Question: An imaginary item has a cash price of $1,500.00. A fictional alternative has a deposit $140.00 plus 24 payments of $62.92; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $140.00+24×$62.92=$1,650.08. The difference total minus cash is +$150.08; under these hypothetical figures, the plan costs $150.08 more than cash.

Common first error: A student who compares one monthly payment $62.92 with the entire cash price $1,500.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,650.08−$1,500.00=+$150.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,670.08, so the cash comparison changes by twenty dollars.

49. Cash price versus complete plan · 9

Question: An imaginary item has a cash price of $2,200.00. A fictional alternative has a deposit $200.00 plus 4 payments of $600.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $200.00+4×$600.00=$2,600.00. The difference total minus cash is +$400.00; under these hypothetical figures, the plan costs $400.00 more than cash.

Common first error: A student who compares one monthly payment $600.00 with the entire cash price $2,200.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,600.00−$2,200.00=+$400.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,620.00, so the cash comparison changes by twenty dollars.

50. Cash price versus complete plan · 10

Question: An imaginary item has a cash price of $2,900.00. A fictional alternative has a deposit $260.00 plus 6 payments of $456.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $260.00+6×$456.67=$3,000.02. The difference total minus cash is +$100.02; under these hypothetical figures, the plan costs $100.02 more than cash.

Common first error: A student who compares one monthly payment $456.67 with the entire cash price $2,900.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,000.02−$2,900.00=+$100.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,020.02, so the cash comparison changes by twenty dollars.

51. Cash price versus complete plan · 11

Question: An imaginary item has a cash price of $1,300.00. A fictional alternative has a deposit $320.00 plus 8 payments of $166.25; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $320.00+8×$166.25=$1,650.00. The difference total minus cash is +$350.00; under these hypothetical figures, the plan costs $350.00 more than cash.

Common first error: A student who compares one monthly payment $166.25 with the entire cash price $1,300.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,650.00−$1,300.00=+$350.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,670.00, so the cash comparison changes by twenty dollars.

52. Cash price versus complete plan · 12

Question: An imaginary item has a cash price of $2,000.00. A fictional alternative has a deposit $60.00 plus 10 payments of $199.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $60.00+10×$199.00=$2,050.00. The difference total minus cash is +$50.00; under these hypothetical figures, the plan costs $50.00 more than cash.

Common first error: A student who compares one monthly payment $199.00 with the entire cash price $2,000.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,050.00−$2,000.00=+$50.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.00, so the cash comparison changes by twenty dollars.

53. Cash price versus complete plan · 13

Question: An imaginary item has a cash price of $2,700.00. A fictional alternative has a deposit $120.00 plus 12 payments of $190.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $120.00+12×$190.00=$2,400.00. The difference total minus cash is −$300.00; under these hypothetical figures, the plan costs $300.00 less than cash.

Common first error: A student who compares one monthly payment $190.00 with the entire cash price $2,700.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,400.00−$2,700.00=−$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,420.00, so the cash comparison changes by twenty dollars.

54. Cash price versus complete plan · 14

Question: An imaginary item has a cash price of $3,400.00. A fictional alternative has a deposit $180.00 plus 15 payments of $251.33; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $180.00+15×$251.33=$3,949.95. The difference total minus cash is +$549.95; under these hypothetical figures, the plan costs $549.95 more than cash.

Common first error: A student who compares one monthly payment $251.33 with the entire cash price $3,400.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,949.95−$3,400.00=+$549.95. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,969.95, so the cash comparison changes by twenty dollars.

55. Cash price versus complete plan · 15

Question: An imaginary item has a cash price of $1,800.00. A fictional alternative has a deposit $240.00 plus 18 payments of $100.56; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $240.00+18×$100.56=$2,050.08. The difference total minus cash is +$250.08; under these hypothetical figures, the plan costs $250.08 more than cash.

Common first error: A student who compares one monthly payment $100.56 with the entire cash price $1,800.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,050.08−$1,800.00=+$250.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.08, so the cash comparison changes by twenty dollars.

56. Cash price versus complete plan · 16

Question: An imaginary item has a cash price of $2,500.00. A fictional alternative has a deposit $300.00 plus 24 payments of $112.50; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $300.00+24×$112.50=$3,000.00. The difference total minus cash is +$500.00; under these hypothetical figures, the plan costs $500.00 more than cash.

Common first error: A student who compares one monthly payment $112.50 with the entire cash price $2,500.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,000.00−$2,500.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,020.00, so the cash comparison changes by twenty dollars.

57. Cash price versus complete plan · 17

Question: An imaginary item has a cash price of $3,200.00. A fictional alternative has a deposit $40.00 plus 4 payments of $840.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $40.00+4×$840.00=$3,400.00. The difference total minus cash is +$200.00; under these hypothetical figures, the plan costs $200.00 more than cash.

Common first error: A student who compares one monthly payment $840.00 with the entire cash price $3,200.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,400.00−$3,200.00=+$200.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,420.00, so the cash comparison changes by twenty dollars.

58. Cash price versus complete plan · 18

Question: An imaginary item has a cash price of $1,600.00. A fictional alternative has a deposit $100.00 plus 6 payments of $325.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $100.00+6×$325.00=$2,050.00. The difference total minus cash is +$450.00; under these hypothetical figures, the plan costs $450.00 more than cash.

Common first error: A student who compares one monthly payment $325.00 with the entire cash price $1,600.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,050.00−$1,600.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.00, so the cash comparison changes by twenty dollars.

59. Cash price versus complete plan · 19

Question: An imaginary item has a cash price of $2,300.00. A fictional alternative has a deposit $160.00 plus 8 payments of $248.75; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $160.00+8×$248.75=$2,150.00. The difference total minus cash is −$150.00; under these hypothetical figures, the plan costs $150.00 less than cash.

Common first error: A student who compares one monthly payment $248.75 with the entire cash price $2,300.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,150.00−$2,300.00=−$150.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,170.00, so the cash comparison changes by twenty dollars.

60. Cash price versus complete plan · 20

Question: An imaginary item has a cash price of $3,000.00. A fictional alternative has a deposit $220.00 plus 10 payments of $318.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $220.00+10×$318.00=$3,400.00. The difference total minus cash is +$400.00; under these hypothetical figures, the plan costs $400.00 more than cash.

Common first error: A student who compares one monthly payment $318.00 with the entire cash price $3,000.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,400.00−$3,000.00=+$400.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,420.00, so the cash comparison changes by twenty dollars.

61. Cash price versus complete plan · 21

Question: An imaginary item has a cash price of $1,400.00. A fictional alternative has a deposit $280.00 plus 12 payments of $101.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $280.00+12×$101.67=$1,500.04. The difference total minus cash is +$100.04; under these hypothetical figures, the plan costs $100.04 more than cash.

Common first error: A student who compares one monthly payment $101.67 with the entire cash price $1,400.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,500.04−$1,400.00=+$100.04. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,520.04, so the cash comparison changes by twenty dollars.

62. Cash price versus complete plan · 22

Question: An imaginary item has a cash price of $2,100.00. A fictional alternative has a deposit $340.00 plus 15 payments of $140.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $340.00+15×$140.67=$2,450.05. The difference total minus cash is +$350.05; under these hypothetical figures, the plan costs $350.05 more than cash.

Common first error: A student who compares one monthly payment $140.67 with the entire cash price $2,100.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,450.05−$2,100.00=+$350.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,470.05, so the cash comparison changes by twenty dollars.

63. Cash price versus complete plan · 23

Question: An imaginary item has a cash price of $2,800.00. A fictional alternative has a deposit $80.00 plus 18 payments of $153.89; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $80.00+18×$153.89=$2,850.02. The difference total minus cash is +$50.02; under these hypothetical figures, the plan costs $50.02 more than cash.

Common first error: A student who compares one monthly payment $153.89 with the entire cash price $2,800.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,850.02−$2,800.00=+$50.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.02, so the cash comparison changes by twenty dollars.

64. Cash price versus complete plan · 24

Question: An imaginary item has a cash price of $1,200.00. A fictional alternative has a deposit $140.00 plus 24 payments of $56.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $140.00+24×$56.67=$1,500.08. The difference total minus cash is +$300.08; under these hypothetical figures, the plan costs $300.08 more than cash.

Common first error: A student who compares one monthly payment $56.67 with the entire cash price $1,200.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,500.08−$1,200.00=+$300.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,520.08, so the cash comparison changes by twenty dollars.

65. Cash price versus complete plan · 25

Question: An imaginary item has a cash price of $1,900.00. A fictional alternative has a deposit $200.00 plus 4 payments of $287.50; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $200.00+4×$287.50=$1,350.00. The difference total minus cash is −$550.00; under these hypothetical figures, the plan costs $550.00 less than cash.

Common first error: A student who compares one monthly payment $287.50 with the entire cash price $1,900.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,350.00−$1,900.00=−$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,370.00, so the cash comparison changes by twenty dollars.

66. Cash price versus complete plan · 26

Question: An imaginary item has a cash price of $2,600.00. A fictional alternative has a deposit $260.00 plus 6 payments of $431.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $260.00+6×$431.67=$2,850.02. The difference total minus cash is +$250.02; under these hypothetical figures, the plan costs $250.02 more than cash.

Common first error: A student who compares one monthly payment $431.67 with the entire cash price $2,600.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,850.02−$2,600.00=+$250.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.02, so the cash comparison changes by twenty dollars.

67. Cash price versus complete plan · 27

Question: An imaginary item has a cash price of $3,300.00. A fictional alternative has a deposit $320.00 plus 8 payments of $435.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $320.00+8×$435.00=$3,800.00. The difference total minus cash is +$500.00; under these hypothetical figures, the plan costs $500.00 more than cash.

Common first error: A student who compares one monthly payment $435.00 with the entire cash price $3,300.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,800.00−$3,300.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,820.00, so the cash comparison changes by twenty dollars.

68. Cash price versus complete plan · 28

Question: An imaginary item has a cash price of $1,700.00. A fictional alternative has a deposit $60.00 plus 10 payments of $184.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $60.00+10×$184.00=$1,900.00. The difference total minus cash is +$200.00; under these hypothetical figures, the plan costs $200.00 more than cash.

Common first error: A student who compares one monthly payment $184.00 with the entire cash price $1,700.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,900.00−$1,700.00=+$200.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,920.00, so the cash comparison changes by twenty dollars.

69. Cash price versus complete plan · 29

Question: An imaginary item has a cash price of $2,400.00. A fictional alternative has a deposit $120.00 plus 12 payments of $227.50; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $120.00+12×$227.50=$2,850.00. The difference total minus cash is +$450.00; under these hypothetical figures, the plan costs $450.00 more than cash.

Common first error: A student who compares one monthly payment $227.50 with the entire cash price $2,400.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,850.00−$2,400.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.00, so the cash comparison changes by twenty dollars.

70. Cash price versus complete plan · 30

Question: An imaginary item has a cash price of $3,100.00. A fictional alternative has a deposit $180.00 plus 15 payments of $204.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $180.00+15×$204.67=$3,250.05. The difference total minus cash is +$150.05; under these hypothetical figures, the plan costs $150.05 more than cash.

Common first error: A student who compares one monthly payment $204.67 with the entire cash price $3,100.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,250.05−$3,100.00=+$150.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.05, so the cash comparison changes by twenty dollars.

71. Cash price versus complete plan · 31

Question: An imaginary item has a cash price of $1,500.00. A fictional alternative has a deposit $240.00 plus 18 payments of $47.78; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $240.00+18×$47.78=$1,100.04. The difference total minus cash is −$399.96; under these hypothetical figures, the plan costs $399.96 less than cash.

Common first error: A student who compares one monthly payment $47.78 with the entire cash price $1,500.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,100.04−$1,500.00=−$399.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,120.04, so the cash comparison changes by twenty dollars.

72. Cash price versus complete plan · 32

Question: An imaginary item has a cash price of $2,200.00. A fictional alternative has a deposit $300.00 plus 24 payments of $83.33; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $300.00+24×$83.33=$2,299.92. The difference total minus cash is +$99.92; under these hypothetical figures, the plan costs $99.92 more than cash.

Common first error: A student who compares one monthly payment $83.33 with the entire cash price $2,200.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,299.92−$2,200.00=+$99.92. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,319.92, so the cash comparison changes by twenty dollars.

73. Cash price versus complete plan · 33

Question: An imaginary item has a cash price of $2,900.00. A fictional alternative has a deposit $40.00 plus 4 payments of $802.50; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $40.00+4×$802.50=$3,250.00. The difference total minus cash is +$350.00; under these hypothetical figures, the plan costs $350.00 more than cash.

Common first error: A student who compares one monthly payment $802.50 with the entire cash price $2,900.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,250.00−$2,900.00=+$350.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.00, so the cash comparison changes by twenty dollars.

74. Cash price versus complete plan · 34

Question: An imaginary item has a cash price of $1,300.00. A fictional alternative has a deposit $100.00 plus 6 payments of $208.33; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $100.00+6×$208.33=$1,349.98. The difference total minus cash is +$49.98; under these hypothetical figures, the plan costs $49.98 more than cash.

Common first error: A student who compares one monthly payment $208.33 with the entire cash price $1,300.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $1,349.98−$1,300.00=+$49.98. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,369.98, so the cash comparison changes by twenty dollars.

75. Cash price versus complete plan · 35

Question: An imaginary item has a cash price of $2,000.00. A fictional alternative has a deposit $160.00 plus 8 payments of $267.50; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $160.00+8×$267.50=$2,300.00. The difference total minus cash is +$300.00; under these hypothetical figures, the plan costs $300.00 more than cash.

Common first error: A student who compares one monthly payment $267.50 with the entire cash price $2,000.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,300.00−$2,000.00=+$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,320.00, so the cash comparison changes by twenty dollars.

76. Cash price versus complete plan · 36

Question: An imaginary item has a cash price of $2,700.00. A fictional alternative has a deposit $220.00 plus 10 payments of $303.00; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $220.00+10×$303.00=$3,250.00. The difference total minus cash is +$550.00; under these hypothetical figures, the plan costs $550.00 more than cash.

Common first error: A student who compares one monthly payment $303.00 with the entire cash price $2,700.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,250.00−$2,700.00=+$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.00, so the cash comparison changes by twenty dollars.

77. Cash price versus complete plan · 37

Question: An imaginary item has a cash price of $3,400.00. A fictional alternative has a deposit $280.00 plus 12 payments of $239.17; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $280.00+12×$239.17=$3,150.04. The difference total minus cash is −$249.96; under these hypothetical figures, the plan costs $249.96 less than cash.

Common first error: A student who compares one monthly payment $239.17 with the entire cash price $3,400.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,150.04−$3,400.00=−$249.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,170.04, so the cash comparison changes by twenty dollars.

78. Cash price versus complete plan · 38

Question: An imaginary item has a cash price of $1,800.00. A fictional alternative has a deposit $340.00 plus 15 payments of $130.67; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $340.00+15×$130.67=$2,300.05. The difference total minus cash is +$500.05; under these hypothetical figures, the plan costs $500.05 more than cash.

Common first error: A student who compares one monthly payment $130.67 with the entire cash price $1,800.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,300.05−$1,800.00=+$500.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,320.05, so the cash comparison changes by twenty dollars.

79. Cash price versus complete plan · 39

Question: An imaginary item has a cash price of $2,500.00. A fictional alternative has a deposit $80.00 plus 18 payments of $145.56; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $80.00+18×$145.56=$2,700.08. The difference total minus cash is +$200.08; under these hypothetical figures, the plan costs $200.08 more than cash.

Common first error: A student who compares one monthly payment $145.56 with the entire cash price $2,500.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $2,700.08−$2,500.00=+$200.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,720.08, so the cash comparison changes by twenty dollars.

80. Cash price versus complete plan · 40

Question: An imaginary item has a cash price of $3,200.00. A fictional alternative has a deposit $140.00 plus 24 payments of $146.25; there are no additional charges. Calculate the alternative’s full total and the signed difference relative to cash.

Worked answer: The full plan total is $140.00+24×$146.25=$3,650.00. The difference total minus cash is +$450.00; under these hypothetical figures, the plan costs $450.00 more than cash.

Common first error: A student who compares one monthly payment $146.25 with the entire cash price $3,200.00 is comparing unlike time periods. Another common error is inferring an annualised interest rate from a simple total difference without the payment timing and financing assumptions.

Reverse-check: Check $3,650.00−$3,200.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,670.00, so the cash comparison changes by twenty dollars.

81. Find monthly payment from stated total · 1

Question: A simplified fictional schedule costs $140.00 altogether, including a one-time deposit $50.00 and 3 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Interpret the payments: The unknown is an amount per month. Work backward: remove the once-only deposit from the complete sum, then divide the repeated subtotal into the known number of equal payments. This is a one-variable linear equation in ordinary monetary terms.

Worked answer: Write $50.00+3m=$140.00. Then 3m=$90.00, so m=$30.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $140.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $30.00 by 3, obtaining $90.00; add deposit $50.00 to restore the precise stated total $140.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $40.00.

82. Find monthly payment from stated total · 2

Question: A simplified fictional schedule costs $445.00 altogether, including a one-time deposit $125.00 and 4 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $125.00+4m=$445.00. Then 4m=$320.00, so m=$80.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $445.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $80.00 by 4, obtaining $320.00; add deposit $125.00 to restore the precise stated total $445.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $90.00.

83. Find monthly payment from stated total · 3

Question: A simplified fictional schedule costs $980.00 altogether, including a one-time deposit $200.00 and 6 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $200.00+6m=$980.00. Then 6m=$780.00, so m=$130.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $980.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $130.00 by 6, obtaining $780.00; add deposit $200.00 to restore the precise stated total $980.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $140.00.

84. Find monthly payment from stated total · 4

Question: A simplified fictional schedule costs $1,715.00 altogether, including a one-time deposit $275.00 and 8 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $275.00+8m=$1,715.00. Then 8m=$1,440.00, so m=$180.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,715.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $180.00 by 8, obtaining $1,440.00; add deposit $275.00 to restore the precise stated total $1,715.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $190.00.

85. Find monthly payment from stated total · 5

Question: A simplified fictional schedule costs $2,650.00 altogether, including a one-time deposit $350.00 and 10 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $350.00+10m=$2,650.00. Then 10m=$2,300.00, so m=$230.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,650.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $230.00 by 10, obtaining $2,300.00; add deposit $350.00 to restore the precise stated total $2,650.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $240.00.

86. Find monthly payment from stated total · 6

Question: A simplified fictional schedule costs $3,785.00 altogether, including a one-time deposit $425.00 and 12 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $425.00+12m=$3,785.00. Then 12m=$3,360.00, so m=$280.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,785.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $280.00 by 12, obtaining $3,360.00; add deposit $425.00 to restore the precise stated total $3,785.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $290.00.

87. Find monthly payment from stated total · 7

Question: A simplified fictional schedule costs $5,450.00 altogether, including a one-time deposit $500.00 and 15 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $500.00+15m=$5,450.00. Then 15m=$4,950.00, so m=$330.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $5,450.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $330.00 by 15, obtaining $4,950.00; add deposit $500.00 to restore the precise stated total $5,450.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $340.00.

88. Find monthly payment from stated total · 8

Question: A simplified fictional schedule costs $1,655.00 altogether, including a one-time deposit $575.00 and 18 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $575.00+18m=$1,655.00. Then 18m=$1,080.00, so m=$60.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,655.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $60.00 by 18, obtaining $1,080.00; add deposit $575.00 to restore the precise stated total $1,655.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $70.00.

89. Find monthly payment from stated total · 9

Question: A simplified fictional schedule costs $2,740.00 altogether, including a one-time deposit $100.00 and 24 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $100.00+24m=$2,740.00. Then 24m=$2,640.00, so m=$110.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,740.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $110.00 by 24, obtaining $2,640.00; add deposit $100.00 to restore the precise stated total $2,740.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $120.00.

90. Find monthly payment from stated total · 10

Question: A simplified fictional schedule costs $655.00 altogether, including a one-time deposit $175.00 and 3 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $175.00+3m=$655.00. Then 3m=$480.00, so m=$160.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $655.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $160.00 by 3, obtaining $480.00; add deposit $175.00 to restore the precise stated total $655.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $170.00.

91. Find monthly payment from stated total · 11

Question: A simplified fictional schedule costs $1,090.00 altogether, including a one-time deposit $250.00 and 4 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $250.00+4m=$1,090.00. Then 4m=$840.00, so m=$210.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,090.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $210.00 by 4, obtaining $840.00; add deposit $250.00 to restore the precise stated total $1,090.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $220.00.

92. Find monthly payment from stated total · 12

Question: A simplified fictional schedule costs $1,885.00 altogether, including a one-time deposit $325.00 and 6 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $325.00+6m=$1,885.00. Then 6m=$1,560.00, so m=$260.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,885.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $260.00 by 6, obtaining $1,560.00; add deposit $325.00 to restore the precise stated total $1,885.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $270.00.

93. Find monthly payment from stated total · 13

Question: A simplified fictional schedule costs $2,880.00 altogether, including a one-time deposit $400.00 and 8 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $400.00+8m=$2,880.00. Then 8m=$2,480.00, so m=$310.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,880.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $310.00 by 8, obtaining $2,480.00; add deposit $400.00 to restore the precise stated total $2,880.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $320.00.

94. Find monthly payment from stated total · 14

Question: A simplified fictional schedule costs $875.00 altogether, including a one-time deposit $475.00 and 10 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $475.00+10m=$875.00. Then 10m=$400.00, so m=$40.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $875.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $40.00 by 10, obtaining $400.00; add deposit $475.00 to restore the precise stated total $875.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $50.00.

95. Find monthly payment from stated total · 15

Question: A simplified fictional schedule costs $1,630.00 altogether, including a one-time deposit $550.00 and 12 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $550.00+12m=$1,630.00. Then 12m=$1,080.00, so m=$90.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,630.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $90.00 by 12, obtaining $1,080.00; add deposit $550.00 to restore the precise stated total $1,630.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $100.00.

96. Find monthly payment from stated total · 16

Question: A simplified fictional schedule costs $2,175.00 altogether, including a one-time deposit $75.00 and 15 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $75.00+15m=$2,175.00. Then 15m=$2,100.00, so m=$140.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,175.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $140.00 by 15, obtaining $2,100.00; add deposit $75.00 to restore the precise stated total $2,175.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $150.00.

97. Find monthly payment from stated total · 17

Question: A simplified fictional schedule costs $3,570.00 altogether, including a one-time deposit $150.00 and 18 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $150.00+18m=$3,570.00. Then 18m=$3,420.00, so m=$190.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,570.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $190.00 by 18, obtaining $3,420.00; add deposit $150.00 to restore the precise stated total $3,570.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $200.00.

98. Find monthly payment from stated total · 18

Question: A simplified fictional schedule costs $5,985.00 altogether, including a one-time deposit $225.00 and 24 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $225.00+24m=$5,985.00. Then 24m=$5,760.00, so m=$240.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $5,985.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $240.00 by 24, obtaining $5,760.00; add deposit $225.00 to restore the precise stated total $5,985.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $250.00.

99. Find monthly payment from stated total · 19

Question: A simplified fictional schedule costs $1,170.00 altogether, including a one-time deposit $300.00 and 3 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $300.00+3m=$1,170.00. Then 3m=$870.00, so m=$290.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,170.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $290.00 by 3, obtaining $870.00; add deposit $300.00 to restore the precise stated total $1,170.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $300.00.

100. Find monthly payment from stated total · 20

Question: A simplified fictional schedule costs $1,735.00 altogether, including a one-time deposit $375.00 and 4 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $375.00+4m=$1,735.00. Then 4m=$1,360.00, so m=$340.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,735.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $340.00 by 4, obtaining $1,360.00; add deposit $375.00 to restore the precise stated total $1,735.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $350.00.

101. Find monthly payment from stated total · 21

Question: A simplified fictional schedule costs $870.00 altogether, including a one-time deposit $450.00 and 6 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $450.00+6m=$870.00. Then 6m=$420.00, so m=$70.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $870.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $70.00 by 6, obtaining $420.00; add deposit $450.00 to restore the precise stated total $870.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $80.00.

102. Find monthly payment from stated total · 22

Question: A simplified fictional schedule costs $1,485.00 altogether, including a one-time deposit $525.00 and 8 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $525.00+8m=$1,485.00. Then 8m=$960.00, so m=$120.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,485.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $120.00 by 8, obtaining $960.00; add deposit $525.00 to restore the precise stated total $1,485.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $130.00.

103. Find monthly payment from stated total · 23

Question: A simplified fictional schedule costs $1,750.00 altogether, including a one-time deposit $50.00 and 10 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $50.00+10m=$1,750.00. Then 10m=$1,700.00, so m=$170.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,750.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $170.00 by 10, obtaining $1,700.00; add deposit $50.00 to restore the precise stated total $1,750.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $180.00.

104. Find monthly payment from stated total · 24

Question: A simplified fictional schedule costs $2,765.00 altogether, including a one-time deposit $125.00 and 12 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $125.00+12m=$2,765.00. Then 12m=$2,640.00, so m=$220.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,765.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $220.00 by 12, obtaining $2,640.00; add deposit $125.00 to restore the precise stated total $2,765.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $230.00.

105. Find monthly payment from stated total · 25

Question: A simplified fictional schedule costs $4,250.00 altogether, including a one-time deposit $200.00 and 15 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $200.00+15m=$4,250.00. Then 15m=$4,050.00, so m=$270.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $4,250.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $270.00 by 15, obtaining $4,050.00; add deposit $200.00 to restore the precise stated total $4,250.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $280.00.

106. Find monthly payment from stated total · 26

Question: A simplified fictional schedule costs $6,035.00 altogether, including a one-time deposit $275.00 and 18 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $275.00+18m=$6,035.00. Then 18m=$5,760.00, so m=$320.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $6,035.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $320.00 by 18, obtaining $5,760.00; add deposit $275.00 to restore the precise stated total $6,035.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $330.00.

107. Find monthly payment from stated total · 27

Question: A simplified fictional schedule costs $1,550.00 altogether, including a one-time deposit $350.00 and 24 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $350.00+24m=$1,550.00. Then 24m=$1,200.00, so m=$50.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,550.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $50.00 by 24, obtaining $1,200.00; add deposit $350.00 to restore the precise stated total $1,550.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $60.00.

108. Find monthly payment from stated total · 28

Question: A simplified fictional schedule costs $725.00 altogether, including a one-time deposit $425.00 and 3 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $425.00+3m=$725.00. Then 3m=$300.00, so m=$100.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $725.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $100.00 by 3, obtaining $300.00; add deposit $425.00 to restore the precise stated total $725.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $110.00.

109. Find monthly payment from stated total · 29

Question: A simplified fictional schedule costs $1,100.00 altogether, including a one-time deposit $500.00 and 4 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $500.00+4m=$1,100.00. Then 4m=$600.00, so m=$150.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,100.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $150.00 by 4, obtaining $600.00; add deposit $500.00 to restore the precise stated total $1,100.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $160.00.

110. Find monthly payment from stated total · 30

Question: A simplified fictional schedule costs $1,775.00 altogether, including a one-time deposit $575.00 and 6 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $575.00+6m=$1,775.00. Then 6m=$1,200.00, so m=$200.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,775.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $200.00 by 6, obtaining $1,200.00; add deposit $575.00 to restore the precise stated total $1,775.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $210.00.

111. Find monthly payment from stated total · 31

Question: A simplified fictional schedule costs $2,100.00 altogether, including a one-time deposit $100.00 and 8 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $100.00+8m=$2,100.00. Then 8m=$2,000.00, so m=$250.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,100.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $250.00 by 8, obtaining $2,000.00; add deposit $100.00 to restore the precise stated total $2,100.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $260.00.

112. Find monthly payment from stated total · 32

Question: A simplified fictional schedule costs $3,175.00 altogether, including a one-time deposit $175.00 and 10 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $175.00+10m=$3,175.00. Then 10m=$3,000.00, so m=$300.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,175.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $300.00 by 10, obtaining $3,000.00; add deposit $175.00 to restore the precise stated total $3,175.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $310.00.

113. Find monthly payment from stated total · 33

Question: A simplified fictional schedule costs $610.00 altogether, including a one-time deposit $250.00 and 12 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $250.00+12m=$610.00. Then 12m=$360.00, so m=$30.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $610.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $30.00 by 12, obtaining $360.00; add deposit $250.00 to restore the precise stated total $610.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $40.00.

114. Find monthly payment from stated total · 34

Question: A simplified fictional schedule costs $1,525.00 altogether, including a one-time deposit $325.00 and 15 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $325.00+15m=$1,525.00. Then 15m=$1,200.00, so m=$80.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,525.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $80.00 by 15, obtaining $1,200.00; add deposit $325.00 to restore the precise stated total $1,525.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $90.00.

115. Find monthly payment from stated total · 35

Question: A simplified fictional schedule costs $2,740.00 altogether, including a one-time deposit $400.00 and 18 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $400.00+18m=$2,740.00. Then 18m=$2,340.00, so m=$130.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,740.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $130.00 by 18, obtaining $2,340.00; add deposit $400.00 to restore the precise stated total $2,740.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $140.00.

116. Find monthly payment from stated total · 36

Question: A simplified fictional schedule costs $4,795.00 altogether, including a one-time deposit $475.00 and 24 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $475.00+24m=$4,795.00. Then 24m=$4,320.00, so m=$180.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $4,795.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $180.00 by 24, obtaining $4,320.00; add deposit $475.00 to restore the precise stated total $4,795.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $190.00.

117. Find monthly payment from stated total · 37

Question: A simplified fictional schedule costs $1,240.00 altogether, including a one-time deposit $550.00 and 3 equal monthly instalments. No other charges exist in this question. Find one monthly amount.

Worked answer: Write $550.00+3m=$1,240.00. Then 3m=$690.00, so m=$230.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,240.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $230.00 by 3, obtaining $690.00; add deposit $550.00 to restore the precise stated total $1,240.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $240.00.

Recover the unknown number of months

For recover the unknown number of months, list every monetary amount and its frequency before calculating. Use the total to check an unknown monthly payment or payment count by reversing operations. Be clear that comparing two complete arithmetic totals is not the same as recommending a real financial commitment. If the question omits a fee or schedule, don’t invent it.

118. Find how many instalments are stated · 1

Question: The fictional full plan total is $145.00, with a deposit of $40.00 and equal payments of $35.00 per month. How many monthly payments are included?

Interpret the payments: An instalment count is not the same unit as a dollar amount. Subtract the one-time deposit, then divide the monetary remainder by the amount of one payment. Whole payments are counted in nonnegative integers in this simplified case.

Worked answer: Number of payments = ($145.00−$40.00)/$35.00 = $105.00/$35.00=3 payments. The amount $105.00 is the repeated subtotal, not the complete total.

Common first error: Multiplying the total by the monthly charge is not an inverse operation. A decimal number of payments in another example should be questioned if the model requires equal complete monthly amounts; rounding can change the stipulated full total.

Reverse-check: Reconstruct 3×$35.00+$40.00=$145.00. The terms and units are consistent.

Change one condition: If another payment of $35.00 were included, the full total would rise to $180.00 and the count become 4.

119. Find how many instalments are stated · 2

Question: The fictional full plan total is $380.00, with a deposit of $100.00 and equal payments of $70.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($380.00−$100.00)/$70.00 = $280.00/$70.00=4 payments. The amount $280.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$70.00+$100.00=$380.00. The terms and units are consistent.

Change one condition: If another payment of $70.00 were included, the full total would rise to $450.00 and the count become 5.

120. Find how many instalments are stated · 3

Question: The fictional full plan total is $790.00, with a deposit of $160.00 and equal payments of $105.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($790.00−$160.00)/$105.00 = $630.00/$105.00=6 payments. The amount $630.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$105.00+$160.00=$790.00. The terms and units are consistent.

Change one condition: If another payment of $105.00 were included, the full total would rise to $895.00 and the count become 7.

121. Find how many instalments are stated · 4

Question: The fictional full plan total is $1,340.00, with a deposit of $220.00 and equal payments of $140.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,340.00−$220.00)/$140.00 = $1,120.00/$140.00=8 payments. The amount $1,120.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$140.00+$220.00=$1,340.00. The terms and units are consistent.

Change one condition: If another payment of $140.00 were included, the full total would rise to $1,480.00 and the count become 9.

122. Find how many instalments are stated · 5

Question: The fictional full plan total is $775.00, with a deposit of $280.00 and equal payments of $55.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($775.00−$280.00)/$55.00 = $495.00/$55.00=9 payments. The amount $495.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$55.00+$280.00=$775.00. The terms and units are consistent.

Change one condition: If another payment of $55.00 were included, the full total would rise to $830.00 and the count become 10.

123. Find how many instalments are stated · 6

Question: The fictional full plan total is $1,240.00, with a deposit of $340.00 and equal payments of $90.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,240.00−$340.00)/$90.00 = $900.00/$90.00=10 payments. The amount $900.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$90.00+$340.00=$1,240.00. The terms and units are consistent.

Change one condition: If another payment of $90.00 were included, the full total would rise to $1,330.00 and the count become 11.

124. Find how many instalments are stated · 7

Question: The fictional full plan total is $1,900.00, with a deposit of $400.00 and equal payments of $125.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,900.00−$400.00)/$125.00 = $1,500.00/$125.00=12 payments. The amount $1,500.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$125.00+$400.00=$1,900.00. The terms and units are consistent.

Change one condition: If another payment of $125.00 were included, the full total would rise to $2,025.00 and the count become 13.

125. Find how many instalments are stated · 8

Question: The fictional full plan total is $1,060.00, with a deposit of $460.00 and equal payments of $40.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,060.00−$460.00)/$40.00 = $600.00/$40.00=15 payments. The amount $600.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$40.00+$460.00=$1,060.00. The terms and units are consistent.

Change one condition: If another payment of $40.00 were included, the full total would rise to $1,100.00 and the count become 16.

126. Find how many instalments are stated · 9

Question: The fictional full plan total is $1,410.00, with a deposit of $60.00 and equal payments of $75.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,410.00−$60.00)/$75.00 = $1,350.00/$75.00=18 payments. The amount $1,350.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$75.00+$60.00=$1,410.00. The terms and units are consistent.

Change one condition: If another payment of $75.00 were included, the full total would rise to $1,485.00 and the count become 19.

127. Find how many instalments are stated · 10

Question: The fictional full plan total is $2,320.00, with a deposit of $120.00 and equal payments of $110.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,320.00−$120.00)/$110.00 = $2,200.00/$110.00=20 payments. The amount $2,200.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$110.00+$120.00=$2,320.00. The terms and units are consistent.

Change one condition: If another payment of $110.00 were included, the full total would rise to $2,430.00 and the count become 21.

128. Find how many instalments are stated · 11

Question: The fictional full plan total is $3,660.00, with a deposit of $180.00 and equal payments of $145.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($3,660.00−$180.00)/$145.00 = $3,480.00/$145.00=24 payments. The amount $3,480.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$145.00+$180.00=$3,660.00. The terms and units are consistent.

Change one condition: If another payment of $145.00 were included, the full total would rise to $3,805.00 and the count become 25.

129. Find how many instalments are stated · 12

Question: The fictional full plan total is $420.00, with a deposit of $240.00 and equal payments of $60.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($420.00−$240.00)/$60.00 = $180.00/$60.00=3 payments. The amount $180.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$60.00+$240.00=$420.00. The terms and units are consistent.

Change one condition: If another payment of $60.00 were included, the full total would rise to $480.00 and the count become 4.

130. Find how many instalments are stated · 13

Question: The fictional full plan total is $680.00, with a deposit of $300.00 and equal payments of $95.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($680.00−$300.00)/$95.00 = $380.00/$95.00=4 payments. The amount $380.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$95.00+$300.00=$680.00. The terms and units are consistent.

Change one condition: If another payment of $95.00 were included, the full total would rise to $775.00 and the count become 5.

131. Find how many instalments are stated · 14

Question: The fictional full plan total is $1,140.00, with a deposit of $360.00 and equal payments of $130.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,140.00−$360.00)/$130.00 = $780.00/$130.00=6 payments. The amount $780.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$130.00+$360.00=$1,140.00. The terms and units are consistent.

Change one condition: If another payment of $130.00 were included, the full total would rise to $1,270.00 and the count become 7.

132. Find how many instalments are stated · 15

Question: The fictional full plan total is $780.00, with a deposit of $420.00 and equal payments of $45.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($780.00−$420.00)/$45.00 = $360.00/$45.00=8 payments. The amount $360.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$45.00+$420.00=$780.00. The terms and units are consistent.

Change one condition: If another payment of $45.00 were included, the full total would rise to $825.00 and the count become 9.

133. Find how many instalments are stated · 16

Question: The fictional full plan total is $1,200.00, with a deposit of $480.00 and equal payments of $80.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,200.00−$480.00)/$80.00 = $720.00/$80.00=9 payments. The amount $720.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$80.00+$480.00=$1,200.00. The terms and units are consistent.

Change one condition: If another payment of $80.00 were included, the full total would rise to $1,280.00 and the count become 10.

134. Find how many instalments are stated · 17

Question: The fictional full plan total is $1,230.00, with a deposit of $80.00 and equal payments of $115.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,230.00−$80.00)/$115.00 = $1,150.00/$115.00=10 payments. The amount $1,150.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$115.00+$80.00=$1,230.00. The terms and units are consistent.

Change one condition: If another payment of $115.00 were included, the full total would rise to $1,345.00 and the count become 11.

135. Find how many instalments are stated · 18

Question: The fictional full plan total is $1,940.00, with a deposit of $140.00 and equal payments of $150.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,940.00−$140.00)/$150.00 = $1,800.00/$150.00=12 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$150.00+$140.00=$1,940.00. The terms and units are consistent.

Change one condition: If another payment of $150.00 were included, the full total would rise to $2,090.00 and the count become 13.

136. Find how many instalments are stated · 19

Question: The fictional full plan total is $1,175.00, with a deposit of $200.00 and equal payments of $65.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,175.00−$200.00)/$65.00 = $975.00/$65.00=15 payments. The amount $975.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$65.00+$200.00=$1,175.00. The terms and units are consistent.

Change one condition: If another payment of $65.00 were included, the full total would rise to $1,240.00 and the count become 16.

137. Find how many instalments are stated · 20

Question: The fictional full plan total is $2,060.00, with a deposit of $260.00 and equal payments of $100.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,060.00−$260.00)/$100.00 = $1,800.00/$100.00=18 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$100.00+$260.00=$2,060.00. The terms and units are consistent.

Change one condition: If another payment of $100.00 were included, the full total would rise to $2,160.00 and the count become 19.

138. Find how many instalments are stated · 21

Question: The fictional full plan total is $3,020.00, with a deposit of $320.00 and equal payments of $135.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($3,020.00−$320.00)/$135.00 = $2,700.00/$135.00=20 payments. The amount $2,700.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$135.00+$320.00=$3,020.00. The terms and units are consistent.

Change one condition: If another payment of $135.00 were included, the full total would rise to $3,155.00 and the count become 21.

139. Find how many instalments are stated · 22

Question: The fictional full plan total is $1,580.00, with a deposit of $380.00 and equal payments of $50.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,580.00−$380.00)/$50.00 = $1,200.00/$50.00=24 payments. The amount $1,200.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$50.00+$380.00=$1,580.00. The terms and units are consistent.

Change one condition: If another payment of $50.00 were included, the full total would rise to $1,630.00 and the count become 25.

140. Find how many instalments are stated · 23

Question: The fictional full plan total is $695.00, with a deposit of $440.00 and equal payments of $85.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($695.00−$440.00)/$85.00 = $255.00/$85.00=3 payments. The amount $255.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$85.00+$440.00=$695.00. The terms and units are consistent.

Change one condition: If another payment of $85.00 were included, the full total would rise to $780.00 and the count become 4.

141. Find how many instalments are stated · 24

Question: The fictional full plan total is $520.00, with a deposit of $40.00 and equal payments of $120.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($520.00−$40.00)/$120.00 = $480.00/$120.00=4 payments. The amount $480.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$120.00+$40.00=$520.00. The terms and units are consistent.

Change one condition: If another payment of $120.00 were included, the full total would rise to $640.00 and the count become 5.

142. Find how many instalments are stated · 25

Question: The fictional full plan total is $310.00, with a deposit of $100.00 and equal payments of $35.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($310.00−$100.00)/$35.00 = $210.00/$35.00=6 payments. The amount $210.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$35.00+$100.00=$310.00. The terms and units are consistent.

Change one condition: If another payment of $35.00 were included, the full total would rise to $345.00 and the count become 7.

143. Find how many instalments are stated · 26

Question: The fictional full plan total is $720.00, with a deposit of $160.00 and equal payments of $70.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($720.00−$160.00)/$70.00 = $560.00/$70.00=8 payments. The amount $560.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$70.00+$160.00=$720.00. The terms and units are consistent.

Change one condition: If another payment of $70.00 were included, the full total would rise to $790.00 and the count become 9.

144. Find how many instalments are stated · 27

Question: The fictional full plan total is $1,165.00, with a deposit of $220.00 and equal payments of $105.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,165.00−$220.00)/$105.00 = $945.00/$105.00=9 payments. The amount $945.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$105.00+$220.00=$1,165.00. The terms and units are consistent.

Change one condition: If another payment of $105.00 were included, the full total would rise to $1,270.00 and the count become 10.

145. Find how many instalments are stated · 28

Question: The fictional full plan total is $1,680.00, with a deposit of $280.00 and equal payments of $140.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,680.00−$280.00)/$140.00 = $1,400.00/$140.00=10 payments. The amount $1,400.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$140.00+$280.00=$1,680.00. The terms and units are consistent.

Change one condition: If another payment of $140.00 were included, the full total would rise to $1,820.00 and the count become 11.

146. Find how many instalments are stated · 29

Question: The fictional full plan total is $1,000.00, with a deposit of $340.00 and equal payments of $55.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,000.00−$340.00)/$55.00 = $660.00/$55.00=12 payments. The amount $660.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$55.00+$340.00=$1,000.00. The terms and units are consistent.

Change one condition: If another payment of $55.00 were included, the full total would rise to $1,055.00 and the count become 13.

147. Find how many instalments are stated · 30

Question: The fictional full plan total is $1,750.00, with a deposit of $400.00 and equal payments of $90.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,750.00−$400.00)/$90.00 = $1,350.00/$90.00=15 payments. The amount $1,350.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$90.00+$400.00=$1,750.00. The terms and units are consistent.

Change one condition: If another payment of $90.00 were included, the full total would rise to $1,840.00 and the count become 16.

148. Find how many instalments are stated · 31

Question: The fictional full plan total is $2,710.00, with a deposit of $460.00 and equal payments of $125.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,710.00−$460.00)/$125.00 = $2,250.00/$125.00=18 payments. The amount $2,250.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$125.00+$460.00=$2,710.00. The terms and units are consistent.

Change one condition: If another payment of $125.00 were included, the full total would rise to $2,835.00 and the count become 19.

149. Find how many instalments are stated · 32

Question: The fictional full plan total is $860.00, with a deposit of $60.00 and equal payments of $40.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($860.00−$60.00)/$40.00 = $800.00/$40.00=20 payments. The amount $800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$40.00+$60.00=$860.00. The terms and units are consistent.

Change one condition: If another payment of $40.00 were included, the full total would rise to $900.00 and the count become 21.

150. Find how many instalments are stated · 33

Question: The fictional full plan total is $1,920.00, with a deposit of $120.00 and equal payments of $75.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,920.00−$120.00)/$75.00 = $1,800.00/$75.00=24 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$75.00+$120.00=$1,920.00. The terms and units are consistent.

Change one condition: If another payment of $75.00 were included, the full total would rise to $1,995.00 and the count become 25.

151. Find how many instalments are stated · 34

Question: The fictional full plan total is $510.00, with a deposit of $180.00 and equal payments of $110.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($510.00−$180.00)/$110.00 = $330.00/$110.00=3 payments. The amount $330.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$110.00+$180.00=$510.00. The terms and units are consistent.

Change one condition: If another payment of $110.00 were included, the full total would rise to $620.00 and the count become 4.

152. Find how many instalments are stated · 35

Question: The fictional full plan total is $820.00, with a deposit of $240.00 and equal payments of $145.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($820.00−$240.00)/$145.00 = $580.00/$145.00=4 payments. The amount $580.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$145.00+$240.00=$820.00. The terms and units are consistent.

Change one condition: If another payment of $145.00 were included, the full total would rise to $965.00 and the count become 5.

153. Find how many instalments are stated · 36

Question: The fictional full plan total is $660.00, with a deposit of $300.00 and equal payments of $60.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($660.00−$300.00)/$60.00 = $360.00/$60.00=6 payments. The amount $360.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$60.00+$300.00=$660.00. The terms and units are consistent.

Change one condition: If another payment of $60.00 were included, the full total would rise to $720.00 and the count become 7.

Compare two different payment plans

For compare two different payment plans, list every monetary amount and its frequency before calculating. Use the total to check an unknown monthly payment or payment count by reversing operations. Be clear that comparing two complete arithmetic totals is not the same as recommending a real financial commitment. If the question omits a fee or schedule, don’t invent it.

154. Compare deposits, terms and stated fees · 1

Question: Two invented plans cover the same hypothetical item. A: deposit $20.00, 4 payments of $30.00 and a one-time fee $0.00. B: deposit $10.00, 6 payments of $30.00 and a one-time fee $0.00. Find each full cost.

Interpret the payments: Use each plan’s own number of repeated payments. Deposits and explicitly stated administration fees appear once. The mathematical question asks about the total amount paid, not timing, suitability, real borrowing conditions or the value of having cash available today.

Worked answer: Plan A =$20.00+4×$30.00+$0.00=$140.00. Plan B =$10.00+6×$30.00+$0.00=$190.00. Plan A is lower by $50.00.

Common first error: A pupil might choose the lower monthly amount without counting the longer term. Or they may multiply a one-off fee by months. Both are structural errors occurring before the final addition.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $50.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $160.00; recompute which full total is lower.

155. Compare deposits, terms and stated fees · 2

Question: Two invented plans cover the same hypothetical item. A: deposit $50.00, 6 payments of $65.00 and a one-time fee $10.00. B: deposit $60.00, 9 payments of $85.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$50.00+6×$65.00+$10.00=$450.00. Plan B =$60.00+9×$85.00+$20.00=$845.00. Plan A is lower by $395.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $395.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $470.00; recompute which full total is lower.

156. Compare deposits, terms and stated fees · 3

Question: Two invented plans cover the same hypothetical item. A: deposit $80.00, 8 payments of $100.00 and a one-time fee $20.00. B: deposit $110.00, 12 payments of $140.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$80.00+8×$100.00+$20.00=$900.00. Plan B =$110.00+12×$140.00+$40.00=$1,830.00. Plan A is lower by $930.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $930.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $920.00; recompute which full total is lower.

157. Compare deposits, terms and stated fees · 4

Question: Two invented plans cover the same hypothetical item. A: deposit $110.00, 10 payments of $135.00 and a one-time fee $30.00. B: deposit $160.00, 15 payments of $50.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$110.00+10×$135.00+$30.00=$1,490.00. Plan B =$160.00+15×$50.00+$10.00=$920.00. Plan B is lower by $570.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $570.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,510.00; recompute which full total is lower.

158. Compare deposits, terms and stated fees · 5

Question: Two invented plans cover the same hypothetical item. A: deposit $140.00, 12 payments of $45.00 and a one-time fee $40.00. B: deposit $210.00, 18 payments of $105.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$140.00+12×$45.00+$40.00=$720.00. Plan B =$210.00+18×$105.00+$30.00=$2,130.00. Plan A is lower by $1,410.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,410.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $740.00; recompute which full total is lower.

159. Compare deposits, terms and stated fees · 6

Question: Two invented plans cover the same hypothetical item. A: deposit $170.00, 18 payments of $80.00 and a one-time fee $0.00. B: deposit $30.00, 24 payments of $160.00 and a one-time fee $0.00. Find each full cost.

Worked answer: Plan A =$170.00+18×$80.00+$0.00=$1,610.00. Plan B =$30.00+24×$160.00+$0.00=$3,870.00. Plan A is lower by $2,260.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $2,260.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,630.00; recompute which full total is lower.

160. Compare deposits, terms and stated fees · 7

Question: Two invented plans cover the same hypothetical item. A: deposit $200.00, 4 payments of $115.00 and a one-time fee $10.00. B: deposit $80.00, 6 payments of $70.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$200.00+4×$115.00+$10.00=$670.00. Plan B =$80.00+6×$70.00+$20.00=$520.00. Plan B is lower by $150.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $150.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $690.00; recompute which full total is lower.

161. Compare deposits, terms and stated fees · 8

Question: Two invented plans cover the same hypothetical item. A: deposit $20.00, 6 payments of $150.00 and a one-time fee $20.00. B: deposit $130.00, 9 payments of $125.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$20.00+6×$150.00+$20.00=$940.00. Plan B =$130.00+9×$125.00+$40.00=$1,295.00. Plan A is lower by $355.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $355.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $960.00; recompute which full total is lower.

162. Compare deposits, terms and stated fees · 9

Question: Two invented plans cover the same hypothetical item. A: deposit $50.00, 8 payments of $60.00 and a one-time fee $30.00. B: deposit $180.00, 12 payments of $35.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$50.00+8×$60.00+$30.00=$560.00. Plan B =$180.00+12×$35.00+$10.00=$610.00. Plan A is lower by $50.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $50.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $580.00; recompute which full total is lower.

163. Compare deposits, terms and stated fees · 10

Question: Two invented plans cover the same hypothetical item. A: deposit $80.00, 10 payments of $95.00 and a one-time fee $40.00. B: deposit $230.00, 15 payments of $90.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$80.00+10×$95.00+$40.00=$1,070.00. Plan B =$230.00+15×$90.00+$30.00=$1,610.00. Plan A is lower by $540.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $540.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,090.00; recompute which full total is lower.

164. Compare deposits, terms and stated fees · 11

Question: Two invented plans cover the same hypothetical item. A: deposit $110.00, 12 payments of $130.00 and a one-time fee $0.00. B: deposit $50.00, 18 payments of $145.00 and a one-time fee $0.00. Find each full cost.

Worked answer: Plan A =$110.00+12×$130.00+$0.00=$1,670.00. Plan B =$50.00+18×$145.00+$0.00=$2,660.00. Plan A is lower by $990.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $990.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,690.00; recompute which full total is lower.

165. Compare deposits, terms and stated fees · 12

Question: Two invented plans cover the same hypothetical item. A: deposit $140.00, 18 payments of $40.00 and a one-time fee $10.00. B: deposit $100.00, 24 payments of $55.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$140.00+18×$40.00+$10.00=$870.00. Plan B =$100.00+24×$55.00+$20.00=$1,440.00. Plan A is lower by $570.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $570.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $890.00; recompute which full total is lower.

166. Compare deposits, terms and stated fees · 13

Question: Two invented plans cover the same hypothetical item. A: deposit $170.00, 4 payments of $75.00 and a one-time fee $20.00. B: deposit $150.00, 6 payments of $110.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$170.00+4×$75.00+$20.00=$490.00. Plan B =$150.00+6×$110.00+$40.00=$850.00. Plan A is lower by $360.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $360.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $510.00; recompute which full total is lower.

167. Compare deposits, terms and stated fees · 14

Question: Two invented plans cover the same hypothetical item. A: deposit $200.00, 6 payments of $110.00 and a one-time fee $30.00. B: deposit $200.00, 9 payments of $165.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$200.00+6×$110.00+$30.00=$890.00. Plan B =$200.00+9×$165.00+$10.00=$1,695.00. Plan A is lower by $805.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $805.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $910.00; recompute which full total is lower.

168. Compare deposits, terms and stated fees · 15

Question: Two invented plans cover the same hypothetical item. A: deposit $20.00, 8 payments of $145.00 and a one-time fee $40.00. B: deposit $20.00, 12 payments of $75.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$20.00+8×$145.00+$40.00=$1,220.00. Plan B =$20.00+12×$75.00+$30.00=$950.00. Plan B is lower by $270.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $270.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,240.00; recompute which full total is lower.

169. Compare deposits, terms and stated fees · 16

Question: Two invented plans cover the same hypothetical item. A: deposit $50.00, 10 payments of $55.00 and a one-time fee $0.00. B: deposit $70.00, 15 payments of $130.00 and a one-time fee $0.00. Find each full cost.

Worked answer: Plan A =$50.00+10×$55.00+$0.00=$600.00. Plan B =$70.00+15×$130.00+$0.00=$2,020.00. Plan A is lower by $1,420.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,420.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $620.00; recompute which full total is lower.

170. Compare deposits, terms and stated fees · 17

Question: Two invented plans cover the same hypothetical item. A: deposit $80.00, 12 payments of $90.00 and a one-time fee $10.00. B: deposit $120.00, 18 payments of $40.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$80.00+12×$90.00+$10.00=$1,170.00. Plan B =$120.00+18×$40.00+$20.00=$860.00. Plan B is lower by $310.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $310.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,190.00; recompute which full total is lower.

171. Compare deposits, terms and stated fees · 18

Question: Two invented plans cover the same hypothetical item. A: deposit $110.00, 18 payments of $125.00 and a one-time fee $20.00. B: deposit $170.00, 24 payments of $95.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$110.00+18×$125.00+$20.00=$2,380.00. Plan B =$170.00+24×$95.00+$40.00=$2,490.00. Plan A is lower by $110.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $110.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $2,400.00; recompute which full total is lower.

172. Compare deposits, terms and stated fees · 19

Question: Two invented plans cover the same hypothetical item. A: deposit $140.00, 4 payments of $35.00 and a one-time fee $30.00. B: deposit $220.00, 6 payments of $150.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$140.00+4×$35.00+$30.00=$310.00. Plan B =$220.00+6×$150.00+$10.00=$1,130.00. Plan A is lower by $820.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $820.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $330.00; recompute which full total is lower.

173. Compare deposits, terms and stated fees · 20

Question: Two invented plans cover the same hypothetical item. A: deposit $170.00, 6 payments of $70.00 and a one-time fee $40.00. B: deposit $40.00, 9 payments of $60.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$170.00+6×$70.00+$40.00=$630.00. Plan B =$40.00+9×$60.00+$30.00=$610.00. Plan B is lower by $20.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $20.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $650.00; recompute which full total is lower.

174. Compare deposits, terms and stated fees · 21

Question: Two invented plans cover the same hypothetical item. A: deposit $200.00, 8 payments of $105.00 and a one-time fee $0.00. B: deposit $90.00, 12 payments of $115.00 and a one-time fee $0.00. Find each full cost.

Worked answer: Plan A =$200.00+8×$105.00+$0.00=$1,040.00. Plan B =$90.00+12×$115.00+$0.00=$1,470.00. Plan A is lower by $430.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $430.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,060.00; recompute which full total is lower.

175. Compare deposits, terms and stated fees · 22

Question: Two invented plans cover the same hypothetical item. A: deposit $20.00, 10 payments of $140.00 and a one-time fee $10.00. B: deposit $140.00, 15 payments of $170.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$20.00+10×$140.00+$10.00=$1,430.00. Plan B =$140.00+15×$170.00+$20.00=$2,710.00. Plan A is lower by $1,280.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,280.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,450.00; recompute which full total is lower.

176. Compare deposits, terms and stated fees · 23

Question: Two invented plans cover the same hypothetical item. A: deposit $50.00, 12 payments of $50.00 and a one-time fee $20.00. B: deposit $190.00, 18 payments of $80.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$50.00+12×$50.00+$20.00=$670.00. Plan B =$190.00+18×$80.00+$40.00=$1,670.00. Plan A is lower by $1,000.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,000.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $690.00; recompute which full total is lower.

177. Compare deposits, terms and stated fees · 24

Question: Two invented plans cover the same hypothetical item. A: deposit $80.00, 18 payments of $85.00 and a one-time fee $30.00. B: deposit $10.00, 24 payments of $135.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$80.00+18×$85.00+$30.00=$1,640.00. Plan B =$10.00+24×$135.00+$10.00=$3,260.00. Plan A is lower by $1,620.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,620.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,660.00; recompute which full total is lower.

178. Compare deposits, terms and stated fees · 25

Question: Two invented plans cover the same hypothetical item. A: deposit $110.00, 4 payments of $120.00 and a one-time fee $40.00. B: deposit $60.00, 6 payments of $45.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$110.00+4×$120.00+$40.00=$630.00. Plan B =$60.00+6×$45.00+$30.00=$360.00. Plan B is lower by $270.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $270.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $650.00; recompute which full total is lower.

179. Compare deposits, terms and stated fees · 26

Question: Two invented plans cover the same hypothetical item. A: deposit $140.00, 6 payments of $30.00 and a one-time fee $0.00. B: deposit $110.00, 9 payments of $100.00 and a one-time fee $0.00. Find each full cost.

Worked answer: Plan A =$140.00+6×$30.00+$0.00=$320.00. Plan B =$110.00+9×$100.00+$0.00=$1,010.00. Plan A is lower by $690.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $690.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $340.00; recompute which full total is lower.

180. Compare deposits, terms and stated fees · 27

Question: Two invented plans cover the same hypothetical item. A: deposit $170.00, 8 payments of $65.00 and a one-time fee $10.00. B: deposit $160.00, 12 payments of $155.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$170.00+8×$65.00+$10.00=$700.00. Plan B =$160.00+12×$155.00+$20.00=$2,040.00. Plan A is lower by $1,340.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,340.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $720.00; recompute which full total is lower.

181. Compare deposits, terms and stated fees · 28

Question: Two invented plans cover the same hypothetical item. A: deposit $200.00, 10 payments of $100.00 and a one-time fee $20.00. B: deposit $210.00, 15 payments of $65.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$200.00+10×$100.00+$20.00=$1,220.00. Plan B =$210.00+15×$65.00+$40.00=$1,225.00. Plan A is lower by $5.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $5.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,240.00; recompute which full total is lower.

182. Compare deposits, terms and stated fees · 29

Question: Two invented plans cover the same hypothetical item. A: deposit $20.00, 12 payments of $135.00 and a one-time fee $30.00. B: deposit $30.00, 18 payments of $120.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$20.00+12×$135.00+$30.00=$1,670.00. Plan B =$30.00+18×$120.00+$10.00=$2,200.00. Plan A is lower by $530.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $530.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,690.00; recompute which full total is lower.

183. Compare deposits, terms and stated fees · 30

Question: Two invented plans cover the same hypothetical item. A: deposit $50.00, 18 payments of $45.00 and a one-time fee $40.00. B: deposit $80.00, 24 payments of $30.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$50.00+18×$45.00+$40.00=$900.00. Plan B =$80.00+24×$30.00+$30.00=$830.00. Plan B is lower by $70.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $70.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $920.00; recompute which full total is lower.

184. Compare deposits, terms and stated fees · 31

Question: Two invented plans cover the same hypothetical item. A: deposit $80.00, 4 payments of $80.00 and a one-time fee $0.00. B: deposit $130.00, 6 payments of $85.00 and a one-time fee $0.00. Find each full cost.

Worked answer: Plan A =$80.00+4×$80.00+$0.00=$400.00. Plan B =$130.00+6×$85.00+$0.00=$640.00. Plan A is lower by $240.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $240.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $420.00; recompute which full total is lower.

185. Compare deposits, terms and stated fees · 32

Question: Two invented plans cover the same hypothetical item. A: deposit $110.00, 6 payments of $115.00 and a one-time fee $10.00. B: deposit $180.00, 9 payments of $140.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$110.00+6×$115.00+$10.00=$810.00. Plan B =$180.00+9×$140.00+$20.00=$1,460.00. Plan A is lower by $650.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $650.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $830.00; recompute which full total is lower.

186. Compare deposits, terms and stated fees · 33

Question: Two invented plans cover the same hypothetical item. A: deposit $140.00, 8 payments of $150.00 and a one-time fee $20.00. B: deposit $230.00, 12 payments of $50.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$140.00+8×$150.00+$20.00=$1,360.00. Plan B =$230.00+12×$50.00+$40.00=$870.00. Plan B is lower by $490.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $490.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,380.00; recompute which full total is lower.

187. Compare deposits, terms and stated fees · 34

Question: Two invented plans cover the same hypothetical item. A: deposit $170.00, 10 payments of $60.00 and a one-time fee $30.00. B: deposit $50.00, 15 payments of $105.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$170.00+10×$60.00+$30.00=$800.00. Plan B =$50.00+15×$105.00+$10.00=$1,635.00. Plan A is lower by $835.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $835.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $820.00; recompute which full total is lower.

188. Compare deposits, terms and stated fees · 35

Question: Two invented plans cover the same hypothetical item. A: deposit $200.00, 12 payments of $95.00 and a one-time fee $40.00. B: deposit $100.00, 18 payments of $160.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$200.00+12×$95.00+$40.00=$1,380.00. Plan B =$100.00+18×$160.00+$30.00=$3,010.00. Plan A is lower by $1,630.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,630.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,400.00; recompute which full total is lower.

189. Compare deposits, terms and stated fees · 36

Question: Two invented plans cover the same hypothetical item. A: deposit $20.00, 18 payments of $130.00 and a one-time fee $0.00. B: deposit $150.00, 24 payments of $70.00 and a one-time fee $0.00. Find each full cost.

Worked answer: Plan A =$20.00+18×$130.00+$0.00=$2,360.00. Plan B =$150.00+24×$70.00+$0.00=$1,830.00. Plan B is lower by $530.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $530.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $2,380.00; recompute which full total is lower.

190. Compare deposits, terms and stated fees · 37

Question: Two invented plans cover the same hypothetical item. A: deposit $50.00, 4 payments of $40.00 and a one-time fee $10.00. B: deposit $200.00, 6 payments of $125.00 and a one-time fee $20.00. Find each full cost.

Worked answer: Plan A =$50.00+4×$40.00+$10.00=$220.00. Plan B =$200.00+6×$125.00+$20.00=$970.00. Plan A is lower by $750.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $750.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $240.00; recompute which full total is lower.

191. Compare deposits, terms and stated fees · 38

Question: Two invented plans cover the same hypothetical item. A: deposit $80.00, 6 payments of $75.00 and a one-time fee $20.00. B: deposit $20.00, 9 payments of $35.00 and a one-time fee $40.00. Find each full cost.

Worked answer: Plan A =$80.00+6×$75.00+$20.00=$550.00. Plan B =$20.00+9×$35.00+$40.00=$375.00. Plan B is lower by $175.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $175.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $570.00; recompute which full total is lower.

192. Compare deposits, terms and stated fees · 39

Question: Two invented plans cover the same hypothetical item. A: deposit $110.00, 8 payments of $110.00 and a one-time fee $30.00. B: deposit $70.00, 12 payments of $90.00 and a one-time fee $10.00. Find each full cost.

Worked answer: Plan A =$110.00+8×$110.00+$30.00=$1,020.00. Plan B =$70.00+12×$90.00+$10.00=$1,160.00. Plan A is lower by $140.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $140.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,040.00; recompute which full total is lower.

193. Compare deposits, terms and stated fees · 40

Question: Two invented plans cover the same hypothetical item. A: deposit $140.00, 10 payments of $145.00 and a one-time fee $40.00. B: deposit $120.00, 15 payments of $145.00 and a one-time fee $30.00. Find each full cost.

Worked answer: Plan A =$140.00+10×$145.00+$40.00=$1,630.00. Plan B =$120.00+15×$145.00+$30.00=$2,325.00. Plan A is lower by $695.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $695.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,650.00; recompute which full total is lower.

Make a household budget arithmetic check

For make a household budget arithmetic check, list every monetary amount and its frequency before calculating. Use the total to check an unknown monthly payment or payment count by reversing operations. Be clear that comparing two complete arithmetic totals is not the same as recommending a real financial commitment. If the question omits a fee or schedule, don’t invent it.

194. A monthly residual is not a whole-plan total · 1

Question: A fictional monthly budget has income $1,200.00, known commitments $350.00 and one plan payment $30.00. The invented plan also requires deposit $20.00 plus 6 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Interpret the payments: Cash-flow arithmetic uses amounts from the same month. The deposit is a separate up-front requirement and should not silently be added to recurring income or expenses every month. The full plan cost is calculated over its term, a different horizon from the single-month residual.

Worked answer: The illustrative monthly residual is $1,200.00−$350.00−$30.00=$820.00 before omitted costs. The plan’s full total is $20.00+6×$30.00=$200.00. These answer different questions.

Common first error: A positive monthly residual is not a guarantee that a real offer is prudent or affordable. Real budgets have other needs, uncertain income and timing effects; the article does not claim to assess a household’s finances.

Reverse-check: Reconstruct monthly income: $350.00+$30.00+($820.00)=$1,200.00. Also verify 6×$30.00+$20.00=$200.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $770.00; the plan’s contract total under the stated schedule remains $200.00.

195. A monthly residual is not a whole-plan total · 2

Question: A fictional monthly budget has income $1,500.00, known commitments $600.00 and one plan payment $140.00. The invented plan also requires deposit $160.00 plus 9 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,500.00−$600.00−$140.00=$760.00 before omitted costs. The plan’s full total is $160.00+9×$140.00=$1,420.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $600.00+$140.00+($760.00)=$1,500.00. Also verify 9×$140.00+$160.00=$1,420.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $710.00; the plan’s contract total under the stated schedule remains $1,420.00.

196. A monthly residual is not a whole-plan total · 3

Question: A fictional monthly budget has income $1,800.00, known commitments $850.00 and one plan payment $40.00. The invented plan also requires deposit $40.00 plus 12 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,800.00−$850.00−$40.00=$910.00 before omitted costs. The plan’s full total is $40.00+12×$40.00=$520.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $850.00+$40.00+($910.00)=$1,800.00. Also verify 12×$40.00+$40.00=$520.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $860.00; the plan’s contract total under the stated schedule remains $520.00.

197. A monthly residual is not a whole-plan total · 4

Question: A fictional monthly budget has income $2,100.00, known commitments $1,100.00 and one plan payment $150.00. The invented plan also requires deposit $180.00 plus 15 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,100.00−$1,100.00−$150.00=$850.00 before omitted costs. The plan’s full total is $180.00+15×$150.00=$2,430.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,100.00+$150.00+($850.00)=$2,100.00. Also verify 15×$150.00+$180.00=$2,430.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $800.00; the plan’s contract total under the stated schedule remains $2,430.00.

198. A monthly residual is not a whole-plan total · 5

Question: A fictional monthly budget has income $2,400.00, known commitments $1,350.00 and one plan payment $50.00. The invented plan also requires deposit $60.00 plus 18 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,400.00−$1,350.00−$50.00=$1,000.00 before omitted costs. The plan’s full total is $60.00+18×$50.00=$960.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,350.00+$50.00+($1,000.00)=$2,400.00. Also verify 18×$50.00+$60.00=$960.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $950.00; the plan’s contract total under the stated schedule remains $960.00.

199. A monthly residual is not a whole-plan total · 6

Question: A fictional monthly budget has income $2,700.00, known commitments $450.00 and one plan payment $160.00. The invented plan also requires deposit $200.00 plus 21 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,700.00−$450.00−$160.00=$2,090.00 before omitted costs. The plan’s full total is $200.00+21×$160.00=$3,560.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $450.00+$160.00+($2,090.00)=$2,700.00. Also verify 21×$160.00+$200.00=$3,560.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,040.00; the plan’s contract total under the stated schedule remains $3,560.00.

200. A monthly residual is not a whole-plan total · 7

Question: A fictional monthly budget has income $3,000.00, known commitments $700.00 and one plan payment $60.00. The invented plan also requires deposit $80.00 plus 24 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,000.00−$700.00−$60.00=$2,240.00 before omitted costs. The plan’s full total is $80.00+24×$60.00=$1,520.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $700.00+$60.00+($2,240.00)=$3,000.00. Also verify 24×$60.00+$80.00=$1,520.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,190.00; the plan’s contract total under the stated schedule remains $1,520.00.

201. A monthly residual is not a whole-plan total · 8

Question: A fictional monthly budget has income $3,300.00, known commitments $950.00 and one plan payment $170.00. The invented plan also requires deposit $220.00 plus 8 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,300.00−$950.00−$170.00=$2,180.00 before omitted costs. The plan’s full total is $220.00+8×$170.00=$1,580.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $950.00+$170.00+($2,180.00)=$3,300.00. Also verify 8×$170.00+$220.00=$1,580.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,130.00; the plan’s contract total under the stated schedule remains $1,580.00.

202. A monthly residual is not a whole-plan total · 9

Question: A fictional monthly budget has income $3,600.00, known commitments $1,200.00 and one plan payment $70.00. The invented plan also requires deposit $100.00 plus 11 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,600.00−$1,200.00−$70.00=$2,330.00 before omitted costs. The plan’s full total is $100.00+11×$70.00=$870.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,200.00+$70.00+($2,330.00)=$3,600.00. Also verify 11×$70.00+$100.00=$870.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,280.00; the plan’s contract total under the stated schedule remains $870.00.

203. A monthly residual is not a whole-plan total · 10

Question: A fictional monthly budget has income $3,900.00, known commitments $1,450.00 and one plan payment $180.00. The invented plan also requires deposit $240.00 plus 14 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,900.00−$1,450.00−$180.00=$2,270.00 before omitted costs. The plan’s full total is $240.00+14×$180.00=$2,760.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,450.00+$180.00+($2,270.00)=$3,900.00. Also verify 14×$180.00+$240.00=$2,760.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,220.00; the plan’s contract total under the stated schedule remains $2,760.00.

204. A monthly residual is not a whole-plan total · 11

Question: A fictional monthly budget has income $4,200.00, known commitments $550.00 and one plan payment $80.00. The invented plan also requires deposit $120.00 plus 17 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $4,200.00−$550.00−$80.00=$3,570.00 before omitted costs. The plan’s full total is $120.00+17×$80.00=$1,480.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $550.00+$80.00+($3,570.00)=$4,200.00. Also verify 17×$80.00+$120.00=$1,480.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $3,520.00; the plan’s contract total under the stated schedule remains $1,480.00.

205. A monthly residual is not a whole-plan total · 12

Question: A fictional monthly budget has income $1,300.00, known commitments $800.00 and one plan payment $190.00. The invented plan also requires deposit $260.00 plus 20 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,300.00−$800.00−$190.00=$310.00 before omitted costs. The plan’s full total is $260.00+20×$190.00=$4,060.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $800.00+$190.00+($310.00)=$1,300.00. Also verify 20×$190.00+$260.00=$4,060.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $260.00; the plan’s contract total under the stated schedule remains $4,060.00.

206. A monthly residual is not a whole-plan total · 13

Question: A fictional monthly budget has income $1,600.00, known commitments $1,050.00 and one plan payment $90.00. The invented plan also requires deposit $140.00 plus 23 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,600.00−$1,050.00−$90.00=$460.00 before omitted costs. The plan’s full total is $140.00+23×$90.00=$2,210.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,050.00+$90.00+($460.00)=$1,600.00. Also verify 23×$90.00+$140.00=$2,210.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $410.00; the plan’s contract total under the stated schedule remains $2,210.00.

207. A monthly residual is not a whole-plan total · 14

Question: A fictional monthly budget has income $1,900.00, known commitments $1,300.00 and one plan payment $200.00. The invented plan also requires deposit $20.00 plus 7 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,900.00−$1,300.00−$200.00=$400.00 before omitted costs. The plan’s full total is $20.00+7×$200.00=$1,420.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,300.00+$200.00+($400.00)=$1,900.00. Also verify 7×$200.00+$20.00=$1,420.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $350.00; the plan’s contract total under the stated schedule remains $1,420.00.

208. A monthly residual is not a whole-plan total · 15

Question: A fictional monthly budget has income $2,200.00, known commitments $400.00 and one plan payment $100.00. The invented plan also requires deposit $160.00 plus 10 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,200.00−$400.00−$100.00=$1,700.00 before omitted costs. The plan’s full total is $160.00+10×$100.00=$1,160.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $400.00+$100.00+($1,700.00)=$2,200.00. Also verify 10×$100.00+$160.00=$1,160.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,650.00; the plan’s contract total under the stated schedule remains $1,160.00.

209. A monthly residual is not a whole-plan total · 16

Question: A fictional monthly budget has income $2,500.00, known commitments $650.00 and one plan payment $210.00. The invented plan also requires deposit $40.00 plus 13 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,500.00−$650.00−$210.00=$1,640.00 before omitted costs. The plan’s full total is $40.00+13×$210.00=$2,770.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $650.00+$210.00+($1,640.00)=$2,500.00. Also verify 13×$210.00+$40.00=$2,770.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,590.00; the plan’s contract total under the stated schedule remains $2,770.00.

210. A monthly residual is not a whole-plan total · 17

Question: A fictional monthly budget has income $2,800.00, known commitments $900.00 and one plan payment $110.00. The invented plan also requires deposit $180.00 plus 16 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,800.00−$900.00−$110.00=$1,790.00 before omitted costs. The plan’s full total is $180.00+16×$110.00=$1,940.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $900.00+$110.00+($1,790.00)=$2,800.00. Also verify 16×$110.00+$180.00=$1,940.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,740.00; the plan’s contract total under the stated schedule remains $1,940.00.

211. A monthly residual is not a whole-plan total · 18

Question: A fictional monthly budget has income $3,100.00, known commitments $1,150.00 and one plan payment $220.00. The invented plan also requires deposit $60.00 plus 19 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,100.00−$1,150.00−$220.00=$1,730.00 before omitted costs. The plan’s full total is $60.00+19×$220.00=$4,240.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,150.00+$220.00+($1,730.00)=$3,100.00. Also verify 19×$220.00+$60.00=$4,240.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,680.00; the plan’s contract total under the stated schedule remains $4,240.00.

212. A monthly residual is not a whole-plan total · 19

Question: A fictional monthly budget has income $3,400.00, known commitments $1,400.00 and one plan payment $120.00. The invented plan also requires deposit $200.00 plus 22 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,400.00−$1,400.00−$120.00=$1,880.00 before omitted costs. The plan’s full total is $200.00+22×$120.00=$2,840.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,400.00+$120.00+($1,880.00)=$3,400.00. Also verify 22×$120.00+$200.00=$2,840.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,830.00; the plan’s contract total under the stated schedule remains $2,840.00.

213. A monthly residual is not a whole-plan total · 20

Question: A fictional monthly budget has income $3,700.00, known commitments $500.00 and one plan payment $230.00. The invented plan also requires deposit $80.00 plus 6 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,700.00−$500.00−$230.00=$2,970.00 before omitted costs. The plan’s full total is $80.00+6×$230.00=$1,460.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $500.00+$230.00+($2,970.00)=$3,700.00. Also verify 6×$230.00+$80.00=$1,460.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,920.00; the plan’s contract total under the stated schedule remains $1,460.00.

214. A monthly residual is not a whole-plan total · 21

Question: A fictional monthly budget has income $4,000.00, known commitments $750.00 and one plan payment $130.00. The invented plan also requires deposit $220.00 plus 9 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $4,000.00−$750.00−$130.00=$3,120.00 before omitted costs. The plan’s full total is $220.00+9×$130.00=$1,390.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $750.00+$130.00+($3,120.00)=$4,000.00. Also verify 9×$130.00+$220.00=$1,390.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $3,070.00; the plan’s contract total under the stated schedule remains $1,390.00.

215. A monthly residual is not a whole-plan total · 22

Question: A fictional monthly budget has income $4,300.00, known commitments $1,000.00 and one plan payment $30.00. The invented plan also requires deposit $100.00 plus 12 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $4,300.00−$1,000.00−$30.00=$3,270.00 before omitted costs. The plan’s full total is $100.00+12×$30.00=$460.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,000.00+$30.00+($3,270.00)=$4,300.00. Also verify 12×$30.00+$100.00=$460.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $3,220.00; the plan’s contract total under the stated schedule remains $460.00.

216. A monthly residual is not a whole-plan total · 23

Question: A fictional monthly budget has income $1,400.00, known commitments $1,250.00 and one plan payment $140.00. The invented plan also requires deposit $240.00 plus 15 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,400.00−$1,250.00−$140.00=$10.00 before omitted costs. The plan’s full total is $240.00+15×$140.00=$2,340.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,250.00+$140.00+($10.00)=$1,400.00. Also verify 15×$140.00+$240.00=$2,340.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes −$40.00; the plan’s contract total under the stated schedule remains $2,340.00.

217. A monthly residual is not a whole-plan total · 24

Question: A fictional monthly budget has income $1,700.00, known commitments $350.00 and one plan payment $40.00. The invented plan also requires deposit $120.00 plus 18 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,700.00−$350.00−$40.00=$1,310.00 before omitted costs. The plan’s full total is $120.00+18×$40.00=$840.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $350.00+$40.00+($1,310.00)=$1,700.00. Also verify 18×$40.00+$120.00=$840.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,260.00; the plan’s contract total under the stated schedule remains $840.00.

218. A monthly residual is not a whole-plan total · 25

Question: A fictional monthly budget has income $2,000.00, known commitments $600.00 and one plan payment $150.00. The invented plan also requires deposit $260.00 plus 21 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,000.00−$600.00−$150.00=$1,250.00 before omitted costs. The plan’s full total is $260.00+21×$150.00=$3,410.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $600.00+$150.00+($1,250.00)=$2,000.00. Also verify 21×$150.00+$260.00=$3,410.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,200.00; the plan’s contract total under the stated schedule remains $3,410.00.

219. A monthly residual is not a whole-plan total · 26

Question: A fictional monthly budget has income $2,300.00, known commitments $850.00 and one plan payment $50.00. The invented plan also requires deposit $140.00 plus 24 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,300.00−$850.00−$50.00=$1,400.00 before omitted costs. The plan’s full total is $140.00+24×$50.00=$1,340.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $850.00+$50.00+($1,400.00)=$2,300.00. Also verify 24×$50.00+$140.00=$1,340.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,350.00; the plan’s contract total under the stated schedule remains $1,340.00.

220. A monthly residual is not a whole-plan total · 27

Question: A fictional monthly budget has income $2,600.00, known commitments $1,100.00 and one plan payment $160.00. The invented plan also requires deposit $20.00 plus 8 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,600.00−$1,100.00−$160.00=$1,340.00 before omitted costs. The plan’s full total is $20.00+8×$160.00=$1,300.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,100.00+$160.00+($1,340.00)=$2,600.00. Also verify 8×$160.00+$20.00=$1,300.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,290.00; the plan’s contract total under the stated schedule remains $1,300.00.

221. A monthly residual is not a whole-plan total · 28

Question: A fictional monthly budget has income $2,900.00, known commitments $1,350.00 and one plan payment $60.00. The invented plan also requires deposit $160.00 plus 11 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,900.00−$1,350.00−$60.00=$1,490.00 before omitted costs. The plan’s full total is $160.00+11×$60.00=$820.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,350.00+$60.00+($1,490.00)=$2,900.00. Also verify 11×$60.00+$160.00=$820.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $1,440.00; the plan’s contract total under the stated schedule remains $820.00.

222. A monthly residual is not a whole-plan total · 29

Question: A fictional monthly budget has income $3,200.00, known commitments $450.00 and one plan payment $170.00. The invented plan also requires deposit $40.00 plus 14 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,200.00−$450.00−$170.00=$2,580.00 before omitted costs. The plan’s full total is $40.00+14×$170.00=$2,420.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $450.00+$170.00+($2,580.00)=$3,200.00. Also verify 14×$170.00+$40.00=$2,420.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,530.00; the plan’s contract total under the stated schedule remains $2,420.00.

223. A monthly residual is not a whole-plan total · 30

Question: A fictional monthly budget has income $3,500.00, known commitments $700.00 and one plan payment $70.00. The invented plan also requires deposit $180.00 plus 17 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,500.00−$700.00−$70.00=$2,730.00 before omitted costs. The plan’s full total is $180.00+17×$70.00=$1,370.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $700.00+$70.00+($2,730.00)=$3,500.00. Also verify 17×$70.00+$180.00=$1,370.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,680.00; the plan’s contract total under the stated schedule remains $1,370.00.

224. A monthly residual is not a whole-plan total · 31

Question: A fictional monthly budget has income $3,800.00, known commitments $950.00 and one plan payment $180.00. The invented plan also requires deposit $60.00 plus 20 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $3,800.00−$950.00−$180.00=$2,670.00 before omitted costs. The plan’s full total is $60.00+20×$180.00=$3,660.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $950.00+$180.00+($2,670.00)=$3,800.00. Also verify 20×$180.00+$60.00=$3,660.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,620.00; the plan’s contract total under the stated schedule remains $3,660.00.

225. A monthly residual is not a whole-plan total · 32

Question: A fictional monthly budget has income $4,100.00, known commitments $1,200.00 and one plan payment $80.00. The invented plan also requires deposit $200.00 plus 23 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $4,100.00−$1,200.00−$80.00=$2,820.00 before omitted costs. The plan’s full total is $200.00+23×$80.00=$2,040.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,200.00+$80.00+($2,820.00)=$4,100.00. Also verify 23×$80.00+$200.00=$2,040.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $2,770.00; the plan’s contract total under the stated schedule remains $2,040.00.

226. A monthly residual is not a whole-plan total · 33

Question: A fictional monthly budget has income $1,200.00, known commitments $1,450.00 and one plan payment $190.00. The invented plan also requires deposit $80.00 plus 7 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,200.00−$1,450.00−$190.00=−$440.00 before omitted costs. The plan’s full total is $80.00+7×$190.00=$1,410.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,450.00+$190.00+(−$440.00)=$1,200.00. Also verify 7×$190.00+$80.00=$1,410.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes −$490.00; the plan’s contract total under the stated schedule remains $1,410.00.

227. A monthly residual is not a whole-plan total · 34

Question: A fictional monthly budget has income $1,500.00, known commitments $550.00 and one plan payment $90.00. The invented plan also requires deposit $220.00 plus 10 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,500.00−$550.00−$90.00=$860.00 before omitted costs. The plan’s full total is $220.00+10×$90.00=$1,120.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $550.00+$90.00+($860.00)=$1,500.00. Also verify 10×$90.00+$220.00=$1,120.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $810.00; the plan’s contract total under the stated schedule remains $1,120.00.

228. A monthly residual is not a whole-plan total · 35

Question: A fictional monthly budget has income $1,800.00, known commitments $800.00 and one plan payment $200.00. The invented plan also requires deposit $100.00 plus 13 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $1,800.00−$800.00−$200.00=$800.00 before omitted costs. The plan’s full total is $100.00+13×$200.00=$2,700.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $800.00+$200.00+($800.00)=$1,800.00. Also verify 13×$200.00+$100.00=$2,700.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $750.00; the plan’s contract total under the stated schedule remains $2,700.00.

229. A monthly residual is not a whole-plan total · 36

Question: A fictional monthly budget has income $2,100.00, known commitments $1,050.00 and one plan payment $100.00. The invented plan also requires deposit $240.00 plus 16 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,100.00−$1,050.00−$100.00=$950.00 before omitted costs. The plan’s full total is $240.00+16×$100.00=$1,840.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,050.00+$100.00+($950.00)=$2,100.00. Also verify 16×$100.00+$240.00=$1,840.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $900.00; the plan’s contract total under the stated schedule remains $1,840.00.

230. A monthly residual is not a whole-plan total · 37

Question: A fictional monthly budget has income $2,400.00, known commitments $1,300.00 and one plan payment $210.00. The invented plan also requires deposit $120.00 plus 19 monthly payments. Calculate the residual before other unlisted expenses and full stated plan total.

Worked answer: The illustrative monthly residual is $2,400.00−$1,300.00−$210.00=$890.00 before omitted costs. The plan’s full total is $120.00+19×$210.00=$4,110.00. These answer different questions.

Reverse-check: Reconstruct monthly income: $1,300.00+$210.00+($890.00)=$2,400.00. Also verify 19×$210.00+$120.00=$4,110.00.

Change one condition: If monthly income changed by −$50.00 but all modelled monthly outgoings stayed fixed, the residual becomes $840.00; the plan’s contract total under the stated schedule remains $4,110.00.

Identify missing or misleading plan terms

For identify missing or misleading plan terms, list every monetary amount and its frequency before calculating. Use the total to check an unknown monthly payment or payment count by reversing operations. Be clear that comparing two complete arithmetic totals is not the same as recommending a real financial commitment. If the question omits a fee or schedule, don’t invent it.

231. Deposit is not the full purchase total

Question: An advertisement mentions a fictional $100 deposit but gives no term or monthly charge. Can a full total be found?

Interpret the payments: A full instalment comparison must distinguish once-only amounts from repeated amounts and must identify the stated time interval. The mathematical model must not invent real fees, borrowing rates, cancellation rules or product claims. When information is missing, identify the missing term rather than guessing.

Worked answer: No. The payment count and amount remain unknown.

Common first error: Calling the deposit the final price ignores further payments.

Reverse-check: Name missing terms.

Change one condition: Change one supplied amount or period and recalculate, making the unit of each payment explicit. Compare full totals only when the schedules and their assumptions are clear. Any actual financial decision needs its own current terms; this is an educational arithmetic example.

232. Small monthly versus total cost

Question: Compare $20 each month for 36 months against $35 for 18 months, no other costs.

Worked answer: First $720, second $630. Larger monthly payment has lower full total.

Common first error: Monthly amounts are not directly comparable as complete costs.

Reverse-check: 20×36=720 and 35×18=630.

233. Cash price and total plan price differ

Question: Cash $500, fictional plan $575. Difference?

Worked answer: $75 more by plan under specified terms.

Common first error: Using the cash price as though it were the monthly payment total.

Reverse-check: 575−500=75.

234. One-time fees count once

Question: Deposit 80 plus six payments of 45. Total?

Worked answer: $350.

Common first error: 80×6 repeats deposit wrongly.

Reverse-check: 80+270=350.

235. A fractional payment count is a warning

Question: Total $275, deposit $50, equal monthly payments $40. How many complete payments?

Worked answer: (275−50)/40=5.625, incompatible with an integer count of complete equal payments under the stated conditions.

Common first error: Rounding to six changes total.

Reverse-check: Six payments would total $290.

236. Deposit creates upfront cash requirement

Question: Can a small monthly amount prove a $150 deposit can be paid today?

Worked answer: No. Immediate cash availability is a separate fact not supplied.

Common first error: Monthly surplus alone doesn’t establish available deposit.

Reverse-check: State payment timing.

237. Unstated fees must not be invented

Question: The fictional problem says no other fees. Should the student add a guessed $30 late charge?

Worked answer: No. Compute only stated terms.

Common first error: Adding invented charges violates the model.

Reverse-check: Read the precise assumptions.

238. Zero interest is not zero extra fees

Question: A fictional offer advertises zero interest but has a $50 stated one-off fee. Can the fee be ignored?

Worked answer: No. The full arithmetic cost includes any stated fee.

Common first error: A marketing phrase does not override stated amounts.

Reverse-check: Add fee once.

239. Percent difference cash baseline

Question: Cash price $400, plan total $460. Percent higher relative to cash?

Worked answer: $60/$400=15%.

Common first error: Using the plan total as base answers another question.

Reverse-check: 400×1.15=460.

240. A negative difference can occur

Question: Cash $500, invented plan $470. Difference plan minus cash?

Worked answer: −$30.

Common first error: Assuming every hypothetical plan must cost more is false.

Reverse-check: 470−500=−30.

241. Overpayment is not APR

Question: Total plan exceeds cash by $100. Does this reveal effective yearly interest rate?

Worked answer: No. Timing, financed principal and charges matter.

Common first error: Percentage overpayment is not automatically annualised cost.

Reverse-check: Identify cash flows and dates.

242. Exact due dates need a start date

Question: Ten monthly payments listed, no first due date. Can their calendar dates be known?

Worked answer: No. Actual dates require the starting date and terms.

Common first error: Inventing dates from count alone is invalid.

Reverse-check: Request payment schedule.

243. A positive residual is not guaranteed saving

Question: Monthly budget has $500 available and payment $480. Is $20 guaranteed saved?

Worked answer: No. It is only the residual before all other needs.

Common first error: Limited budget categories may omit expenses.

Reverse-check: 500−480=20 mathematically.

244. Deposit as share of cash price

Question: Deposit $120 and cash quote $800. What percent is deposit of cash?

Worked answer: 15%.

Common first error: The base is $800, not $120.

Reverse-check: 120/800=0.15.

245. Change deposit with unchanged total

Question: Total $600 over ten monthly payments; deposit rises $100 to $150. Find new monthly amount.

Worked answer: (600−150)/10=$45.

Common first error: Treating monthly amount as unchanged would increase total.

Reverse-check: 150+450=600.

246. Payment frequency matters

Question: $60 every two months for twelve months, with a payment after each period. Total?

Worked answer: Six payments, $360.

Common first error: Twelve payments assumes monthly frequency not given.

Reverse-check: 12/2=6.

247. Annual fee is once per year

Question: One $24 annual fee and 12 monthly $10 payments. Total one year?

Worked answer: $144.

Common first error: 24×12 charges annual fee each month.

Reverse-check: 24+120=144.

248. Identical full totals with different timing

Question: A: $100+6×$50, B: $40+12×$30. Compare totals.

Worked answer: Both $400, though payment timing differs.

Common first error: Equal total does not imply identical monthly burden.

Reverse-check: 100+300=40+360.

249. Instalment minus cash

Question: Cash $560; plan $100+12×$40. Difference?

Worked answer: Plan $580, $20 above cash.

Common first error: Comparing $40 with $560 ignores term and deposit.

Reverse-check: 100+480=580.

250. Deposit discount changes the deposit

Question: Deposit $100 is discounted 20%, monthly charges unchanged. Total reduction?

Worked answer: $20.

Common first error: Applying 20% to entire plan changes percentage base.

Reverse-check: 0.2×100=20.

251. No deposit plan

Question: Zero deposit and eight $65 payments. Total?

Worked answer: $520.

Common first error: Adding an imaginary deposit changes the question.

Reverse-check: 8×65=520.

252. Label monthly count and monetary amount

Question: A calculation gives 6 payments of $40. Which value is dollars and which a count?

Worked answer: $40 is money per payment; six is the number of payments; total $240.

Common first error: Switching units can make a seemingly correct answer unclear.

Reverse-check: 6×$40=$240.

253. Negative budget residual

Question: Income $1000, commitments $900, plan payment $150. Residual?

Worked answer: −$50 in simplified monthly budget.

Common first error: A negative residual cannot be called an available surplus.

Reverse-check: 1000−900−150=−50.

254. Decimal-dollar payments

Question: Deposit $25.50 and three $19.95 payments. Full total?

Worked answer: $85.35.

Common first error: Rounding each before multiplication changes pennies.

Reverse-check: 25.50+59.85=85.35.

255. Recover monthly from total

Question: Total $900 includes deposit $180 and 12 equal monthly payments. Find each.

Worked answer: $60.

Common first error: $900/12 includes deposit incorrectly.

Reverse-check: 180+12×60=900.

256. Actual terms need current verification

Question: Can one select a real finance provider solely from two made-up classroom totals?

Worked answer: No. It is a numerical illustration, not a real-world recommendation.

Common first error: Terms, fees and conditions may differ.

Reverse-check: Check current written terms.

257. Identical monthly, different deposit

Question: Two plans both pay $30/month over 12 months; deposits $50 and $100. Compare totals.

Worked answer: $410 versus $460.

Common first error: Same monthly number does not mean same overall total.

Reverse-check: 360+50 vs 360+100.

258. Longer term with unchanged monthly cost

Question: Deposit $100 and payment $40, terms 12 and 18 months. Compare totals.

Worked answer: $580 versus $820, difference $240.

Common first error: More payments at same amount increase total.

Reverse-check: 40×6=240 extra.

259. Currency units must match

Question: Deposit quoted SGD and payments in another currency, no FX rate. Can exact SGD total be found?

Worked answer: No. A conversion rate is necessary.

Common first error: Adding numbers in different currencies is invalid.

Reverse-check: Identify missing exchange information.

260. Cash price does not determine monthly schedule

Question: Only cash price $1000 is given. Can monthly instalment be calculated?

Worked answer: No. Term, deposit and charges are unspecified.

Common first error: Assuming twelve months invents data.

Reverse-check: Request schedule.

261. Final balloon payment counts

Question: Ten payments $30 plus final separately stated $100 balloon. Full total?

Worked answer: $400.

Common first error: Omitting final special charge understates total.

Reverse-check: 300+100=400.

262. Ignore tax only if stated

Question: A fictional Maths question says ignore tax. Add an estimated local sales tax?

Worked answer: No. Follow the written assumption.

Common first error: Invented tax changes the scenario.

Reverse-check: Use stated costs.

263. APR cannot be inferred from simple overpayment

Question: Plan total is 12% higher than cash. Is annual percentage rate 12%?

Worked answer: Not necessarily. Time, principal and payments matter.

Common first error: Equating simple total comparison with annual rate is wrong.

Reverse-check: Define difference separately.

264. Equal dollar totals but different cash flows

Question: Is $500 cash at once identical in timing to ten monthly $50 payments?

Worked answer: No. Arithmetic totals match but timing differs.

Common first error: A total-only comparison omits timing.

Reverse-check: State totals and dates separately.

265. Advertised starting price can be incomplete

Question: A headline says ‘from $20/month’ but no term. Does it fix the full total?

Worked answer: No. Payment count and fees remain missing.

Common first error: Multiplying by a guessed term invents terms.

Reverse-check: Request complete schedule.

266. Rounding payments changes exact totals

Question: Six $49.99 instalments total what?

Worked answer: $299.94.

Common first error: Rounding to $50 before multiplying inflates six cents.

Reverse-check: 6×49.99=299.94.

267. Full total is not the same as affordability

Question: Two plans total $500 and $480. Which has lower numerical cost?

Worked answer: The $480 plan, by $20; this does not prove personal affordability.

Common first error: Conflating a numeric comparison with a personal finance decision is wrong.

Reverse-check: 480<500.

268. Missing contract details

Question: No cancellation rule is given. Can the pupil calculate a cancellation fee?

Worked answer: No. Missing rules prevent that calculation.

Common first error: Assuming imaginary penalties is not valid.

Reverse-check: Ask for written terms.

269. The question’s percentage base matters

Question: Plan total $600 vs cash $250. Total as % of cash?

Worked answer: 240%.

Common first error: Assuming every percentage must be under 100 is wrong for comparing different quantities.

Reverse-check: 600/250=2.4.

270. A deposit could be handled differently in contracts

Question: Can a maths solution assume an unstated deposit is refundable?

Worked answer: No. A specific real agreement would need terms; these examples treat deposits as paid within total.

Common first error: Assuming refund changes arithmetic.

Reverse-check: State whether refundable.

271. Monthly cost versus total fee

Question: Two offers with $20 and $30 monthly, missing lengths. Is the cheaper total known?

Worked answer: No. Counts of payments are missing.

Common first error: Smaller monthly does not determine full total.

Reverse-check: Give possible terms that reverse comparison.

272. Multiple payment schedules

Question: A fee $50 once plus two semiannual payments $100. Total?

Worked answer: $250.

Common first error: Calling them monthly changes frequency.

Reverse-check: 50+200=250.

273. Cash savings are not automatically profit

Question: Income $3000, known expenses $2500. Is $500 certain savings?

Worked answer: No. It is a limited residual before omitted needs.

Common first error: Incomplete budget doesn’t establish exact savings.

Reverse-check: Name assumptions.

274. Fictional amounts are not commercial quotes

Question: Are the article’s examples real deals?

Worked answer: No. They are invented G1 Mathematics problems.

Common first error: Treating a classroom payment as an offer misinforms.

Reverse-check: Check real sources separately.

275. A deposit changes the upfront burden

Question: Why might two equal-total plans feel different?

Worked answer: Their deposits and payment timing may differ.

Common first error: Full total alone does not describe the schedule.

Reverse-check: List upfront and repeated amounts.

276. One-time fees must appear once

Question: Deposit $50, 5 monthly $100, admin fee $20 once. Total?

Worked answer: $570.

Common first error: Multiplying admin fee by five is wrong.

Reverse-check: 50+500+20=570.

277. Student focus is interpretation, not real financing

Question: What should a learner explain after comparing schedules?

Worked answer: Which full total is lower under the stated amounts and which assumptions limit the comparison.

Common first error: Claims about real providers, credit eligibility or suitability exceed the classroom data.

Reverse-check: State conditional result.

278. A total overpayment may be negative in a fictional example

Question: Cash $800, plan $750. Is total difference negative?

Worked answer: Yes, −$50 plan-minus-cash.

Common first error: There is no rule that all imaginary instalment totals must exceed cash.

Reverse-check: 750−800=−50.

279. Count payments rather than visual calendar boxes

Question: A schedule has monthly payments from month 1 through month 12 inclusive. How many?

Worked answer: Twelve payments.

Common first error: Counting 11 gaps instead of 12 named months is wrong.

Reverse-check: List months 1–12.

280. Budget questions can use exact cents

Question: Monthly net $1200.50 and stated expense $300.25. Residual?

Worked answer: $900.25 before all other needs.

Common first error: Dropping cents prematurely changes exact sum.

Reverse-check: 1200.50−300.25=900.25.

281. The payee and payer roles differ

Question: Is ‘amount received’ always identical to ‘amount paid by buyer’ in an unstated financing model?

Worked answer: Not necessarily; fees and counterparties may change cash flows. State the perspective.

Common first error: Inventing a one-to-one transfer assumption may be misleading.

Reverse-check: Identify whose total is requested.

282. Compare actual unit of rate

Question: Monthly amount $25 per month, 12 months. What is the repeated total?

Worked answer: $300.

Common first error: Leaving rate at $25 without multiplying count misses duration.

Reverse-check: 25×12=300.

How a three-pupil Maths tutorial could teach full-cost thinking

The immutable eduKateSG Clementi three-pupil Mathematics reference describes 90-minute small-group lessons near Sixth Avenue MRT. One pupil might require multiplication of equal payments, another an equation for the missing monthly amount, and a third a comparison with different deposits and terms. The shared skill is naming the once-only and repeated parts correctly. The programme reference does not confirm an available Secondary 2 class or a guaranteed result.

10 minutes: identify deposit, per-period charge, number of periods and any one-time fee.
20 minutes: build a payment schedule as blocks and a one-variable equation.
25 minutes: solve full totals and reverse questions individually.
15 minutes: compare two fictional complete schedules.
10 minutes: spot one missing term or unjustified inference.
10 minutes: reverse-check the total and choose a short delayed retest.

Five manageable parent practice sessions

Day one: add one deposit to a multiplied number of monthly payments.
Day two: compare a plan’s full total against a supplied cash price.
Day three: find the unknown monthly payment from the complete sum.
Day four: compare two made-up terms, including one stated once-only fee.
Day five: explain why ‘lowest monthly payment’ and ‘lowest full cost’ do not mean the same thing.

Frequently asked questions

How do I find total paid?

Add the deposit once, every scheduled periodic payment and any other separately stated amount under the specified terms.

Is a lower monthly payment always cheaper?

No. The number of payments, deposit and fees can alter the full total.

How do I find an unknown monthly payment?

Subtract once-only charges from the complete stated total and divide by the number of equal payments.

Does overpaying the cash price tell us APR?

No. Annualised financing rates require more detailed cash-flow and financing assumptions.

Are these genuine offers or personal advice?

No. Every plan in this guide is fictional and used only for mathematical literacy.

Are instalments mentioned in G1 Mathematics?

The 2027 K110 graduating syllabus names instalments as a possible household-finance context. Current year-level teaching depends on the school.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

A sixty-second full-cost comparison
Once-only versus repeated amounts
What a total cannot tell you
Complete a deposit-plus-payments total
Compare cash price with full instalment cost
Recover the unknown monthly payment
Recover the unknown number of months
Compare two different payment plans
Make a household budget arithmetic check
Identify missing or misleading plan terms
A three-pupil tutorial
Questions and answers
Official references

Which option has the lower full total?

A deposit has a different time role from a monthly fee

Lower total and easier cash flow are different questions

282 original instalment cost and comparison clinics

Complete a deposit-plus-payments total

1. One deposit and 3 repeated payments · 1

Worked answer: The repeated subtotal is 3×$30.00=$90.00. Adding the deposit once gives $130.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $130.00−$40.00=$90.00, which exactly equals 3 payments of $30.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $30.00 were added without changing the deposit, the new full cost would be $160.00. The deposit should not be repeated.

2. One deposit and 4 repeated payments · 2

Worked answer: The repeated subtotal is 4×$140.00=$560.00. Adding the deposit once gives $740.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $740.00−$180.00=$560.00, which exactly equals 4 payments of $140.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $140.00 were added without changing the deposit, the new full cost would be $880.00. The deposit should not be repeated.

3. One deposit and 6 repeated payments · 3

Worked answer: The repeated subtotal is 6×$250.00=$1,500.00. Adding the deposit once gives $1,820.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,820.00−$320.00=$1,500.00, which exactly equals 6 payments of $250.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $250.00 were added without changing the deposit, the new full cost would be $2,070.00. The deposit should not be repeated.

4. One deposit and 8 repeated payments · 4

Worked answer: The repeated subtotal is 8×$360.00=$2,880.00. Adding the deposit once gives $3,340.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,340.00−$460.00=$2,880.00, which exactly equals 8 payments of $360.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $360.00 were added without changing the deposit, the new full cost would be $3,700.00. The deposit should not be repeated.

5. One deposit and 10 repeated payments · 5

Worked answer: The repeated subtotal is 10×$120.00=$1,200.00. Adding the deposit once gives $1,800.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,800.00−$600.00=$1,200.00, which exactly equals 10 payments of $120.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $120.00 were added without changing the deposit, the new full cost would be $1,920.00. The deposit should not be repeated.

6. One deposit and 12 repeated payments · 6

Worked answer: The repeated subtotal is 12×$230.00=$2,760.00. Adding the deposit once gives $2,900.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,900.00−$140.00=$2,760.00, which exactly equals 12 payments of $230.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $230.00 were added without changing the deposit, the new full cost would be $3,130.00. The deposit should not be repeated.

7. One deposit and 15 repeated payments · 7

Worked answer: The repeated subtotal is 15×$340.00=$5,100.00. Adding the deposit once gives $5,380.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $5,380.00−$280.00=$5,100.00, which exactly equals 15 payments of $340.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $340.00 were added without changing the deposit, the new full cost would be $5,720.00. The deposit should not be repeated.

8. One deposit and 18 repeated payments · 8

Worked answer: The repeated subtotal is 18×$100.00=$1,800.00. Adding the deposit once gives $2,220.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,220.00−$420.00=$1,800.00, which exactly equals 18 payments of $100.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $100.00 were added without changing the deposit, the new full cost would be $2,320.00. The deposit should not be repeated.

9. One deposit and 24 repeated payments · 9

Worked answer: The repeated subtotal is 24×$210.00=$5,040.00. Adding the deposit once gives $5,600.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $5,600.00−$560.00=$5,040.00, which exactly equals 24 payments of $210.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $210.00 were added without changing the deposit, the new full cost would be $5,810.00. The deposit should not be repeated.

10. One deposit and 3 repeated payments · 10

Worked answer: The repeated subtotal is 3×$320.00=$960.00. Adding the deposit once gives $1,060.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,060.00−$100.00=$960.00, which exactly equals 3 payments of $320.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $320.00 were added without changing the deposit, the new full cost would be $1,380.00. The deposit should not be repeated.

11. One deposit and 4 repeated payments · 11

Worked answer: The repeated subtotal is 4×$80.00=$320.00. Adding the deposit once gives $560.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $560.00−$240.00=$320.00, which exactly equals 4 payments of $80.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $80.00 were added without changing the deposit, the new full cost would be $640.00. The deposit should not be repeated.

12. One deposit and 6 repeated payments · 12

Worked answer: The repeated subtotal is 6×$190.00=$1,140.00. Adding the deposit once gives $1,520.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,520.00−$380.00=$1,140.00, which exactly equals 6 payments of $190.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $190.00 were added without changing the deposit, the new full cost would be $1,710.00. The deposit should not be repeated.

13. One deposit and 8 repeated payments · 13

Worked answer: The repeated subtotal is 8×$300.00=$2,400.00. Adding the deposit once gives $2,920.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,920.00−$520.00=$2,400.00, which exactly equals 8 payments of $300.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $300.00 were added without changing the deposit, the new full cost would be $3,220.00. The deposit should not be repeated.

14. One deposit and 10 repeated payments · 14

Worked answer: The repeated subtotal is 10×$60.00=$600.00. Adding the deposit once gives $660.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $660.00−$60.00=$600.00, which exactly equals 10 payments of $60.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $60.00 were added without changing the deposit, the new full cost would be $720.00. The deposit should not be repeated.

15. One deposit and 12 repeated payments · 15

Worked answer: The repeated subtotal is 12×$170.00=$2,040.00. Adding the deposit once gives $2,240.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,240.00−$200.00=$2,040.00, which exactly equals 12 payments of $170.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $170.00 were added without changing the deposit, the new full cost would be $2,410.00. The deposit should not be repeated.

16. One deposit and 15 repeated payments · 16

Worked answer: The repeated subtotal is 15×$280.00=$4,200.00. Adding the deposit once gives $4,540.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $4,540.00−$340.00=$4,200.00, which exactly equals 15 payments of $280.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $280.00 were added without changing the deposit, the new full cost would be $4,820.00. The deposit should not be repeated.

17. One deposit and 18 repeated payments · 17

Worked answer: The repeated subtotal is 18×$40.00=$720.00. Adding the deposit once gives $1,200.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,200.00−$480.00=$720.00, which exactly equals 18 payments of $40.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $40.00 were added without changing the deposit, the new full cost would be $1,240.00. The deposit should not be repeated.

18. One deposit and 24 repeated payments · 18

Worked answer: The repeated subtotal is 24×$150.00=$3,600.00. Adding the deposit once gives $4,220.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $4,220.00−$620.00=$3,600.00, which exactly equals 24 payments of $150.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $150.00 were added without changing the deposit, the new full cost would be $4,370.00. The deposit should not be repeated.

19. One deposit and 3 repeated payments · 19

Worked answer: The repeated subtotal is 3×$260.00=$780.00. Adding the deposit once gives $940.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $940.00−$160.00=$780.00, which exactly equals 3 payments of $260.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $260.00 were added without changing the deposit, the new full cost would be $1,200.00. The deposit should not be repeated.

20. One deposit and 4 repeated payments · 20

Worked answer: The repeated subtotal is 4×$370.00=$1,480.00. Adding the deposit once gives $1,780.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,780.00−$300.00=$1,480.00, which exactly equals 4 payments of $370.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $370.00 were added without changing the deposit, the new full cost would be $2,150.00. The deposit should not be repeated.

21. One deposit and 6 repeated payments · 21

Worked answer: The repeated subtotal is 6×$130.00=$780.00. Adding the deposit once gives $1,220.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,220.00−$440.00=$780.00, which exactly equals 6 payments of $130.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $130.00 were added without changing the deposit, the new full cost would be $1,350.00. The deposit should not be repeated.

22. One deposit and 8 repeated payments · 22

Worked answer: The repeated subtotal is 8×$240.00=$1,920.00. Adding the deposit once gives $2,500.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,500.00−$580.00=$1,920.00, which exactly equals 8 payments of $240.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $240.00 were added without changing the deposit, the new full cost would be $2,740.00. The deposit should not be repeated.

23. One deposit and 10 repeated payments · 23

Worked answer: The repeated subtotal is 10×$350.00=$3,500.00. Adding the deposit once gives $3,620.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,620.00−$120.00=$3,500.00, which exactly equals 10 payments of $350.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $350.00 were added without changing the deposit, the new full cost would be $3,970.00. The deposit should not be repeated.

24. One deposit and 12 repeated payments · 24

Worked answer: The repeated subtotal is 12×$110.00=$1,320.00. Adding the deposit once gives $1,580.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,580.00−$260.00=$1,320.00, which exactly equals 12 payments of $110.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $110.00 were added without changing the deposit, the new full cost would be $1,690.00. The deposit should not be repeated.

25. One deposit and 15 repeated payments · 25

Worked answer: The repeated subtotal is 15×$220.00=$3,300.00. Adding the deposit once gives $3,700.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,700.00−$400.00=$3,300.00, which exactly equals 15 payments of $220.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $220.00 were added without changing the deposit, the new full cost would be $3,920.00. The deposit should not be repeated.

26. One deposit and 18 repeated payments · 26

Worked answer: The repeated subtotal is 18×$330.00=$5,940.00. Adding the deposit once gives $6,480.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $6,480.00−$540.00=$5,940.00, which exactly equals 18 payments of $330.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $330.00 were added without changing the deposit, the new full cost would be $6,810.00. The deposit should not be repeated.

27. One deposit and 24 repeated payments · 27

Worked answer: The repeated subtotal is 24×$90.00=$2,160.00. Adding the deposit once gives $2,240.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,240.00−$80.00=$2,160.00, which exactly equals 24 payments of $90.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $90.00 were added without changing the deposit, the new full cost would be $2,330.00. The deposit should not be repeated.

28. One deposit and 3 repeated payments · 28

Worked answer: The repeated subtotal is 3×$200.00=$600.00. Adding the deposit once gives $820.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $820.00−$220.00=$600.00, which exactly equals 3 payments of $200.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $200.00 were added without changing the deposit, the new full cost would be $1,020.00. The deposit should not be repeated.

29. One deposit and 4 repeated payments · 29

Worked answer: The repeated subtotal is 4×$310.00=$1,240.00. Adding the deposit once gives $1,600.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,600.00−$360.00=$1,240.00, which exactly equals 4 payments of $310.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $310.00 were added without changing the deposit, the new full cost would be $1,910.00. The deposit should not be repeated.

30. One deposit and 6 repeated payments · 30

Worked answer: The repeated subtotal is 6×$70.00=$420.00. Adding the deposit once gives $920.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $920.00−$500.00=$420.00, which exactly equals 6 payments of $70.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $70.00 were added without changing the deposit, the new full cost would be $990.00. The deposit should not be repeated.

31. One deposit and 8 repeated payments · 31

Worked answer: The repeated subtotal is 8×$180.00=$1,440.00. Adding the deposit once gives $1,480.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,480.00−$40.00=$1,440.00, which exactly equals 8 payments of $180.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $180.00 were added without changing the deposit, the new full cost would be $1,660.00. The deposit should not be repeated.

32. One deposit and 10 repeated payments · 32

Worked answer: The repeated subtotal is 10×$290.00=$2,900.00. Adding the deposit once gives $3,080.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,080.00−$180.00=$2,900.00, which exactly equals 10 payments of $290.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $290.00 were added without changing the deposit, the new full cost would be $3,370.00. The deposit should not be repeated.

33. One deposit and 12 repeated payments · 33

Worked answer: The repeated subtotal is 12×$50.00=$600.00. Adding the deposit once gives $920.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $920.00−$320.00=$600.00, which exactly equals 12 payments of $50.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $50.00 were added without changing the deposit, the new full cost would be $970.00. The deposit should not be repeated.

34. One deposit and 15 repeated payments · 34

Worked answer: The repeated subtotal is 15×$160.00=$2,400.00. Adding the deposit once gives $2,860.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,860.00−$460.00=$2,400.00, which exactly equals 15 payments of $160.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $160.00 were added without changing the deposit, the new full cost would be $3,020.00. The deposit should not be repeated.

35. One deposit and 18 repeated payments · 35

Worked answer: The repeated subtotal is 18×$270.00=$4,860.00. Adding the deposit once gives $5,460.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $5,460.00−$600.00=$4,860.00, which exactly equals 18 payments of $270.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $270.00 were added without changing the deposit, the new full cost would be $5,730.00. The deposit should not be repeated.

36. One deposit and 24 repeated payments · 36

Worked answer: The repeated subtotal is 24×$30.00=$720.00. Adding the deposit once gives $860.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $860.00−$140.00=$720.00, which exactly equals 24 payments of $30.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $30.00 were added without changing the deposit, the new full cost would be $890.00. The deposit should not be repeated.

37. One deposit and 3 repeated payments · 37

Worked answer: The repeated subtotal is 3×$140.00=$420.00. Adding the deposit once gives $700.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $700.00−$280.00=$420.00, which exactly equals 3 payments of $140.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $140.00 were added without changing the deposit, the new full cost would be $840.00. The deposit should not be repeated.

38. One deposit and 4 repeated payments · 38

Worked answer: The repeated subtotal is 4×$250.00=$1,000.00. Adding the deposit once gives $1,420.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,420.00−$420.00=$1,000.00, which exactly equals 4 payments of $250.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $250.00 were added without changing the deposit, the new full cost would be $1,670.00. The deposit should not be repeated.

39. One deposit and 6 repeated payments · 39

Worked answer: The repeated subtotal is 6×$360.00=$2,160.00. Adding the deposit once gives $2,720.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,720.00−$560.00=$2,160.00, which exactly equals 6 payments of $360.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $360.00 were added without changing the deposit, the new full cost would be $3,080.00. The deposit should not be repeated.

40. One deposit and 8 repeated payments · 40

Worked answer: The repeated subtotal is 8×$120.00=$960.00. Adding the deposit once gives $1,060.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,060.00−$100.00=$960.00, which exactly equals 8 payments of $120.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $120.00 were added without changing the deposit, the new full cost would be $1,180.00. The deposit should not be repeated.

Compare cash price with full instalment cost

41. Cash price versus complete plan · 1

Reverse-check: Check $1,150.00−$1,200.00=−$50.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,170.00, so the cash comparison changes by twenty dollars.

42. Cash price versus complete plan · 2

Reverse-check: Check $2,200.00−$1,900.00=+$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,220.00, so the cash comparison changes by twenty dollars.

43. Cash price versus complete plan · 3

Reverse-check: Check $3,150.00−$2,600.00=+$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,170.00, so the cash comparison changes by twenty dollars.

44. Cash price versus complete plan · 4

Reverse-check: Check $3,550.00−$3,300.00=+$250.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,570.00, so the cash comparison changes by twenty dollars.

45. Cash price versus complete plan · 5

Reverse-check: Check $2,200.00−$1,700.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,220.00, so the cash comparison changes by twenty dollars.

46. Cash price versus complete plan · 6

Reverse-check: Check $2,600.05−$2,400.00=+$200.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,620.05, so the cash comparison changes by twenty dollars.

47. Cash price versus complete plan · 7

Reverse-check: Check $2,650.04−$3,100.00=−$449.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,670.04, so the cash comparison changes by twenty dollars.

48. Cash price versus complete plan · 8

Reverse-check: Check $1,650.08−$1,500.00=+$150.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,670.08, so the cash comparison changes by twenty dollars.

49. Cash price versus complete plan · 9

Reverse-check: Check $2,600.00−$2,200.00=+$400.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,620.00, so the cash comparison changes by twenty dollars.

50. Cash price versus complete plan · 10

Reverse-check: Check $3,000.02−$2,900.00=+$100.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,020.02, so the cash comparison changes by twenty dollars.

51. Cash price versus complete plan · 11

Reverse-check: Check $1,650.00−$1,300.00=+$350.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,670.00, so the cash comparison changes by twenty dollars.

52. Cash price versus complete plan · 12

Worked answer: The full plan total is $60.00+10×$199.00=$2,050.00. The difference total minus cash is +$50.00; under these hypothetical figures, the plan costs $50.00 more than cash.

Reverse-check: Check $2,050.00−$2,000.00=+$50.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.00, so the cash comparison changes by twenty dollars.

53. Cash price versus complete plan · 13

Reverse-check: Check $2,400.00−$2,700.00=−$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,420.00, so the cash comparison changes by twenty dollars.

54. Cash price versus complete plan · 14

Reverse-check: Check $3,949.95−$3,400.00=+$549.95. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,969.95, so the cash comparison changes by twenty dollars.

55. Cash price versus complete plan · 15

Reverse-check: Check $2,050.08−$1,800.00=+$250.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.08, so the cash comparison changes by twenty dollars.

56. Cash price versus complete plan · 16

Reverse-check: Check $3,000.00−$2,500.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,020.00, so the cash comparison changes by twenty dollars.

57. Cash price versus complete plan · 17

Reverse-check: Check $3,400.00−$3,200.00=+$200.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,420.00, so the cash comparison changes by twenty dollars.

58. Cash price versus complete plan · 18

Reverse-check: Check $2,050.00−$1,600.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.00, so the cash comparison changes by twenty dollars.

59. Cash price versus complete plan · 19

Reverse-check: Check $2,150.00−$2,300.00=−$150.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,170.00, so the cash comparison changes by twenty dollars.

60. Cash price versus complete plan · 20

Reverse-check: Check $3,400.00−$3,000.00=+$400.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,420.00, so the cash comparison changes by twenty dollars.

61. Cash price versus complete plan · 21

Reverse-check: Check $1,500.04−$1,400.00=+$100.04. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,520.04, so the cash comparison changes by twenty dollars.

62. Cash price versus complete plan · 22

Reverse-check: Check $2,450.05−$2,100.00=+$350.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,470.05, so the cash comparison changes by twenty dollars.

63. Cash price versus complete plan · 23

Worked answer: The full plan total is $80.00+18×$153.89=$2,850.02. The difference total minus cash is +$50.02; under these hypothetical figures, the plan costs $50.02 more than cash.

Reverse-check: Check $2,850.02−$2,800.00=+$50.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.02, so the cash comparison changes by twenty dollars.

64. Cash price versus complete plan · 24

Reverse-check: Check $1,500.08−$1,200.00=+$300.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,520.08, so the cash comparison changes by twenty dollars.

65. Cash price versus complete plan · 25

Reverse-check: Check $1,350.00−$1,900.00=−$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,370.00, so the cash comparison changes by twenty dollars.

66. Cash price versus complete plan · 26

Reverse-check: Check $2,850.02−$2,600.00=+$250.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.02, so the cash comparison changes by twenty dollars.

67. Cash price versus complete plan · 27

Reverse-check: Check $3,800.00−$3,300.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,820.00, so the cash comparison changes by twenty dollars.

68. Cash price versus complete plan · 28

Reverse-check: Check $1,900.00−$1,700.00=+$200.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,920.00, so the cash comparison changes by twenty dollars.

69. Cash price versus complete plan · 29

Reverse-check: Check $2,850.00−$2,400.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.00, so the cash comparison changes by twenty dollars.

70. Cash price versus complete plan · 30

Reverse-check: Check $3,250.05−$3,100.00=+$150.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.05, so the cash comparison changes by twenty dollars.

71. Cash price versus complete plan · 31

Reverse-check: Check $1,100.04−$1,500.00=−$399.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,120.04, so the cash comparison changes by twenty dollars.

72. Cash price versus complete plan · 32

Worked answer: The full plan total is $300.00+24×$83.33=$2,299.92. The difference total minus cash is +$99.92; under these hypothetical figures, the plan costs $99.92 more than cash.

Reverse-check: Check $2,299.92−$2,200.00=+$99.92. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,319.92, so the cash comparison changes by twenty dollars.

73. Cash price versus complete plan · 33

Reverse-check: Check $3,250.00−$2,900.00=+$350.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.00, so the cash comparison changes by twenty dollars.

74. Cash price versus complete plan · 34

Worked answer: The full plan total is $100.00+6×$208.33=$1,349.98. The difference total minus cash is +$49.98; under these hypothetical figures, the plan costs $49.98 more than cash.

Reverse-check: Check $1,349.98−$1,300.00=+$49.98. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,369.98, so the cash comparison changes by twenty dollars.

75. Cash price versus complete plan · 35

Reverse-check: Check $2,300.00−$2,000.00=+$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,320.00, so the cash comparison changes by twenty dollars.

76. Cash price versus complete plan · 36

Reverse-check: Check $3,250.00−$2,700.00=+$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.00, so the cash comparison changes by twenty dollars.

77. Cash price versus complete plan · 37

Reverse-check: Check $3,150.04−$3,400.00=−$249.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,170.04, so the cash comparison changes by twenty dollars.

78. Cash price versus complete plan · 38

Reverse-check: Check $2,300.05−$1,800.00=+$500.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,320.05, so the cash comparison changes by twenty dollars.

79. Cash price versus complete plan · 39

Reverse-check: Check $2,700.08−$2,500.00=+$200.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,720.08, so the cash comparison changes by twenty dollars.

80. Cash price versus complete plan · 40

Reverse-check: Check $3,650.00−$3,200.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,670.00, so the cash comparison changes by twenty dollars.

81. Find monthly payment from stated total · 1

Worked answer: Write $50.00+3m=$140.00. Then 3m=$90.00, so m=$30.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $140.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $30.00 by 3, obtaining $90.00; add deposit $50.00 to restore the precise stated total $140.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $40.00.

82. Find monthly payment from stated total · 2

Worked answer: Write $125.00+4m=$445.00. Then 4m=$320.00, so m=$80.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $445.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $80.00 by 4, obtaining $320.00; add deposit $125.00 to restore the precise stated total $445.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $90.00.

83. Find monthly payment from stated total · 3

Worked answer: Write $200.00+6m=$980.00. Then 6m=$780.00, so m=$130.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $980.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $130.00 by 6, obtaining $780.00; add deposit $200.00 to restore the precise stated total $980.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $140.00.

84. Find monthly payment from stated total · 4

Worked answer: Write $275.00+8m=$1,715.00. Then 8m=$1,440.00, so m=$180.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,715.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $180.00 by 8, obtaining $1,440.00; add deposit $275.00 to restore the precise stated total $1,715.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $190.00.

85. Find monthly payment from stated total · 5

Worked answer: Write $350.00+10m=$2,650.00. Then 10m=$2,300.00, so m=$230.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,650.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $230.00 by 10, obtaining $2,300.00; add deposit $350.00 to restore the precise stated total $2,650.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $240.00.

86. Find monthly payment from stated total · 6

Worked answer: Write $425.00+12m=$3,785.00. Then 12m=$3,360.00, so m=$280.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,785.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $280.00 by 12, obtaining $3,360.00; add deposit $425.00 to restore the precise stated total $3,785.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $290.00.

87. Find monthly payment from stated total · 7

Worked answer: Write $500.00+15m=$5,450.00. Then 15m=$4,950.00, so m=$330.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $5,450.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $330.00 by 15, obtaining $4,950.00; add deposit $500.00 to restore the precise stated total $5,450.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $340.00.

88. Find monthly payment from stated total · 8

Worked answer: Write $575.00+18m=$1,655.00. Then 18m=$1,080.00, so m=$60.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,655.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $60.00 by 18, obtaining $1,080.00; add deposit $575.00 to restore the precise stated total $1,655.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $70.00.

89. Find monthly payment from stated total · 9

Worked answer: Write $100.00+24m=$2,740.00. Then 24m=$2,640.00, so m=$110.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,740.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $110.00 by 24, obtaining $2,640.00; add deposit $100.00 to restore the precise stated total $2,740.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $120.00.

90. Find monthly payment from stated total · 10

Worked answer: Write $175.00+3m=$655.00. Then 3m=$480.00, so m=$160.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $655.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $160.00 by 3, obtaining $480.00; add deposit $175.00 to restore the precise stated total $655.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $170.00.

91. Find monthly payment from stated total · 11

Worked answer: Write $250.00+4m=$1,090.00. Then 4m=$840.00, so m=$210.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,090.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $210.00 by 4, obtaining $840.00; add deposit $250.00 to restore the precise stated total $1,090.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $220.00.

92. Find monthly payment from stated total · 12

Worked answer: Write $325.00+6m=$1,885.00. Then 6m=$1,560.00, so m=$260.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,885.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $260.00 by 6, obtaining $1,560.00; add deposit $325.00 to restore the precise stated total $1,885.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $270.00.

93. Find monthly payment from stated total · 13

Worked answer: Write $400.00+8m=$2,880.00. Then 8m=$2,480.00, so m=$310.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,880.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $310.00 by 8, obtaining $2,480.00; add deposit $400.00 to restore the precise stated total $2,880.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $320.00.

94. Find monthly payment from stated total · 14

Worked answer: Write $475.00+10m=$875.00. Then 10m=$400.00, so m=$40.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $875.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $40.00 by 10, obtaining $400.00; add deposit $475.00 to restore the precise stated total $875.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $50.00.

95. Find monthly payment from stated total · 15

Worked answer: Write $550.00+12m=$1,630.00. Then 12m=$1,080.00, so m=$90.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,630.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $90.00 by 12, obtaining $1,080.00; add deposit $550.00 to restore the precise stated total $1,630.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $100.00.

96. Find monthly payment from stated total · 16

Worked answer: Write $75.00+15m=$2,175.00. Then 15m=$2,100.00, so m=$140.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,175.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $140.00 by 15, obtaining $2,100.00; add deposit $75.00 to restore the precise stated total $2,175.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $150.00.

97. Find monthly payment from stated total · 17

Worked answer: Write $150.00+18m=$3,570.00. Then 18m=$3,420.00, so m=$190.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,570.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $190.00 by 18, obtaining $3,420.00; add deposit $150.00 to restore the precise stated total $3,570.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $200.00.

98. Find monthly payment from stated total · 18

Worked answer: Write $225.00+24m=$5,985.00. Then 24m=$5,760.00, so m=$240.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $5,985.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $240.00 by 24, obtaining $5,760.00; add deposit $225.00 to restore the precise stated total $5,985.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $250.00.

99. Find monthly payment from stated total · 19

Worked answer: Write $300.00+3m=$1,170.00. Then 3m=$870.00, so m=$290.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,170.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $290.00 by 3, obtaining $870.00; add deposit $300.00 to restore the precise stated total $1,170.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $300.00.

100. Find monthly payment from stated total · 20

Worked answer: Write $375.00+4m=$1,735.00. Then 4m=$1,360.00, so m=$340.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,735.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $340.00 by 4, obtaining $1,360.00; add deposit $375.00 to restore the precise stated total $1,735.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $350.00.

101. Find monthly payment from stated total · 21

Worked answer: Write $450.00+6m=$870.00. Then 6m=$420.00, so m=$70.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $870.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $70.00 by 6, obtaining $420.00; add deposit $450.00 to restore the precise stated total $870.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $80.00.

102. Find monthly payment from stated total · 22

Worked answer: Write $525.00+8m=$1,485.00. Then 8m=$960.00, so m=$120.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,485.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $120.00 by 8, obtaining $960.00; add deposit $525.00 to restore the precise stated total $1,485.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $130.00.

103. Find monthly payment from stated total · 23

Worked answer: Write $50.00+10m=$1,750.00. Then 10m=$1,700.00, so m=$170.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,750.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $170.00 by 10, obtaining $1,700.00; add deposit $50.00 to restore the precise stated total $1,750.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $180.00.

104. Find monthly payment from stated total · 24

Worked answer: Write $125.00+12m=$2,765.00. Then 12m=$2,640.00, so m=$220.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,765.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $220.00 by 12, obtaining $2,640.00; add deposit $125.00 to restore the precise stated total $2,765.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $230.00.

105. Find monthly payment from stated total · 25

Worked answer: Write $200.00+15m=$4,250.00. Then 15m=$4,050.00, so m=$270.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $4,250.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $270.00 by 15, obtaining $4,050.00; add deposit $200.00 to restore the precise stated total $4,250.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $280.00.

106. Find monthly payment from stated total · 26

Worked answer: Write $275.00+18m=$6,035.00. Then 18m=$5,760.00, so m=$320.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $6,035.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $320.00 by 18, obtaining $5,760.00; add deposit $275.00 to restore the precise stated total $6,035.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $330.00.

107. Find monthly payment from stated total · 27

Worked answer: Write $350.00+24m=$1,550.00. Then 24m=$1,200.00, so m=$50.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,550.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $50.00 by 24, obtaining $1,200.00; add deposit $350.00 to restore the precise stated total $1,550.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $60.00.

108. Find monthly payment from stated total · 28

Worked answer: Write $425.00+3m=$725.00. Then 3m=$300.00, so m=$100.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $725.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $100.00 by 3, obtaining $300.00; add deposit $425.00 to restore the precise stated total $725.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $110.00.

109. Find monthly payment from stated total · 29

Worked answer: Write $500.00+4m=$1,100.00. Then 4m=$600.00, so m=$150.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,100.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $150.00 by 4, obtaining $600.00; add deposit $500.00 to restore the precise stated total $1,100.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $160.00.

110. Find monthly payment from stated total · 30

Worked answer: Write $575.00+6m=$1,775.00. Then 6m=$1,200.00, so m=$200.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,775.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $200.00 by 6, obtaining $1,200.00; add deposit $575.00 to restore the precise stated total $1,775.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $210.00.

111. Find monthly payment from stated total · 31

Worked answer: Write $100.00+8m=$2,100.00. Then 8m=$2,000.00, so m=$250.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,100.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $250.00 by 8, obtaining $2,000.00; add deposit $100.00 to restore the precise stated total $2,100.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $260.00.

112. Find monthly payment from stated total · 32

Worked answer: Write $175.00+10m=$3,175.00. Then 10m=$3,000.00, so m=$300.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,175.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $300.00 by 10, obtaining $3,000.00; add deposit $175.00 to restore the precise stated total $3,175.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $310.00.

113. Find monthly payment from stated total · 33

Worked answer: Write $250.00+12m=$610.00. Then 12m=$360.00, so m=$30.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $610.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $30.00 by 12, obtaining $360.00; add deposit $250.00 to restore the precise stated total $610.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $40.00.

114. Find monthly payment from stated total · 34

Worked answer: Write $325.00+15m=$1,525.00. Then 15m=$1,200.00, so m=$80.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,525.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $80.00 by 15, obtaining $1,200.00; add deposit $325.00 to restore the precise stated total $1,525.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $90.00.

115. Find monthly payment from stated total · 35

Worked answer: Write $400.00+18m=$2,740.00. Then 18m=$2,340.00, so m=$130.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,740.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $130.00 by 18, obtaining $2,340.00; add deposit $400.00 to restore the precise stated total $2,740.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $140.00.

116. Find monthly payment from stated total · 36

Worked answer: Write $475.00+24m=$4,795.00. Then 24m=$4,320.00, so m=$180.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $4,795.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $180.00 by 24, obtaining $4,320.00; add deposit $475.00 to restore the precise stated total $4,795.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $190.00.

117. Find monthly payment from stated total · 37

Worked answer: Write $550.00+3m=$1,240.00. Then 3m=$690.00, so m=$230.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,240.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $230.00 by 3, obtaining $690.00; add deposit $550.00 to restore the precise stated total $1,240.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $240.00.

Recover the unknown number of months

118. Find how many instalments are stated · 1

Question: The fictional full plan total is $145.00, with a deposit of $40.00 and equal payments of $35.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($145.00−$40.00)/$35.00 = $105.00/$35.00=3 payments. The amount $105.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$35.00+$40.00=$145.00. The terms and units are consistent.

Change one condition: If another payment of $35.00 were included, the full total would rise to $180.00 and the count become 4.

119. Find how many instalments are stated · 2

Question: The fictional full plan total is $380.00, with a deposit of $100.00 and equal payments of $70.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($380.00−$100.00)/$70.00 = $280.00/$70.00=4 payments. The amount $280.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$70.00+$100.00=$380.00. The terms and units are consistent.

Change one condition: If another payment of $70.00 were included, the full total would rise to $450.00 and the count become 5.

120. Find how many instalments are stated · 3

Question: The fictional full plan total is $790.00, with a deposit of $160.00 and equal payments of $105.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($790.00−$160.00)/$105.00 = $630.00/$105.00=6 payments. The amount $630.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$105.00+$160.00=$790.00. The terms and units are consistent.

Change one condition: If another payment of $105.00 were included, the full total would rise to $895.00 and the count become 7.

121. Find how many instalments are stated · 4

Question: The fictional full plan total is $1,340.00, with a deposit of $220.00 and equal payments of $140.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,340.00−$220.00)/$140.00 = $1,120.00/$140.00=8 payments. The amount $1,120.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$140.00+$220.00=$1,340.00. The terms and units are consistent.

Change one condition: If another payment of $140.00 were included, the full total would rise to $1,480.00 and the count become 9.

122. Find how many instalments are stated · 5

Question: The fictional full plan total is $775.00, with a deposit of $280.00 and equal payments of $55.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($775.00−$280.00)/$55.00 = $495.00/$55.00=9 payments. The amount $495.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$55.00+$280.00=$775.00. The terms and units are consistent.

Change one condition: If another payment of $55.00 were included, the full total would rise to $830.00 and the count become 10.

123. Find how many instalments are stated · 6

Question: The fictional full plan total is $1,240.00, with a deposit of $340.00 and equal payments of $90.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,240.00−$340.00)/$90.00 = $900.00/$90.00=10 payments. The amount $900.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$90.00+$340.00=$1,240.00. The terms and units are consistent.

Change one condition: If another payment of $90.00 were included, the full total would rise to $1,330.00 and the count become 11.

124. Find how many instalments are stated · 7

Question: The fictional full plan total is $1,900.00, with a deposit of $400.00 and equal payments of $125.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,900.00−$400.00)/$125.00 = $1,500.00/$125.00=12 payments. The amount $1,500.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$125.00+$400.00=$1,900.00. The terms and units are consistent.

Change one condition: If another payment of $125.00 were included, the full total would rise to $2,025.00 and the count become 13.

125. Find how many instalments are stated · 8

Question: The fictional full plan total is $1,060.00, with a deposit of $460.00 and equal payments of $40.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,060.00−$460.00)/$40.00 = $600.00/$40.00=15 payments. The amount $600.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$40.00+$460.00=$1,060.00. The terms and units are consistent.

Change one condition: If another payment of $40.00 were included, the full total would rise to $1,100.00 and the count become 16.

126. Find how many instalments are stated · 9

Question: The fictional full plan total is $1,410.00, with a deposit of $60.00 and equal payments of $75.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,410.00−$60.00)/$75.00 = $1,350.00/$75.00=18 payments. The amount $1,350.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$75.00+$60.00=$1,410.00. The terms and units are consistent.

Change one condition: If another payment of $75.00 were included, the full total would rise to $1,485.00 and the count become 19.

127. Find how many instalments are stated · 10

Question: The fictional full plan total is $2,320.00, with a deposit of $120.00 and equal payments of $110.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,320.00−$120.00)/$110.00 = $2,200.00/$110.00=20 payments. The amount $2,200.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$110.00+$120.00=$2,320.00. The terms and units are consistent.

Change one condition: If another payment of $110.00 were included, the full total would rise to $2,430.00 and the count become 21.

128. Find how many instalments are stated · 11

Question: The fictional full plan total is $3,660.00, with a deposit of $180.00 and equal payments of $145.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($3,660.00−$180.00)/$145.00 = $3,480.00/$145.00=24 payments. The amount $3,480.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$145.00+$180.00=$3,660.00. The terms and units are consistent.

Change one condition: If another payment of $145.00 were included, the full total would rise to $3,805.00 and the count become 25.

129. Find how many instalments are stated · 12

Question: The fictional full plan total is $420.00, with a deposit of $240.00 and equal payments of $60.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($420.00−$240.00)/$60.00 = $180.00/$60.00=3 payments. The amount $180.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$60.00+$240.00=$420.00. The terms and units are consistent.

Change one condition: If another payment of $60.00 were included, the full total would rise to $480.00 and the count become 4.

130. Find how many instalments are stated · 13

Question: The fictional full plan total is $680.00, with a deposit of $300.00 and equal payments of $95.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($680.00−$300.00)/$95.00 = $380.00/$95.00=4 payments. The amount $380.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$95.00+$300.00=$680.00. The terms and units are consistent.

Change one condition: If another payment of $95.00 were included, the full total would rise to $775.00 and the count become 5.

131. Find how many instalments are stated · 14

Question: The fictional full plan total is $1,140.00, with a deposit of $360.00 and equal payments of $130.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,140.00−$360.00)/$130.00 = $780.00/$130.00=6 payments. The amount $780.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$130.00+$360.00=$1,140.00. The terms and units are consistent.

Change one condition: If another payment of $130.00 were included, the full total would rise to $1,270.00 and the count become 7.

132. Find how many instalments are stated · 15

Question: The fictional full plan total is $780.00, with a deposit of $420.00 and equal payments of $45.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($780.00−$420.00)/$45.00 = $360.00/$45.00=8 payments. The amount $360.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$45.00+$420.00=$780.00. The terms and units are consistent.

Change one condition: If another payment of $45.00 were included, the full total would rise to $825.00 and the count become 9.

133. Find how many instalments are stated · 16

Question: The fictional full plan total is $1,200.00, with a deposit of $480.00 and equal payments of $80.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,200.00−$480.00)/$80.00 = $720.00/$80.00=9 payments. The amount $720.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$80.00+$480.00=$1,200.00. The terms and units are consistent.

Change one condition: If another payment of $80.00 were included, the full total would rise to $1,280.00 and the count become 10.

134. Find how many instalments are stated · 17

Question: The fictional full plan total is $1,230.00, with a deposit of $80.00 and equal payments of $115.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,230.00−$80.00)/$115.00 = $1,150.00/$115.00=10 payments. The amount $1,150.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$115.00+$80.00=$1,230.00. The terms and units are consistent.

Change one condition: If another payment of $115.00 were included, the full total would rise to $1,345.00 and the count become 11.

135. Find how many instalments are stated · 18

Question: The fictional full plan total is $1,940.00, with a deposit of $140.00 and equal payments of $150.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,940.00−$140.00)/$150.00 = $1,800.00/$150.00=12 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$150.00+$140.00=$1,940.00. The terms and units are consistent.

Change one condition: If another payment of $150.00 were included, the full total would rise to $2,090.00 and the count become 13.

136. Find how many instalments are stated · 19

Question: The fictional full plan total is $1,175.00, with a deposit of $200.00 and equal payments of $65.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,175.00−$200.00)/$65.00 = $975.00/$65.00=15 payments. The amount $975.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$65.00+$200.00=$1,175.00. The terms and units are consistent.

Change one condition: If another payment of $65.00 were included, the full total would rise to $1,240.00 and the count become 16.

137. Find how many instalments are stated · 20

Question: The fictional full plan total is $2,060.00, with a deposit of $260.00 and equal payments of $100.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,060.00−$260.00)/$100.00 = $1,800.00/$100.00=18 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$100.00+$260.00=$2,060.00. The terms and units are consistent.

Change one condition: If another payment of $100.00 were included, the full total would rise to $2,160.00 and the count become 19.

138. Find how many instalments are stated · 21

Question: The fictional full plan total is $3,020.00, with a deposit of $320.00 and equal payments of $135.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($3,020.00−$320.00)/$135.00 = $2,700.00/$135.00=20 payments. The amount $2,700.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$135.00+$320.00=$3,020.00. The terms and units are consistent.

Change one condition: If another payment of $135.00 were included, the full total would rise to $3,155.00 and the count become 21.

139. Find how many instalments are stated · 22

Question: The fictional full plan total is $1,580.00, with a deposit of $380.00 and equal payments of $50.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,580.00−$380.00)/$50.00 = $1,200.00/$50.00=24 payments. The amount $1,200.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$50.00+$380.00=$1,580.00. The terms and units are consistent.

Change one condition: If another payment of $50.00 were included, the full total would rise to $1,630.00 and the count become 25.

140. Find how many instalments are stated · 23

Question: The fictional full plan total is $695.00, with a deposit of $440.00 and equal payments of $85.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($695.00−$440.00)/$85.00 = $255.00/$85.00=3 payments. The amount $255.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$85.00+$440.00=$695.00. The terms and units are consistent.

Change one condition: If another payment of $85.00 were included, the full total would rise to $780.00 and the count become 4.

141. Find how many instalments are stated · 24

Question: The fictional full plan total is $520.00, with a deposit of $40.00 and equal payments of $120.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($520.00−$40.00)/$120.00 = $480.00/$120.00=4 payments. The amount $480.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$120.00+$40.00=$520.00. The terms and units are consistent.

Change one condition: If another payment of $120.00 were included, the full total would rise to $640.00 and the count become 5.

142. Find how many instalments are stated · 25

Question: The fictional full plan total is $310.00, with a deposit of $100.00 and equal payments of $35.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($310.00−$100.00)/$35.00 = $210.00/$35.00=6 payments. The amount $210.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$35.00+$100.00=$310.00. The terms and units are consistent.

Change one condition: If another payment of $35.00 were included, the full total would rise to $345.00 and the count become 7.

143. Find how many instalments are stated · 26

Question: The fictional full plan total is $720.00, with a deposit of $160.00 and equal payments of $70.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($720.00−$160.00)/$70.00 = $560.00/$70.00=8 payments. The amount $560.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$70.00+$160.00=$720.00. The terms and units are consistent.

Change one condition: If another payment of $70.00 were included, the full total would rise to $790.00 and the count become 9.

144. Find how many instalments are stated · 27

Question: The fictional full plan total is $1,165.00, with a deposit of $220.00 and equal payments of $105.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,165.00−$220.00)/$105.00 = $945.00/$105.00=9 payments. The amount $945.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$105.00+$220.00=$1,165.00. The terms and units are consistent.

Change one condition: If another payment of $105.00 were included, the full total would rise to $1,270.00 and the count become 10.

145. Find how many instalments are stated · 28

Question: The fictional full plan total is $1,680.00, with a deposit of $280.00 and equal payments of $140.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,680.00−$280.00)/$140.00 = $1,400.00/$140.00=10 payments. The amount $1,400.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$140.00+$280.00=$1,680.00. The terms and units are consistent.

Change one condition: If another payment of $140.00 were included, the full total would rise to $1,820.00 and the count become 11.

146. Find how many instalments are stated · 29

Question: The fictional full plan total is $1,000.00, with a deposit of $340.00 and equal payments of $55.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,000.00−$340.00)/$55.00 = $660.00/$55.00=12 payments. The amount $660.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$55.00+$340.00=$1,000.00. The terms and units are consistent.

Change one condition: If another payment of $55.00 were included, the full total would rise to $1,055.00 and the count become 13.

147. Find how many instalments are stated · 30

Question: The fictional full plan total is $1,750.00, with a deposit of $400.00 and equal payments of $90.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,750.00−$400.00)/$90.00 = $1,350.00/$90.00=15 payments. The amount $1,350.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$90.00+$400.00=$1,750.00. The terms and units are consistent.

Change one condition: If another payment of $90.00 were included, the full total would rise to $1,840.00 and the count become 16.

148. Find how many instalments are stated · 31

Question: The fictional full plan total is $2,710.00, with a deposit of $460.00 and equal payments of $125.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,710.00−$460.00)/$125.00 = $2,250.00/$125.00=18 payments. The amount $2,250.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$125.00+$460.00=$2,710.00. The terms and units are consistent.

Change one condition: If another payment of $125.00 were included, the full total would rise to $2,835.00 and the count become 19.

149. Find how many instalments are stated · 32

Question: The fictional full plan total is $860.00, with a deposit of $60.00 and equal payments of $40.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($860.00−$60.00)/$40.00 = $800.00/$40.00=20 payments. The amount $800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$40.00+$60.00=$860.00. The terms and units are consistent.

Change one condition: If another payment of $40.00 were included, the full total would rise to $900.00 and the count become 21.

150. Find how many instalments are stated · 33

Question: The fictional full plan total is $1,920.00, with a deposit of $120.00 and equal payments of $75.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,920.00−$120.00)/$75.00 = $1,800.00/$75.00=24 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$75.00+$120.00=$1,920.00. The terms and units are consistent.

Change one condition: If another payment of $75.00 were included, the full total would rise to $1,995.00 and the count become 25.

151. Find how many instalments are stated · 34

Question: The fictional full plan total is $510.00, with a deposit of $180.00 and equal payments of $110.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($510.00−$180.00)/$110.00 = $330.00/$110.00=3 payments. The amount $330.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$110.00+$180.00=$510.00. The terms and units are consistent.

Change one condition: If another payment of $110.00 were included, the full total would rise to $620.00 and the count become 4.

152. Find how many instalments are stated · 35

Question: The fictional full plan total is $820.00, with a deposit of $240.00 and equal payments of $145.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($820.00−$240.00)/$145.00 = $580.00/$145.00=4 payments. The amount $580.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$145.00+$240.00=$820.00. The terms and units are consistent.

Change one condition: If another payment of $145.00 were included, the full total would rise to $965.00 and the count become 5.

153. Find how many instalments are stated · 36

Question: The fictional full plan total is $660.00, with a deposit of $300.00 and equal payments of $60.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($660.00−$300.00)/$60.00 = $360.00/$60.00=6 payments. The amount $360.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$60.00+$300.00=$660.00. The terms and units are consistent.

Change one condition: If another payment of $60.00 were included, the full total would rise to $720.00 and the count become 7.

Compare two different payment plans

154. Compare deposits, terms and stated fees · 1

Worked answer: Plan A =$20.00+4×$30.00+$0.00=$140.00. Plan B =$10.00+6×$30.00+$0.00=$190.00. Plan A is lower by $50.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $50.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $160.00; recompute which full total is lower.

155. Compare deposits, terms and stated fees · 2

Worked answer: Plan A =$50.00+6×$65.00+$10.00=$450.00. Plan B =$60.00+9×$85.00+$20.00=$845.00. Plan A is lower by $395.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $395.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $470.00; recompute which full total is lower.

156. Compare deposits, terms and stated fees · 3

Worked answer: Plan A =$80.00+8×$100.00+$20.00=$900.00. Plan B =$110.00+12×$140.00+$40.00=$1,830.00. Plan A is lower by $930.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $930.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $920.00; recompute which full total is lower.

157. Compare deposits, terms and stated fees · 4

Worked answer: Plan A =$110.00+10×$135.00+$30.00=$1,490.00. Plan B =$160.00+15×$50.00+$10.00=$920.00. Plan B is lower by $570.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $570.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,510.00; recompute which full total is lower.

158. Compare deposits, terms and stated fees · 5

Worked answer: Plan A =$140.00+12×$45.00+$40.00=$720.00. Plan B =$210.00+18×$105.00+$30.00=$2,130.00. Plan A is lower by $1,410.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,410.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $740.00; recompute which full total is lower.

159. Compare deposits, terms and stated fees · 6

Worked answer: Plan A =$170.00+18×$80.00+$0.00=$1,610.00. Plan B =$30.00+24×$160.00+$0.00=$3,870.00. Plan A is lower by $2,260.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $2,260.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,630.00; recompute which full total is lower.

160. Compare deposits, terms and stated fees · 7

Worked answer: Plan A =$200.00+4×$115.00+$10.00=$670.00. Plan B =$80.00+6×$70.00+$20.00=$520.00. Plan B is lower by $150.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $150.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $690.00; recompute which full total is lower.

161. Compare deposits, terms and stated fees · 8

Worked answer: Plan A =$20.00+6×$150.00+$20.00=$940.00. Plan B =$130.00+9×$125.00+$40.00=$1,295.00. Plan A is lower by $355.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $355.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $960.00; recompute which full total is lower.

162. Compare deposits, terms and stated fees · 9

Worked answer: Plan A =$50.00+8×$60.00+$30.00=$560.00. Plan B =$180.00+12×$35.00+$10.00=$610.00. Plan A is lower by $50.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $50.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $580.00; recompute which full total is lower.

163. Compare deposits, terms and stated fees · 10

Worked answer: Plan A =$80.00+10×$95.00+$40.00=$1,070.00. Plan B =$230.00+15×$90.00+$30.00=$1,610.00. Plan A is lower by $540.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $540.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,090.00; recompute which full total is lower.

164. Compare deposits, terms and stated fees · 11

Worked answer: Plan A =$110.00+12×$130.00+$0.00=$1,670.00. Plan B =$50.00+18×$145.00+$0.00=$2,660.00. Plan A is lower by $990.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $990.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,690.00; recompute which full total is lower.

165. Compare deposits, terms and stated fees · 12

Worked answer: Plan A =$140.00+18×$40.00+$10.00=$870.00. Plan B =$100.00+24×$55.00+$20.00=$1,440.00. Plan A is lower by $570.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $570.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $890.00; recompute which full total is lower.

166. Compare deposits, terms and stated fees · 13

Worked answer: Plan A =$170.00+4×$75.00+$20.00=$490.00. Plan B =$150.00+6×$110.00+$40.00=$850.00. Plan A is lower by $360.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $360.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $510.00; recompute which full total is lower.

167. Compare deposits, terms and stated fees · 14

Worked answer: Plan A =$200.00+6×$110.00+$30.00=$890.00. Plan B =$200.00+9×$165.00+$10.00=$1,695.00. Plan A is lower by $805.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $805.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $910.00; recompute which full total is lower.

168. Compare deposits, terms and stated fees · 15

Worked answer: Plan A =$20.00+8×$145.00+$40.00=$1,220.00. Plan B =$20.00+12×$75.00+$30.00=$950.00. Plan B is lower by $270.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $270.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,240.00; recompute which full total is lower.

169. Compare deposits, terms and stated fees · 16

Worked answer: Plan A =$50.00+10×$55.00+$0.00=$600.00. Plan B =$70.00+15×$130.00+$0.00=$2,020.00. Plan A is lower by $1,420.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,420.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $620.00; recompute which full total is lower.

170. Compare deposits, terms and stated fees · 17

Worked answer: Plan A =$80.00+12×$90.00+$10.00=$1,170.00. Plan B =$120.00+18×$40.00+$20.00=$860.00. Plan B is lower by $310.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $310.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,190.00; recompute which full total is lower.

171. Compare deposits, terms and stated fees · 18

Worked answer: Plan A =$110.00+18×$125.00+$20.00=$2,380.00. Plan B =$170.00+24×$95.00+$40.00=$2,490.00. Plan A is lower by $110.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $110.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $2,400.00; recompute which full total is lower.

172. Compare deposits, terms and stated fees · 19

Worked answer: Plan A =$140.00+4×$35.00+$30.00=$310.00. Plan B =$220.00+6×$150.00+$10.00=$1,130.00. Plan A is lower by $820.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $820.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $330.00; recompute which full total is lower.

173. Compare deposits, terms and stated fees · 20

Worked answer: Plan A =$170.00+6×$70.00+$40.00=$630.00. Plan B =$40.00+9×$60.00+$30.00=$610.00. Plan B is lower by $20.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $20.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $650.00; recompute which full total is lower.

174. Compare deposits, terms and stated fees · 21

Worked answer: Plan A =$200.00+8×$105.00+$0.00=$1,040.00. Plan B =$90.00+12×$115.00+$0.00=$1,470.00. Plan A is lower by $430.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $430.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,060.00; recompute which full total is lower.

175. Compare deposits, terms and stated fees · 22

Worked answer: Plan A =$20.00+10×$140.00+$10.00=$1,430.00. Plan B =$140.00+15×$170.00+$20.00=$2,710.00. Plan A is lower by $1,280.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,280.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,450.00; recompute which full total is lower.

176. Compare deposits, terms and stated fees · 23

Worked answer: Plan A =$50.00+12×$50.00+$20.00=$670.00. Plan B =$190.00+18×$80.00+$40.00=$1,670.00. Plan A is lower by $1,000.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,000.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $690.00; recompute which full total is lower.

177. Compare deposits, terms and stated fees · 24

Worked answer: Plan A =$80.00+18×$85.00+$30.00=$1,640.00. Plan B =$10.00+24×$135.00+$10.00=$3,260.00. Plan A is lower by $1,620.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,620.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,660.00; recompute which full total is lower.

178. Compare deposits, terms and stated fees · 25

Worked answer: Plan A =$110.00+4×$120.00+$40.00=$630.00. Plan B =$60.00+6×$45.00+$30.00=$360.00. Plan B is lower by $270.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $270.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $650.00; recompute which full total is lower.

179. Compare deposits, terms and stated fees · 26

Worked answer: Plan A =$140.00+6×$30.00+$0.00=$320.00. Plan B =$110.00+9×$100.00+$0.00=$1,010.00. Plan A is lower by $690.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $690.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $340.00; recompute which full total is lower.

180. Compare deposits, terms and stated fees · 27

Worked answer: Plan A =$170.00+8×$65.00+$10.00=$700.00. Plan B =$160.00+12×$155.00+$20.00=$2,040.00. Plan A is lower by $1,340.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,340.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $720.00; recompute which full total is lower.

181. Compare deposits, terms and stated fees · 28

Worked answer: Plan A =$200.00+10×$100.00+$20.00=$1,220.00. Plan B =$210.00+15×$65.00+$40.00=$1,225.00. Plan A is lower by $5.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $5.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,240.00; recompute which full total is lower.

182. Compare deposits, terms and stated fees · 29

Worked answer: Plan A =$20.00+12×$135.00+$30.00=$1,670.00. Plan B =$30.00+18×$120.00+$10.00=$2,200.00. Plan A is lower by $530.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $530.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,690.00; recompute which full total is lower.

183. Compare deposits, terms and stated fees · 30

Worked answer: Plan A =$50.00+18×$45.00+$40.00=$900.00. Plan B =$80.00+24×$30.00+$30.00=$830.00. Plan B is lower by $70.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $70.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $920.00; recompute which full total is lower.

184. Compare deposits, terms and stated fees · 31

Worked answer: Plan A =$80.00+4×$80.00+$0.00=$400.00. Plan B =$130.00+6×$85.00+$0.00=$640.00. Plan A is lower by $240.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $240.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $420.00; recompute which full total is lower.

185. Compare deposits, terms and stated fees · 32

Worked answer: Plan A =$110.00+6×$115.00+$10.00=$810.00. Plan B =$180.00+9×$140.00+$20.00=$1,460.00. Plan A is lower by $650.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $650.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $830.00; recompute which full total is lower.

186. Compare deposits, terms and stated fees · 33

Worked answer: Plan A =$140.00+8×$150.00+$20.00=$1,360.00. Plan B =$230.00+12×$50.00+$40.00=$870.00. Plan B is lower by $490.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $490.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,380.00; recompute which full total is lower.

187. Compare deposits, terms and stated fees · 34

Worked answer: Plan A =$170.00+10×$60.00+$30.00=$800.00. Plan B =$50.00+15×$105.00+$10.00=$1,635.00. Plan A is lower by $835.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $835.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $820.00; recompute which full total is lower.

188. Compare deposits, terms and stated fees · 35

Worked answer: Plan A =$200.00+12×$95.00+$40.00=$1,380.00. Plan B =$100.00+18×$160.00+$30.00=$3,010.00. Plan A is lower by $1,630.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,630.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,400.00; recompute which full total is lower.

189. Compare deposits, terms and stated fees · 36

Worked answer: Plan A =$20.00+18×$130.00+$0.00=$2,360.00. Plan B =$150.00+24×$70.00+$0.00=$1,830.00. Plan B is lower by $530.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $530.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $2,380.00; recompute which full total is lower.

190. Compare deposits, terms and stated fees · 37

Worked answer: Plan A =$50.00+4×$40.00+$10.00=$220.00. Plan B =$200.00+6×$125.00+$20.00=$970.00. Plan A is lower by $750.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $750.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $240.00; recompute which full total is lower.

191. Compare deposits, terms and stated fees · 38

Worked answer: Plan A =$80.00+6×$75.00+$20.00=$550.00. Plan B =$20.00+9×$35.00+$40.00=$375.00. Plan B is lower by $175.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $175.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $570.00; recompute which full total is lower.

192. Compare deposits, terms and stated fees · 39

Worked answer: Plan A =$110.00+8×$110.00+$30.00=$1,020.00. Plan B =$70.00+12×$90.00+$10.00=$1,160.00. Plan A is lower by $140.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $140.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,040.00; recompute which full total is lower.

193. Compare deposits, terms and stated fees · 40

Worked answer: Plan A =$140.00+10×$145.00+$40.00=$1,630.00. Plan B =$120.00+15×$145.00+$30.00=$2,325.00. Plan A is lower by $695.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $695.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,650.00; recompute which full total is lower.

Make a household budget arithmetic check

194. A monthly residual is not a whole-plan total · 1

Reverse-check: Reconstruct monthly income: $350.00+$30.00+($820.00)=$1,200.00. Also verify 6×$30.00+$20.00=$200.00.

195. A monthly residual is not a whole-plan total · 2

Reverse-check: Reconstruct monthly income: $600.00+$140.00+($760.00)=$1,500.00. Also verify 9×$140.00+$160.00=$1,420.00.

196. A monthly residual is not a whole-plan total · 3

Reverse-check: Reconstruct monthly income: $850.00+$40.00+($910.00)=$1,800.00. Also verify 12×$40.00+$40.00=$520.00.

197. A monthly residual is not a whole-plan total · 4

Reverse-check: Reconstruct monthly income: $1,100.00+$150.00+($850.00)=$2,100.00. Also verify 15×$150.00+$180.00=$2,430.00.

198. A monthly residual is not a whole-plan total · 5

Reverse-check: Reconstruct monthly income: $1,350.00+$50.00+($1,000.00)=$2,400.00. Also verify 18×$50.00+$60.00=$960.00.

199. A monthly residual is not a whole-plan total · 6

Reverse-check: Reconstruct monthly income: $450.00+$160.00+($2,090.00)=$2,700.00. Also verify 21×$160.00+$200.00=$3,560.00.

200. A monthly residual is not a whole-plan total · 7

Reverse-check: Reconstruct monthly income: $700.00+$60.00+($2,240.00)=$3,000.00. Also verify 24×$60.00+$80.00=$1,520.00.

201. A monthly residual is not a whole-plan total · 8

Reverse-check: Reconstruct monthly income: $950.00+$170.00+($2,180.00)=$3,300.00. Also verify 8×$170.00+$220.00=$1,580.00.

202. A monthly residual is not a whole-plan total · 9

Reverse-check: Reconstruct monthly income: $1,200.00+$70.00+($2,330.00)=$3,600.00. Also verify 11×$70.00+$100.00=$870.00.

203. A monthly residual is not a whole-plan total · 10

Reverse-check: Reconstruct monthly income: $1,450.00+$180.00+($2,270.00)=$3,900.00. Also verify 14×$180.00+$240.00=$2,760.00.

204. A monthly residual is not a whole-plan total · 11

Reverse-check: Reconstruct monthly income: $550.00+$80.00+($3,570.00)=$4,200.00. Also verify 17×$80.00+$120.00=$1,480.00.

205. A monthly residual is not a whole-plan total · 12

Reverse-check: Reconstruct monthly income: $800.00+$190.00+($310.00)=$1,300.00. Also verify 20×$190.00+$260.00=$4,060.00.

206. A monthly residual is not a whole-plan total · 13

Reverse-check: Reconstruct monthly income: $1,050.00+$90.00+($460.00)=$1,600.00. Also verify 23×$90.00+$140.00=$2,210.00.

207. A monthly residual is not a whole-plan total · 14

Reverse-check: Reconstruct monthly income: $1,300.00+$200.00+($400.00)=$1,900.00. Also verify 7×$200.00+$20.00=$1,420.00.

208. A monthly residual is not a whole-plan total · 15

Reverse-check: Reconstruct monthly income: $400.00+$100.00+($1,700.00)=$2,200.00. Also verify 10×$100.00+$160.00=$1,160.00.

209. A monthly residual is not a whole-plan total · 16

Reverse-check: Reconstruct monthly income: $650.00+$210.00+($1,640.00)=$2,500.00. Also verify 13×$210.00+$40.00=$2,770.00.

210. A monthly residual is not a whole-plan total · 17

Reverse-check: Reconstruct monthly income: $900.00+$110.00+($1,790.00)=$2,800.00. Also verify 16×$110.00+$180.00=$1,940.00.

211. A monthly residual is not a whole-plan total · 18

Reverse-check: Reconstruct monthly income: $1,150.00+$220.00+($1,730.00)=$3,100.00. Also verify 19×$220.00+$60.00=$4,240.00.

212. A monthly residual is not a whole-plan total · 19

Reverse-check: Reconstruct monthly income: $1,400.00+$120.00+($1,880.00)=$3,400.00. Also verify 22×$120.00+$200.00=$2,840.00.

213. A monthly residual is not a whole-plan total · 20

Reverse-check: Reconstruct monthly income: $500.00+$230.00+($2,970.00)=$3,700.00. Also verify 6×$230.00+$80.00=$1,460.00.

214. A monthly residual is not a whole-plan total · 21

Reverse-check: Reconstruct monthly income: $750.00+$130.00+($3,120.00)=$4,000.00. Also verify 9×$130.00+$220.00=$1,390.00.

215. A monthly residual is not a whole-plan total · 22

Reverse-check: Reconstruct monthly income: $1,000.00+$30.00+($3,270.00)=$4,300.00. Also verify 12×$30.00+$100.00=$460.00.

216. A monthly residual is not a whole-plan total · 23

Reverse-check: Reconstruct monthly income: $1,250.00+$140.00+($10.00)=$1,400.00. Also verify 15×$140.00+$240.00=$2,340.00.

217. A monthly residual is not a whole-plan total · 24

Reverse-check: Reconstruct monthly income: $350.00+$40.00+($1,310.00)=$1,700.00. Also verify 18×$40.00+$120.00=$840.00.

218. A monthly residual is not a whole-plan total · 25

Reverse-check: Reconstruct monthly income: $600.00+$150.00+($1,250.00)=$2,000.00. Also verify 21×$150.00+$260.00=$3,410.00.

219. A monthly residual is not a whole-plan total · 26

Reverse-check: Reconstruct monthly income: $850.00+$50.00+($1,400.00)=$2,300.00. Also verify 24×$50.00+$140.00=$1,340.00.

220. A monthly residual is not a whole-plan total · 27

Reverse-check: Reconstruct monthly income: $1,100.00+$160.00+($1,340.00)=$2,600.00. Also verify 8×$160.00+$20.00=$1,300.00.

221. A monthly residual is not a whole-plan total · 28

Reverse-check: Reconstruct monthly income: $1,350.00+$60.00+($1,490.00)=$2,900.00. Also verify 11×$60.00+$160.00=$820.00.

222. A monthly residual is not a whole-plan total · 29

Reverse-check: Reconstruct monthly income: $450.00+$170.00+($2,580.00)=$3,200.00. Also verify 14×$170.00+$40.00=$2,420.00.

223. A monthly residual is not a whole-plan total · 30

Reverse-check: Reconstruct monthly income: $700.00+$70.00+($2,730.00)=$3,500.00. Also verify 17×$70.00+$180.00=$1,370.00.

224. A monthly residual is not a whole-plan total · 31

Reverse-check: Reconstruct monthly income: $950.00+$180.00+($2,670.00)=$3,800.00. Also verify 20×$180.00+$60.00=$3,660.00.

225. A monthly residual is not a whole-plan total · 32

Reverse-check: Reconstruct monthly income: $1,200.00+$80.00+($2,820.00)=$4,100.00. Also verify 23×$80.00+$200.00=$2,040.00.

226. A monthly residual is not a whole-plan total · 33

Reverse-check: Reconstruct monthly income: $1,450.00+$190.00+(−$440.00)=$1,200.00. Also verify 7×$190.00+$80.00=$1,410.00.

227. A monthly residual is not a whole-plan total · 34

Reverse-check: Reconstruct monthly income: $550.00+$90.00+($860.00)=$1,500.00. Also verify 10×$90.00+$220.00=$1,120.00.

228. A monthly residual is not a whole-plan total · 35

Reverse-check: Reconstruct monthly income: $800.00+$200.00+($800.00)=$1,800.00. Also verify 13×$200.00+$100.00=$2,700.00.

229. A monthly residual is not a whole-plan total · 36

Reverse-check: Reconstruct monthly income: $1,050.00+$100.00+($950.00)=$2,100.00. Also verify 16×$100.00+$240.00=$1,840.00.

230. A monthly residual is not a whole-plan total · 37

Reverse-check: Reconstruct monthly income: $1,300.00+$210.00+($890.00)=$2,400.00. Also verify 19×$210.00+$120.00=$4,110.00.

Identify missing or misleading plan terms

231. Deposit is not the full purchase total

Question: An advertisement mentions a fictional $100 deposit but gives no term or monthly charge. Can a full total be found?

Worked answer: No. The payment count and amount remain unknown.

Common first error: Calling the deposit the final price ignores further payments.

Reverse-check: Name missing terms.

232. Small monthly versus total cost

Question: Compare $20 each month for 36 months against $35 for 18 months, no other costs.

Worked answer: First $720, second $630. Larger monthly payment has lower full total.

Common first error: Monthly amounts are not directly comparable as complete costs.

Reverse-check: 20×36=720 and 35×18=630.

233. Cash price and total plan price differ

Question: Cash $500, fictional plan $575. Difference?

Worked answer: $75 more by plan under specified terms.

Common first error: Using the cash price as though it were the monthly payment total.

Reverse-check: 575−500=75.

234. One-time fees count once

Question: Deposit 80 plus six payments of 45. Total?

Worked answer: $350.

Common first error: 80×6 repeats deposit wrongly.

Reverse-check: 80+270=350.

235. A fractional payment count is a warning

Question: Total $275, deposit $50, equal monthly payments $40. How many complete payments?

Worked answer: (275−50)/40=5.625, incompatible with an integer count of complete equal payments under the stated conditions.

Common first error: Rounding to six changes total.

Reverse-check: Six payments would total $290.

236. Deposit creates upfront cash requirement

Question: Can a small monthly amount prove a $150 deposit can be paid today?

Worked answer: No. Immediate cash availability is a separate fact not supplied.

Common first error: Monthly surplus alone doesn’t establish available deposit.

Reverse-check: State payment timing.

237. Unstated fees must not be invented

Question: The fictional problem says no other fees. Should the student add a guessed $30 late charge?

Worked answer: No. Compute only stated terms.

Common first error: Adding invented charges violates the model.

Reverse-check: Read the precise assumptions.

238. Zero interest is not zero extra fees

Question: A fictional offer advertises zero interest but has a $50 stated one-off fee. Can the fee be ignored?

Worked answer: No. The full arithmetic cost includes any stated fee.

Common first error: A marketing phrase does not override stated amounts.

Reverse-check: Add fee once.

239. Percent difference cash baseline

Question: Cash price $400, plan total $460. Percent higher relative to cash?

Worked answer: $60/$400=15%.

Common first error: Using the plan total as base answers another question.

Reverse-check: 400×1.15=460.

240. A negative difference can occur

Question: Cash $500, invented plan $470. Difference plan minus cash?

Worked answer: −$30.

Common first error: Assuming every hypothetical plan must cost more is false.

Reverse-check: 470−500=−30.

241. Overpayment is not APR

Question: Total plan exceeds cash by $100. Does this reveal effective yearly interest rate?

Worked answer: No. Timing, financed principal and charges matter.

Common first error: Percentage overpayment is not automatically annualised cost.

Reverse-check: Identify cash flows and dates.

242. Exact due dates need a start date

Question: Ten monthly payments listed, no first due date. Can their calendar dates be known?

Worked answer: No. Actual dates require the starting date and terms.

Common first error: Inventing dates from count alone is invalid.

Reverse-check: Request payment schedule.

243. A positive residual is not guaranteed saving

Question: Monthly budget has $500 available and payment $480. Is $20 guaranteed saved?

Worked answer: No. It is only the residual before all other needs.

Common first error: Limited budget categories may omit expenses.

Reverse-check: 500−480=20 mathematically.

244. Deposit as share of cash price

Question: Deposit $120 and cash quote $800. What percent is deposit of cash?

Worked answer: 15%.

Common first error: The base is $800, not $120.

Reverse-check: 120/800=0.15.

245. Change deposit with unchanged total

Question: Total $600 over ten monthly payments; deposit rises $100 to $150. Find new monthly amount.

Worked answer: (600−150)/10=$45.

Common first error: Treating monthly amount as unchanged would increase total.

Reverse-check: 150+450=600.

246. Payment frequency matters

Question: $60 every two months for twelve months, with a payment after each period. Total?

Worked answer: Six payments, $360.

Common first error: Twelve payments assumes monthly frequency not given.

Reverse-check: 12/2=6.

247. Annual fee is once per year

Question: One $24 annual fee and 12 monthly $10 payments. Total one year?

Worked answer: $144.

Common first error: 24×12 charges annual fee each month.

Reverse-check: 24+120=144.

248. Identical full totals with different timing

Question: A: $100+6×$50, B: $40+12×$30. Compare totals.

Worked answer: Both $400, though payment timing differs.

Common first error: Equal total does not imply identical monthly burden.

Reverse-check: 100+300=40+360.

249. Instalment minus cash

Question: Cash $560; plan $100+12×$40. Difference?

Worked answer: Plan $580, $20 above cash.

Common first error: Comparing $40 with $560 ignores term and deposit.

Reverse-check: 100+480=580.

250. Deposit discount changes the deposit

Question: Deposit $100 is discounted 20%, monthly charges unchanged. Total reduction?

Worked answer: $20.

Common first error: Applying 20% to entire plan changes percentage base.

Reverse-check: 0.2×100=20.

251. No deposit plan

Question: Zero deposit and eight $65 payments. Total?

Worked answer: $520.

Common first error: Adding an imaginary deposit changes the question.

Reverse-check: 8×65=520.

252. Label monthly count and monetary amount

Question: A calculation gives 6 payments of $40. Which value is dollars and which a count?

Worked answer: $40 is money per payment; six is the number of payments; total $240.

Common first error: Switching units can make a seemingly correct answer unclear.

Reverse-check: 6×$40=$240.

253. Negative budget residual

Question: Income $1000, commitments $900, plan payment $150. Residual?

Worked answer: −$50 in simplified monthly budget.

Common first error: A negative residual cannot be called an available surplus.

Reverse-check: 1000−900−150=−50.

254. Decimal-dollar payments

Question: Deposit $25.50 and three $19.95 payments. Full total?

Worked answer: $85.35.

Common first error: Rounding each before multiplication changes pennies.

Reverse-check: 25.50+59.85=85.35.

255. Recover monthly from total

Question: Total $900 includes deposit $180 and 12 equal monthly payments. Find each.

Worked answer: $60.

Common first error: $900/12 includes deposit incorrectly.

Reverse-check: 180+12×60=900.

256. Actual terms need current verification

Question: Can one select a real finance provider solely from two made-up classroom totals?

Worked answer: No. It is a numerical illustration, not a real-world recommendation.

Common first error: Terms, fees and conditions may differ.

Reverse-check: Check current written terms.

257. Identical monthly, different deposit

Question: Two plans both pay $30/month over 12 months; deposits $50 and $100. Compare totals.

Worked answer: $410 versus $460.

Common first error: Same monthly number does not mean same overall total.

Reverse-check: 360+50 vs 360+100.

258. Longer term with unchanged monthly cost

Question: Deposit $100 and payment $40, terms 12 and 18 months. Compare totals.

Worked answer: $580 versus $820, difference $240.

Common first error: More payments at same amount increase total.

Reverse-check: 40×6=240 extra.

259. Currency units must match

Question: Deposit quoted SGD and payments in another currency, no FX rate. Can exact SGD total be found?

Worked answer: No. A conversion rate is necessary.

Common first error: Adding numbers in different currencies is invalid.

Reverse-check: Identify missing exchange information.

260. Cash price does not determine monthly schedule

Question: Only cash price $1000 is given. Can monthly instalment be calculated?

Worked answer: No. Term, deposit and charges are unspecified.

Common first error: Assuming twelve months invents data.

Reverse-check: Request schedule.

261. Final balloon payment counts

Question: Ten payments $30 plus final separately stated $100 balloon. Full total?

Worked answer: $400.

Common first error: Omitting final special charge understates total.

Reverse-check: 300+100=400.

262. Ignore tax only if stated

Question: A fictional Maths question says ignore tax. Add an estimated local sales tax?

Worked answer: No. Follow the written assumption.

Common first error: Invented tax changes the scenario.

Reverse-check: Use stated costs.

263. APR cannot be inferred from simple overpayment

Question: Plan total is 12% higher than cash. Is annual percentage rate 12%?

Worked answer: Not necessarily. Time, principal and payments matter.

Common first error: Equating simple total comparison with annual rate is wrong.

Reverse-check: Define difference separately.

264. Equal dollar totals but different cash flows

Question: Is $500 cash at once identical in timing to ten monthly $50 payments?

Worked answer: No. Arithmetic totals match but timing differs.

Common first error: A total-only comparison omits timing.

Reverse-check: State totals and dates separately.

265. Advertised starting price can be incomplete

Question: A headline says ‘from $20/month’ but no term. Does it fix the full total?

Worked answer: No. Payment count and fees remain missing.

Common first error: Multiplying by a guessed term invents terms.

Reverse-check: Request complete schedule.

266. Rounding payments changes exact totals

Question: Six $49.99 instalments total what?

Worked answer: $299.94.

Common first error: Rounding to $50 before multiplying inflates six cents.

Reverse-check: 6×49.99=299.94.

267. Full total is not the same as affordability

Question: Two plans total $500 and $480. Which has lower numerical cost?

Worked answer: The $480 plan, by $20; this does not prove personal affordability.

Common first error: Conflating a numeric comparison with a personal finance decision is wrong.

Reverse-check: 480<500.

268. Missing contract details

Question: No cancellation rule is given. Can the pupil calculate a cancellation fee?

Worked answer: No. Missing rules prevent that calculation.

Common first error: Assuming imaginary penalties is not valid.

Reverse-check: Ask for written terms.

269. The question’s percentage base matters

Question: Plan total $600 vs cash $250. Total as % of cash?

Worked answer: 240%.

Common first error: Assuming every percentage must be under 100 is wrong for comparing different quantities.

Reverse-check: 600/250=2.4.

270. A deposit could be handled differently in contracts

Question: Can a maths solution assume an unstated deposit is refundable?

Worked answer: No. A specific real agreement would need terms; these examples treat deposits as paid within total.

Common first error: Assuming refund changes arithmetic.

Reverse-check: State whether refundable.

271. Monthly cost versus total fee

Question: Two offers with $20 and $30 monthly, missing lengths. Is the cheaper total known?

Worked answer: No. Counts of payments are missing.

Common first error: Smaller monthly does not determine full total.

Reverse-check: Give possible terms that reverse comparison.

272. Multiple payment schedules

Question: A fee $50 once plus two semiannual payments $100. Total?

Worked answer: $250.

Common first error: Calling them monthly changes frequency.

Reverse-check: 50+200=250.

273. Cash savings are not automatically profit

Question: Income $3000, known expenses $2500. Is $500 certain savings?

Worked answer: No. It is a limited residual before omitted needs.

Common first error: Incomplete budget doesn’t establish exact savings.

Reverse-check: Name assumptions.

274. Fictional amounts are not commercial quotes

Question: Are the article’s examples real deals?

Worked answer: No. They are invented G1 Mathematics problems.

Common first error: Treating a classroom payment as an offer misinforms.

Reverse-check: Check real sources separately.

275. A deposit changes the upfront burden

Question: Why might two equal-total plans feel different?

Worked answer: Their deposits and payment timing may differ.

Common first error: Full total alone does not describe the schedule.

Reverse-check: List upfront and repeated amounts.

276. One-time fees must appear once

Question: Deposit $50, 5 monthly $100, admin fee $20 once. Total?

Worked answer: $570.

Common first error: Multiplying admin fee by five is wrong.

Reverse-check: 50+500+20=570.

277. Student focus is interpretation, not real financing

Question: What should a learner explain after comparing schedules?

Worked answer: Which full total is lower under the stated amounts and which assumptions limit the comparison.

Common first error: Claims about real providers, credit eligibility or suitability exceed the classroom data.

Reverse-check: State conditional result.

278. A total overpayment may be negative in a fictional example

Question: Cash $800, plan $750. Is total difference negative?

Worked answer: Yes, −$50 plan-minus-cash.

Common first error: There is no rule that all imaginary instalment totals must exceed cash.

Reverse-check: 750−800=−50.

279. Count payments rather than visual calendar boxes

Question: A schedule has monthly payments from month 1 through month 12 inclusive. How many?

Worked answer: Twelve payments.

Common first error: Counting 11 gaps instead of 12 named months is wrong.

Reverse-check: List months 1–12.

280. Budget questions can use exact cents

Question: Monthly net $1200.50 and stated expense $300.25. Residual?

Worked answer: $900.25 before all other needs.

Common first error: Dropping cents prematurely changes exact sum.

Reverse-check: 1200.50−300.25=900.25.

281. The payee and payer roles differ

Question: Is ‘amount received’ always identical to ‘amount paid by buyer’ in an unstated financing model?

Worked answer: Not necessarily; fees and counterparties may change cash flows. State the perspective.

Common first error: Inventing a one-to-one transfer assumption may be misleading.

Reverse-check: Identify whose total is requested.

282. Compare actual unit of rate

Question: Monthly amount $25 per month, 12 months. What is the repeated total?

Worked answer: $300.

Common first error: Leaving rate at $25 without multiplying count misses duration.

Reverse-check: 25×12=300.

How a three-pupil Maths tutorial could teach full-cost thinking

10 minutes: identify deposit, per-period charge, number of periods and any one-time fee.
20 minutes: build a payment schedule as blocks and a one-variable equation.
25 minutes: solve full totals and reverse questions individually.
15 minutes: compare two fictional complete schedules.
10 minutes: spot one missing term or unjustified inference.
10 minutes: reverse-check the total and choose a short delayed retest.

Five manageable parent practice sessions

Day one: add one deposit to a multiplied number of monthly payments.
Day two: compare a plan’s full total against a supplied cash price.
Day three: find the unknown monthly payment from the complete sum.
Day four: compare two made-up terms, including one stated once-only fee.
Day five: explain why ‘lowest monthly payment’ and ‘lowest full cost’ do not mean the same thing.

Frequently asked questions

How do I find total paid?

Add the deposit once, every scheduled periodic payment and any other separately stated amount under the specified terms.

Is a lower monthly payment always cheaper?

No. The number of payments, deposit and fees can alter the full total.

How do I find an unknown monthly payment?

Subtract once-only charges from the complete stated total and divide by the number of equal payments.

Does overpaying the cash price tell us APR?

No. Annualised financing rates require more detailed cash-flow and financing assumptions.

Are these genuine offers or personal advice?

No. Every plan in this guide is fictional and used only for mathematical literacy.

Are instalments mentioned in G1 Mathematics?

The 2027 K110 graduating syllabus names instalments as a possible household-finance context. Current year-level teaching depends on the school.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

Did you know? A payment of $30 per month can cost more overall than one of $50 per month. The complete number of payments matters, and a deposit is not the same thing as the full product price. That is why instalment calculations make a practical Secondary 2 G1 Mathematics lesson in repeated amounts, percentages, equations and careful comparison.

Quick answer: total plan cost

Full stated total = deposit + (number of instalments × payment per instalment) + any separately stated fees. For example, a fictional deposit of $100 followed by twelve payments of $40, with no fees, totals $100+12×$40=$580. If a cash price is given, subtract it to compare full totals. A total difference is not automatically an annual interest rate, and a smaller monthly headline does not establish a smaller complete cost.

This article helps families seeking a Secondary 2 G1 Mathematics tutor in Bukit Timah. SEAB’s published 2027 SEC G1 Mathematics K110 syllabus lists personal and household finance, including instalments, among potential real-world contexts. That is a full graduating-course reference, not a claim that a 2026 Secondary 2 school test includes every financing context. The monetary examples below are invented for Maths and are not advertisements, product offers or personal financial advice.

Choose the payment problem

A sixty-second full-cost comparison
Once-only versus repeated amounts
What a total cannot tell you
Complete a deposit-plus-payments total
Compare cash price with full instalment cost
Recover the unknown monthly payment
Recover the unknown number of months
Compare two different payment plans
Make a household budget arithmetic check
Identify missing or misleading plan terms
A three-pupil tutorial
Questions and answers
Official references

Which option has the lower full total?

A deposit has a different time role from a monthly fee

Lower total and easier cash flow are different questions

282 original instalment cost and comparison clinics

Complete a deposit-plus-payments total

1. One deposit and 3 repeated payments · 1

Worked answer: The repeated subtotal is 3×$30.00=$90.00. Adding the deposit once gives $130.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $130.00−$40.00=$90.00, which exactly equals 3 payments of $30.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $30.00 were added without changing the deposit, the new full cost would be $160.00. The deposit should not be repeated.

2. One deposit and 4 repeated payments · 2

Worked answer: The repeated subtotal is 4×$140.00=$560.00. Adding the deposit once gives $740.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $740.00−$180.00=$560.00, which exactly equals 4 payments of $140.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $140.00 were added without changing the deposit, the new full cost would be $880.00. The deposit should not be repeated.

3. One deposit and 6 repeated payments · 3

Worked answer: The repeated subtotal is 6×$250.00=$1,500.00. Adding the deposit once gives $1,820.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,820.00−$320.00=$1,500.00, which exactly equals 6 payments of $250.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $250.00 were added without changing the deposit, the new full cost would be $2,070.00. The deposit should not be repeated.

4. One deposit and 8 repeated payments · 4

Worked answer: The repeated subtotal is 8×$360.00=$2,880.00. Adding the deposit once gives $3,340.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,340.00−$460.00=$2,880.00, which exactly equals 8 payments of $360.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $360.00 were added without changing the deposit, the new full cost would be $3,700.00. The deposit should not be repeated.

5. One deposit and 10 repeated payments · 5

Worked answer: The repeated subtotal is 10×$120.00=$1,200.00. Adding the deposit once gives $1,800.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,800.00−$600.00=$1,200.00, which exactly equals 10 payments of $120.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $120.00 were added without changing the deposit, the new full cost would be $1,920.00. The deposit should not be repeated.

6. One deposit and 12 repeated payments · 6

Worked answer: The repeated subtotal is 12×$230.00=$2,760.00. Adding the deposit once gives $2,900.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,900.00−$140.00=$2,760.00, which exactly equals 12 payments of $230.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $230.00 were added without changing the deposit, the new full cost would be $3,130.00. The deposit should not be repeated.

7. One deposit and 15 repeated payments · 7

Worked answer: The repeated subtotal is 15×$340.00=$5,100.00. Adding the deposit once gives $5,380.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $5,380.00−$280.00=$5,100.00, which exactly equals 15 payments of $340.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $340.00 were added without changing the deposit, the new full cost would be $5,720.00. The deposit should not be repeated.

8. One deposit and 18 repeated payments · 8

Worked answer: The repeated subtotal is 18×$100.00=$1,800.00. Adding the deposit once gives $2,220.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,220.00−$420.00=$1,800.00, which exactly equals 18 payments of $100.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $100.00 were added without changing the deposit, the new full cost would be $2,320.00. The deposit should not be repeated.

9. One deposit and 24 repeated payments · 9

Worked answer: The repeated subtotal is 24×$210.00=$5,040.00. Adding the deposit once gives $5,600.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $5,600.00−$560.00=$5,040.00, which exactly equals 24 payments of $210.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $210.00 were added without changing the deposit, the new full cost would be $5,810.00. The deposit should not be repeated.

10. One deposit and 3 repeated payments · 10

Worked answer: The repeated subtotal is 3×$320.00=$960.00. Adding the deposit once gives $1,060.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,060.00−$100.00=$960.00, which exactly equals 3 payments of $320.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $320.00 were added without changing the deposit, the new full cost would be $1,380.00. The deposit should not be repeated.

11. One deposit and 4 repeated payments · 11

Worked answer: The repeated subtotal is 4×$80.00=$320.00. Adding the deposit once gives $560.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $560.00−$240.00=$320.00, which exactly equals 4 payments of $80.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $80.00 were added without changing the deposit, the new full cost would be $640.00. The deposit should not be repeated.

12. One deposit and 6 repeated payments · 12

Worked answer: The repeated subtotal is 6×$190.00=$1,140.00. Adding the deposit once gives $1,520.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,520.00−$380.00=$1,140.00, which exactly equals 6 payments of $190.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $190.00 were added without changing the deposit, the new full cost would be $1,710.00. The deposit should not be repeated.

13. One deposit and 8 repeated payments · 13

Worked answer: The repeated subtotal is 8×$300.00=$2,400.00. Adding the deposit once gives $2,920.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,920.00−$520.00=$2,400.00, which exactly equals 8 payments of $300.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $300.00 were added without changing the deposit, the new full cost would be $3,220.00. The deposit should not be repeated.

14. One deposit and 10 repeated payments · 14

Worked answer: The repeated subtotal is 10×$60.00=$600.00. Adding the deposit once gives $660.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $660.00−$60.00=$600.00, which exactly equals 10 payments of $60.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $60.00 were added without changing the deposit, the new full cost would be $720.00. The deposit should not be repeated.

15. One deposit and 12 repeated payments · 15

Worked answer: The repeated subtotal is 12×$170.00=$2,040.00. Adding the deposit once gives $2,240.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,240.00−$200.00=$2,040.00, which exactly equals 12 payments of $170.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $170.00 were added without changing the deposit, the new full cost would be $2,410.00. The deposit should not be repeated.

16. One deposit and 15 repeated payments · 16

Worked answer: The repeated subtotal is 15×$280.00=$4,200.00. Adding the deposit once gives $4,540.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $4,540.00−$340.00=$4,200.00, which exactly equals 15 payments of $280.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $280.00 were added without changing the deposit, the new full cost would be $4,820.00. The deposit should not be repeated.

17. One deposit and 18 repeated payments · 17

Worked answer: The repeated subtotal is 18×$40.00=$720.00. Adding the deposit once gives $1,200.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,200.00−$480.00=$720.00, which exactly equals 18 payments of $40.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $40.00 were added without changing the deposit, the new full cost would be $1,240.00. The deposit should not be repeated.

18. One deposit and 24 repeated payments · 18

Worked answer: The repeated subtotal is 24×$150.00=$3,600.00. Adding the deposit once gives $4,220.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $4,220.00−$620.00=$3,600.00, which exactly equals 24 payments of $150.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $150.00 were added without changing the deposit, the new full cost would be $4,370.00. The deposit should not be repeated.

19. One deposit and 3 repeated payments · 19

Worked answer: The repeated subtotal is 3×$260.00=$780.00. Adding the deposit once gives $940.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $940.00−$160.00=$780.00, which exactly equals 3 payments of $260.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $260.00 were added without changing the deposit, the new full cost would be $1,200.00. The deposit should not be repeated.

20. One deposit and 4 repeated payments · 20

Worked answer: The repeated subtotal is 4×$370.00=$1,480.00. Adding the deposit once gives $1,780.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,780.00−$300.00=$1,480.00, which exactly equals 4 payments of $370.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $370.00 were added without changing the deposit, the new full cost would be $2,150.00. The deposit should not be repeated.

21. One deposit and 6 repeated payments · 21

Worked answer: The repeated subtotal is 6×$130.00=$780.00. Adding the deposit once gives $1,220.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,220.00−$440.00=$780.00, which exactly equals 6 payments of $130.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $130.00 were added without changing the deposit, the new full cost would be $1,350.00. The deposit should not be repeated.

22. One deposit and 8 repeated payments · 22

Worked answer: The repeated subtotal is 8×$240.00=$1,920.00. Adding the deposit once gives $2,500.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,500.00−$580.00=$1,920.00, which exactly equals 8 payments of $240.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $240.00 were added without changing the deposit, the new full cost would be $2,740.00. The deposit should not be repeated.

23. One deposit and 10 repeated payments · 23

Worked answer: The repeated subtotal is 10×$350.00=$3,500.00. Adding the deposit once gives $3,620.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,620.00−$120.00=$3,500.00, which exactly equals 10 payments of $350.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $350.00 were added without changing the deposit, the new full cost would be $3,970.00. The deposit should not be repeated.

24. One deposit and 12 repeated payments · 24

Worked answer: The repeated subtotal is 12×$110.00=$1,320.00. Adding the deposit once gives $1,580.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,580.00−$260.00=$1,320.00, which exactly equals 12 payments of $110.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $110.00 were added without changing the deposit, the new full cost would be $1,690.00. The deposit should not be repeated.

25. One deposit and 15 repeated payments · 25

Worked answer: The repeated subtotal is 15×$220.00=$3,300.00. Adding the deposit once gives $3,700.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,700.00−$400.00=$3,300.00, which exactly equals 15 payments of $220.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $220.00 were added without changing the deposit, the new full cost would be $3,920.00. The deposit should not be repeated.

26. One deposit and 18 repeated payments · 26

Worked answer: The repeated subtotal is 18×$330.00=$5,940.00. Adding the deposit once gives $6,480.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $6,480.00−$540.00=$5,940.00, which exactly equals 18 payments of $330.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $330.00 were added without changing the deposit, the new full cost would be $6,810.00. The deposit should not be repeated.

27. One deposit and 24 repeated payments · 27

Worked answer: The repeated subtotal is 24×$90.00=$2,160.00. Adding the deposit once gives $2,240.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,240.00−$80.00=$2,160.00, which exactly equals 24 payments of $90.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $90.00 were added without changing the deposit, the new full cost would be $2,330.00. The deposit should not be repeated.

28. One deposit and 3 repeated payments · 28

Worked answer: The repeated subtotal is 3×$200.00=$600.00. Adding the deposit once gives $820.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $820.00−$220.00=$600.00, which exactly equals 3 payments of $200.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $200.00 were added without changing the deposit, the new full cost would be $1,020.00. The deposit should not be repeated.

29. One deposit and 4 repeated payments · 29

Worked answer: The repeated subtotal is 4×$310.00=$1,240.00. Adding the deposit once gives $1,600.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,600.00−$360.00=$1,240.00, which exactly equals 4 payments of $310.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $310.00 were added without changing the deposit, the new full cost would be $1,910.00. The deposit should not be repeated.

30. One deposit and 6 repeated payments · 30

Worked answer: The repeated subtotal is 6×$70.00=$420.00. Adding the deposit once gives $920.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $920.00−$500.00=$420.00, which exactly equals 6 payments of $70.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $70.00 were added without changing the deposit, the new full cost would be $990.00. The deposit should not be repeated.

31. One deposit and 8 repeated payments · 31

Worked answer: The repeated subtotal is 8×$180.00=$1,440.00. Adding the deposit once gives $1,480.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,480.00−$40.00=$1,440.00, which exactly equals 8 payments of $180.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $180.00 were added without changing the deposit, the new full cost would be $1,660.00. The deposit should not be repeated.

32. One deposit and 10 repeated payments · 32

Worked answer: The repeated subtotal is 10×$290.00=$2,900.00. Adding the deposit once gives $3,080.00 in full. A bar model could show one deposit block beside 10 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $3,080.00−$180.00=$2,900.00, which exactly equals 10 payments of $290.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $290.00 were added without changing the deposit, the new full cost would be $3,370.00. The deposit should not be repeated.

33. One deposit and 12 repeated payments · 33

Worked answer: The repeated subtotal is 12×$50.00=$600.00. Adding the deposit once gives $920.00 in full. A bar model could show one deposit block beside 12 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $920.00−$320.00=$600.00, which exactly equals 12 payments of $50.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $50.00 were added without changing the deposit, the new full cost would be $970.00. The deposit should not be repeated.

34. One deposit and 15 repeated payments · 34

Worked answer: The repeated subtotal is 15×$160.00=$2,400.00. Adding the deposit once gives $2,860.00 in full. A bar model could show one deposit block beside 15 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,860.00−$460.00=$2,400.00, which exactly equals 15 payments of $160.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $160.00 were added without changing the deposit, the new full cost would be $3,020.00. The deposit should not be repeated.

35. One deposit and 18 repeated payments · 35

Worked answer: The repeated subtotal is 18×$270.00=$4,860.00. Adding the deposit once gives $5,460.00 in full. A bar model could show one deposit block beside 18 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $5,460.00−$600.00=$4,860.00, which exactly equals 18 payments of $270.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $270.00 were added without changing the deposit, the new full cost would be $5,730.00. The deposit should not be repeated.

36. One deposit and 24 repeated payments · 36

Worked answer: The repeated subtotal is 24×$30.00=$720.00. Adding the deposit once gives $860.00 in full. A bar model could show one deposit block beside 24 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $860.00−$140.00=$720.00, which exactly equals 24 payments of $30.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $30.00 were added without changing the deposit, the new full cost would be $890.00. The deposit should not be repeated.

37. One deposit and 3 repeated payments · 37

Worked answer: The repeated subtotal is 3×$140.00=$420.00. Adding the deposit once gives $700.00 in full. A bar model could show one deposit block beside 3 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $700.00−$280.00=$420.00, which exactly equals 3 payments of $140.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $140.00 were added without changing the deposit, the new full cost would be $840.00. The deposit should not be repeated.

38. One deposit and 4 repeated payments · 38

Worked answer: The repeated subtotal is 4×$250.00=$1,000.00. Adding the deposit once gives $1,420.00 in full. A bar model could show one deposit block beside 4 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,420.00−$420.00=$1,000.00, which exactly equals 4 payments of $250.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $250.00 were added without changing the deposit, the new full cost would be $1,670.00. The deposit should not be repeated.

39. One deposit and 6 repeated payments · 39

Worked answer: The repeated subtotal is 6×$360.00=$2,160.00. Adding the deposit once gives $2,720.00 in full. A bar model could show one deposit block beside 6 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $2,720.00−$560.00=$2,160.00, which exactly equals 6 payments of $360.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $360.00 were added without changing the deposit, the new full cost would be $3,080.00. The deposit should not be repeated.

40. One deposit and 8 repeated payments · 40

Worked answer: The repeated subtotal is 8×$120.00=$960.00. Adding the deposit once gives $1,060.00 in full. A bar model could show one deposit block beside 8 equal monthly blocks.

Reverse-check: Subtract the up-front deposit from total: $1,060.00−$100.00=$960.00, which exactly equals 8 payments of $120.00. The reverse reconstruction proves the stated amounts fit.

Change one condition: If one more payment of $120.00 were added without changing the deposit, the new full cost would be $1,180.00. The deposit should not be repeated.

Compare cash price with full instalment cost

41. Cash price versus complete plan · 1

Reverse-check: Check $1,150.00−$1,200.00=−$50.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,170.00, so the cash comparison changes by twenty dollars.

42. Cash price versus complete plan · 2

Reverse-check: Check $2,200.00−$1,900.00=+$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,220.00, so the cash comparison changes by twenty dollars.

43. Cash price versus complete plan · 3

Reverse-check: Check $3,150.00−$2,600.00=+$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,170.00, so the cash comparison changes by twenty dollars.

44. Cash price versus complete plan · 4

Reverse-check: Check $3,550.00−$3,300.00=+$250.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,570.00, so the cash comparison changes by twenty dollars.

45. Cash price versus complete plan · 5

Reverse-check: Check $2,200.00−$1,700.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,220.00, so the cash comparison changes by twenty dollars.

46. Cash price versus complete plan · 6

Reverse-check: Check $2,600.05−$2,400.00=+$200.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,620.05, so the cash comparison changes by twenty dollars.

47. Cash price versus complete plan · 7

Reverse-check: Check $2,650.04−$3,100.00=−$449.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,670.04, so the cash comparison changes by twenty dollars.

48. Cash price versus complete plan · 8

Reverse-check: Check $1,650.08−$1,500.00=+$150.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,670.08, so the cash comparison changes by twenty dollars.

49. Cash price versus complete plan · 9

Reverse-check: Check $2,600.00−$2,200.00=+$400.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,620.00, so the cash comparison changes by twenty dollars.

50. Cash price versus complete plan · 10

Reverse-check: Check $3,000.02−$2,900.00=+$100.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,020.02, so the cash comparison changes by twenty dollars.

51. Cash price versus complete plan · 11

Reverse-check: Check $1,650.00−$1,300.00=+$350.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,670.00, so the cash comparison changes by twenty dollars.

52. Cash price versus complete plan · 12

Worked answer: The full plan total is $60.00+10×$199.00=$2,050.00. The difference total minus cash is +$50.00; under these hypothetical figures, the plan costs $50.00 more than cash.

Reverse-check: Check $2,050.00−$2,000.00=+$50.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.00, so the cash comparison changes by twenty dollars.

53. Cash price versus complete plan · 13

Reverse-check: Check $2,400.00−$2,700.00=−$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,420.00, so the cash comparison changes by twenty dollars.

54. Cash price versus complete plan · 14

Reverse-check: Check $3,949.95−$3,400.00=+$549.95. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,969.95, so the cash comparison changes by twenty dollars.

55. Cash price versus complete plan · 15

Reverse-check: Check $2,050.08−$1,800.00=+$250.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.08, so the cash comparison changes by twenty dollars.

56. Cash price versus complete plan · 16

Reverse-check: Check $3,000.00−$2,500.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,020.00, so the cash comparison changes by twenty dollars.

57. Cash price versus complete plan · 17

Reverse-check: Check $3,400.00−$3,200.00=+$200.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,420.00, so the cash comparison changes by twenty dollars.

58. Cash price versus complete plan · 18

Reverse-check: Check $2,050.00−$1,600.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,070.00, so the cash comparison changes by twenty dollars.

59. Cash price versus complete plan · 19

Reverse-check: Check $2,150.00−$2,300.00=−$150.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,170.00, so the cash comparison changes by twenty dollars.

60. Cash price versus complete plan · 20

Reverse-check: Check $3,400.00−$3,000.00=+$400.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,420.00, so the cash comparison changes by twenty dollars.

61. Cash price versus complete plan · 21

Reverse-check: Check $1,500.04−$1,400.00=+$100.04. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,520.04, so the cash comparison changes by twenty dollars.

62. Cash price versus complete plan · 22

Reverse-check: Check $2,450.05−$2,100.00=+$350.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,470.05, so the cash comparison changes by twenty dollars.

63. Cash price versus complete plan · 23

Worked answer: The full plan total is $80.00+18×$153.89=$2,850.02. The difference total minus cash is +$50.02; under these hypothetical figures, the plan costs $50.02 more than cash.

Reverse-check: Check $2,850.02−$2,800.00=+$50.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.02, so the cash comparison changes by twenty dollars.

64. Cash price versus complete plan · 24

Reverse-check: Check $1,500.08−$1,200.00=+$300.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,520.08, so the cash comparison changes by twenty dollars.

65. Cash price versus complete plan · 25

Reverse-check: Check $1,350.00−$1,900.00=−$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,370.00, so the cash comparison changes by twenty dollars.

66. Cash price versus complete plan · 26

Reverse-check: Check $2,850.02−$2,600.00=+$250.02. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.02, so the cash comparison changes by twenty dollars.

67. Cash price versus complete plan · 27

Reverse-check: Check $3,800.00−$3,300.00=+$500.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,820.00, so the cash comparison changes by twenty dollars.

68. Cash price versus complete plan · 28

Reverse-check: Check $1,900.00−$1,700.00=+$200.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,920.00, so the cash comparison changes by twenty dollars.

69. Cash price versus complete plan · 29

Reverse-check: Check $2,850.00−$2,400.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,870.00, so the cash comparison changes by twenty dollars.

70. Cash price versus complete plan · 30

Reverse-check: Check $3,250.05−$3,100.00=+$150.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.05, so the cash comparison changes by twenty dollars.

71. Cash price versus complete plan · 31

Reverse-check: Check $1,100.04−$1,500.00=−$399.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,120.04, so the cash comparison changes by twenty dollars.

72. Cash price versus complete plan · 32

Worked answer: The full plan total is $300.00+24×$83.33=$2,299.92. The difference total minus cash is +$99.92; under these hypothetical figures, the plan costs $99.92 more than cash.

Reverse-check: Check $2,299.92−$2,200.00=+$99.92. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,319.92, so the cash comparison changes by twenty dollars.

73. Cash price versus complete plan · 33

Reverse-check: Check $3,250.00−$2,900.00=+$350.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.00, so the cash comparison changes by twenty dollars.

74. Cash price versus complete plan · 34

Worked answer: The full plan total is $100.00+6×$208.33=$1,349.98. The difference total minus cash is +$49.98; under these hypothetical figures, the plan costs $49.98 more than cash.

Reverse-check: Check $1,349.98−$1,300.00=+$49.98. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $1,369.98, so the cash comparison changes by twenty dollars.

75. Cash price versus complete plan · 35

Reverse-check: Check $2,300.00−$2,000.00=+$300.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,320.00, so the cash comparison changes by twenty dollars.

76. Cash price versus complete plan · 36

Reverse-check: Check $3,250.00−$2,700.00=+$550.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,270.00, so the cash comparison changes by twenty dollars.

77. Cash price versus complete plan · 37

Reverse-check: Check $3,150.04−$3,400.00=−$249.96. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,170.04, so the cash comparison changes by twenty dollars.

78. Cash price versus complete plan · 38

Reverse-check: Check $2,300.05−$1,800.00=+$500.05. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,320.05, so the cash comparison changes by twenty dollars.

79. Cash price versus complete plan · 39

Reverse-check: Check $2,700.08−$2,500.00=+$200.08. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $2,720.08, so the cash comparison changes by twenty dollars.

80. Cash price versus complete plan · 40

Reverse-check: Check $3,650.00−$3,200.00=+$450.00. Adding this signed difference back to the cash price reconstructs the plan total. No extra fees are invented.

Change one condition: Increase only the plan deposit by $20.00 while monthly charges remain unchanged. The full plan total rises to $3,670.00, so the cash comparison changes by twenty dollars.

81. Find monthly payment from stated total · 1

Worked answer: Write $50.00+3m=$140.00. Then 3m=$90.00, so m=$30.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $140.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $30.00 by 3, obtaining $90.00; add deposit $50.00 to restore the precise stated total $140.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $40.00.

82. Find monthly payment from stated total · 2

Worked answer: Write $125.00+4m=$445.00. Then 4m=$320.00, so m=$80.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $445.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $80.00 by 4, obtaining $320.00; add deposit $125.00 to restore the precise stated total $445.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $90.00.

83. Find monthly payment from stated total · 3

Worked answer: Write $200.00+6m=$980.00. Then 6m=$780.00, so m=$130.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $980.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $130.00 by 6, obtaining $780.00; add deposit $200.00 to restore the precise stated total $980.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $140.00.

84. Find monthly payment from stated total · 4

Worked answer: Write $275.00+8m=$1,715.00. Then 8m=$1,440.00, so m=$180.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,715.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $180.00 by 8, obtaining $1,440.00; add deposit $275.00 to restore the precise stated total $1,715.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $190.00.

85. Find monthly payment from stated total · 5

Worked answer: Write $350.00+10m=$2,650.00. Then 10m=$2,300.00, so m=$230.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,650.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $230.00 by 10, obtaining $2,300.00; add deposit $350.00 to restore the precise stated total $2,650.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $240.00.

86. Find monthly payment from stated total · 6

Worked answer: Write $425.00+12m=$3,785.00. Then 12m=$3,360.00, so m=$280.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,785.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $280.00 by 12, obtaining $3,360.00; add deposit $425.00 to restore the precise stated total $3,785.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $290.00.

87. Find monthly payment from stated total · 7

Worked answer: Write $500.00+15m=$5,450.00. Then 15m=$4,950.00, so m=$330.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $5,450.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $330.00 by 15, obtaining $4,950.00; add deposit $500.00 to restore the precise stated total $5,450.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $340.00.

88. Find monthly payment from stated total · 8

Worked answer: Write $575.00+18m=$1,655.00. Then 18m=$1,080.00, so m=$60.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,655.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $60.00 by 18, obtaining $1,080.00; add deposit $575.00 to restore the precise stated total $1,655.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $70.00.

89. Find monthly payment from stated total · 9

Worked answer: Write $100.00+24m=$2,740.00. Then 24m=$2,640.00, so m=$110.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,740.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $110.00 by 24, obtaining $2,640.00; add deposit $100.00 to restore the precise stated total $2,740.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $120.00.

90. Find monthly payment from stated total · 10

Worked answer: Write $175.00+3m=$655.00. Then 3m=$480.00, so m=$160.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $655.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $160.00 by 3, obtaining $480.00; add deposit $175.00 to restore the precise stated total $655.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $170.00.

91. Find monthly payment from stated total · 11

Worked answer: Write $250.00+4m=$1,090.00. Then 4m=$840.00, so m=$210.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,090.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $210.00 by 4, obtaining $840.00; add deposit $250.00 to restore the precise stated total $1,090.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $220.00.

92. Find monthly payment from stated total · 12

Worked answer: Write $325.00+6m=$1,885.00. Then 6m=$1,560.00, so m=$260.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,885.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $260.00 by 6, obtaining $1,560.00; add deposit $325.00 to restore the precise stated total $1,885.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $270.00.

93. Find monthly payment from stated total · 13

Worked answer: Write $400.00+8m=$2,880.00. Then 8m=$2,480.00, so m=$310.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,880.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $310.00 by 8, obtaining $2,480.00; add deposit $400.00 to restore the precise stated total $2,880.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $320.00.

94. Find monthly payment from stated total · 14

Worked answer: Write $475.00+10m=$875.00. Then 10m=$400.00, so m=$40.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $875.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $40.00 by 10, obtaining $400.00; add deposit $475.00 to restore the precise stated total $875.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $50.00.

95. Find monthly payment from stated total · 15

Worked answer: Write $550.00+12m=$1,630.00. Then 12m=$1,080.00, so m=$90.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,630.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $90.00 by 12, obtaining $1,080.00; add deposit $550.00 to restore the precise stated total $1,630.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $100.00.

96. Find monthly payment from stated total · 16

Worked answer: Write $75.00+15m=$2,175.00. Then 15m=$2,100.00, so m=$140.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,175.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $140.00 by 15, obtaining $2,100.00; add deposit $75.00 to restore the precise stated total $2,175.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $150.00.

97. Find monthly payment from stated total · 17

Worked answer: Write $150.00+18m=$3,570.00. Then 18m=$3,420.00, so m=$190.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,570.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $190.00 by 18, obtaining $3,420.00; add deposit $150.00 to restore the precise stated total $3,570.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $200.00.

98. Find monthly payment from stated total · 18

Worked answer: Write $225.00+24m=$5,985.00. Then 24m=$5,760.00, so m=$240.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $5,985.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $240.00 by 24, obtaining $5,760.00; add deposit $225.00 to restore the precise stated total $5,985.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $250.00.

99. Find monthly payment from stated total · 19

Worked answer: Write $300.00+3m=$1,170.00. Then 3m=$870.00, so m=$290.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,170.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $290.00 by 3, obtaining $870.00; add deposit $300.00 to restore the precise stated total $1,170.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $300.00.

100. Find monthly payment from stated total · 20

Worked answer: Write $375.00+4m=$1,735.00. Then 4m=$1,360.00, so m=$340.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,735.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $340.00 by 4, obtaining $1,360.00; add deposit $375.00 to restore the precise stated total $1,735.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $350.00.

101. Find monthly payment from stated total · 21

Worked answer: Write $450.00+6m=$870.00. Then 6m=$420.00, so m=$70.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $870.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $70.00 by 6, obtaining $420.00; add deposit $450.00 to restore the precise stated total $870.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $80.00.

102. Find monthly payment from stated total · 22

Worked answer: Write $525.00+8m=$1,485.00. Then 8m=$960.00, so m=$120.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,485.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $120.00 by 8, obtaining $960.00; add deposit $525.00 to restore the precise stated total $1,485.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $130.00.

103. Find monthly payment from stated total · 23

Worked answer: Write $50.00+10m=$1,750.00. Then 10m=$1,700.00, so m=$170.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,750.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $170.00 by 10, obtaining $1,700.00; add deposit $50.00 to restore the precise stated total $1,750.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $180.00.

104. Find monthly payment from stated total · 24

Worked answer: Write $125.00+12m=$2,765.00. Then 12m=$2,640.00, so m=$220.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,765.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $220.00 by 12, obtaining $2,640.00; add deposit $125.00 to restore the precise stated total $2,765.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $230.00.

105. Find monthly payment from stated total · 25

Worked answer: Write $200.00+15m=$4,250.00. Then 15m=$4,050.00, so m=$270.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $4,250.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $270.00 by 15, obtaining $4,050.00; add deposit $200.00 to restore the precise stated total $4,250.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $280.00.

106. Find monthly payment from stated total · 26

Worked answer: Write $275.00+18m=$6,035.00. Then 18m=$5,760.00, so m=$320.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $6,035.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $320.00 by 18, obtaining $5,760.00; add deposit $275.00 to restore the precise stated total $6,035.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $330.00.

107. Find monthly payment from stated total · 27

Worked answer: Write $350.00+24m=$1,550.00. Then 24m=$1,200.00, so m=$50.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,550.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $50.00 by 24, obtaining $1,200.00; add deposit $350.00 to restore the precise stated total $1,550.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $60.00.

108. Find monthly payment from stated total · 28

Worked answer: Write $425.00+3m=$725.00. Then 3m=$300.00, so m=$100.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $725.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $100.00 by 3, obtaining $300.00; add deposit $425.00 to restore the precise stated total $725.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $110.00.

109. Find monthly payment from stated total · 29

Worked answer: Write $500.00+4m=$1,100.00. Then 4m=$600.00, so m=$150.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,100.00 by 4 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $150.00 by 4, obtaining $600.00; add deposit $500.00 to restore the precise stated total $1,100.00.

Change one condition: If the full schedule cost rose by $40.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $160.00.

110. Find monthly payment from stated total · 30

Worked answer: Write $575.00+6m=$1,775.00. Then 6m=$1,200.00, so m=$200.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,775.00 by 6 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $200.00 by 6, obtaining $1,200.00; add deposit $575.00 to restore the precise stated total $1,775.00.

Change one condition: If the full schedule cost rose by $60.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $210.00.

111. Find monthly payment from stated total · 31

Worked answer: Write $100.00+8m=$2,100.00. Then 8m=$2,000.00, so m=$250.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,100.00 by 8 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $250.00 by 8, obtaining $2,000.00; add deposit $100.00 to restore the precise stated total $2,100.00.

Change one condition: If the full schedule cost rose by $80.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $260.00.

112. Find monthly payment from stated total · 32

Worked answer: Write $175.00+10m=$3,175.00. Then 10m=$3,000.00, so m=$300.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $3,175.00 by 10 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $300.00 by 10, obtaining $3,000.00; add deposit $175.00 to restore the precise stated total $3,175.00.

Change one condition: If the full schedule cost rose by $100.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $310.00.

113. Find monthly payment from stated total · 33

Worked answer: Write $250.00+12m=$610.00. Then 12m=$360.00, so m=$30.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $610.00 by 12 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $30.00 by 12, obtaining $360.00; add deposit $250.00 to restore the precise stated total $610.00.

Change one condition: If the full schedule cost rose by $120.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $40.00.

114. Find monthly payment from stated total · 34

Worked answer: Write $325.00+15m=$1,525.00. Then 15m=$1,200.00, so m=$80.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,525.00 by 15 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $80.00 by 15, obtaining $1,200.00; add deposit $325.00 to restore the precise stated total $1,525.00.

Change one condition: If the full schedule cost rose by $150.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $90.00.

115. Find monthly payment from stated total · 35

Worked answer: Write $400.00+18m=$2,740.00. Then 18m=$2,340.00, so m=$130.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $2,740.00 by 18 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $130.00 by 18, obtaining $2,340.00; add deposit $400.00 to restore the precise stated total $2,740.00.

Change one condition: If the full schedule cost rose by $180.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $140.00.

116. Find monthly payment from stated total · 36

Worked answer: Write $475.00+24m=$4,795.00. Then 24m=$4,320.00, so m=$180.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $4,795.00 by 24 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $180.00 by 24, obtaining $4,320.00; add deposit $475.00 to restore the precise stated total $4,795.00.

Change one condition: If the full schedule cost rose by $240.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $190.00.

117. Find monthly payment from stated total · 37

Worked answer: Write $550.00+3m=$1,240.00. Then 3m=$690.00, so m=$230.00 per month. The result answers a monthly payment rather than the number of months.

Common first error: Dividing the full $1,240.00 by 3 would spread the deposit across the monthly amount. That does not match a schedule where deposit is a separate up-front payment.

Reverse-check: Multiply the recovered $230.00 by 3, obtaining $690.00; add deposit $550.00 to restore the precise stated total $1,240.00.

Change one condition: If the full schedule cost rose by $30.00 with the same deposit and payment count, the monthly payment would increase by $10.00 to $240.00.

Recover the unknown number of months

118. Find how many instalments are stated · 1

Question: The fictional full plan total is $145.00, with a deposit of $40.00 and equal payments of $35.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($145.00−$40.00)/$35.00 = $105.00/$35.00=3 payments. The amount $105.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$35.00+$40.00=$145.00. The terms and units are consistent.

Change one condition: If another payment of $35.00 were included, the full total would rise to $180.00 and the count become 4.

119. Find how many instalments are stated · 2

Question: The fictional full plan total is $380.00, with a deposit of $100.00 and equal payments of $70.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($380.00−$100.00)/$70.00 = $280.00/$70.00=4 payments. The amount $280.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$70.00+$100.00=$380.00. The terms and units are consistent.

Change one condition: If another payment of $70.00 were included, the full total would rise to $450.00 and the count become 5.

120. Find how many instalments are stated · 3

Question: The fictional full plan total is $790.00, with a deposit of $160.00 and equal payments of $105.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($790.00−$160.00)/$105.00 = $630.00/$105.00=6 payments. The amount $630.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$105.00+$160.00=$790.00. The terms and units are consistent.

Change one condition: If another payment of $105.00 were included, the full total would rise to $895.00 and the count become 7.

121. Find how many instalments are stated · 4

Question: The fictional full plan total is $1,340.00, with a deposit of $220.00 and equal payments of $140.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,340.00−$220.00)/$140.00 = $1,120.00/$140.00=8 payments. The amount $1,120.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$140.00+$220.00=$1,340.00. The terms and units are consistent.

Change one condition: If another payment of $140.00 were included, the full total would rise to $1,480.00 and the count become 9.

122. Find how many instalments are stated · 5

Question: The fictional full plan total is $775.00, with a deposit of $280.00 and equal payments of $55.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($775.00−$280.00)/$55.00 = $495.00/$55.00=9 payments. The amount $495.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$55.00+$280.00=$775.00. The terms and units are consistent.

Change one condition: If another payment of $55.00 were included, the full total would rise to $830.00 and the count become 10.

123. Find how many instalments are stated · 6

Question: The fictional full plan total is $1,240.00, with a deposit of $340.00 and equal payments of $90.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,240.00−$340.00)/$90.00 = $900.00/$90.00=10 payments. The amount $900.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$90.00+$340.00=$1,240.00. The terms and units are consistent.

Change one condition: If another payment of $90.00 were included, the full total would rise to $1,330.00 and the count become 11.

124. Find how many instalments are stated · 7

Question: The fictional full plan total is $1,900.00, with a deposit of $400.00 and equal payments of $125.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,900.00−$400.00)/$125.00 = $1,500.00/$125.00=12 payments. The amount $1,500.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$125.00+$400.00=$1,900.00. The terms and units are consistent.

Change one condition: If another payment of $125.00 were included, the full total would rise to $2,025.00 and the count become 13.

125. Find how many instalments are stated · 8

Question: The fictional full plan total is $1,060.00, with a deposit of $460.00 and equal payments of $40.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,060.00−$460.00)/$40.00 = $600.00/$40.00=15 payments. The amount $600.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$40.00+$460.00=$1,060.00. The terms and units are consistent.

Change one condition: If another payment of $40.00 were included, the full total would rise to $1,100.00 and the count become 16.

126. Find how many instalments are stated · 9

Question: The fictional full plan total is $1,410.00, with a deposit of $60.00 and equal payments of $75.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,410.00−$60.00)/$75.00 = $1,350.00/$75.00=18 payments. The amount $1,350.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$75.00+$60.00=$1,410.00. The terms and units are consistent.

Change one condition: If another payment of $75.00 were included, the full total would rise to $1,485.00 and the count become 19.

127. Find how many instalments are stated · 10

Question: The fictional full plan total is $2,320.00, with a deposit of $120.00 and equal payments of $110.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,320.00−$120.00)/$110.00 = $2,200.00/$110.00=20 payments. The amount $2,200.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$110.00+$120.00=$2,320.00. The terms and units are consistent.

Change one condition: If another payment of $110.00 were included, the full total would rise to $2,430.00 and the count become 21.

128. Find how many instalments are stated · 11

Question: The fictional full plan total is $3,660.00, with a deposit of $180.00 and equal payments of $145.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($3,660.00−$180.00)/$145.00 = $3,480.00/$145.00=24 payments. The amount $3,480.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$145.00+$180.00=$3,660.00. The terms and units are consistent.

Change one condition: If another payment of $145.00 were included, the full total would rise to $3,805.00 and the count become 25.

129. Find how many instalments are stated · 12

Question: The fictional full plan total is $420.00, with a deposit of $240.00 and equal payments of $60.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($420.00−$240.00)/$60.00 = $180.00/$60.00=3 payments. The amount $180.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$60.00+$240.00=$420.00. The terms and units are consistent.

Change one condition: If another payment of $60.00 were included, the full total would rise to $480.00 and the count become 4.

130. Find how many instalments are stated · 13

Question: The fictional full plan total is $680.00, with a deposit of $300.00 and equal payments of $95.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($680.00−$300.00)/$95.00 = $380.00/$95.00=4 payments. The amount $380.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$95.00+$300.00=$680.00. The terms and units are consistent.

Change one condition: If another payment of $95.00 were included, the full total would rise to $775.00 and the count become 5.

131. Find how many instalments are stated · 14

Question: The fictional full plan total is $1,140.00, with a deposit of $360.00 and equal payments of $130.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,140.00−$360.00)/$130.00 = $780.00/$130.00=6 payments. The amount $780.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$130.00+$360.00=$1,140.00. The terms and units are consistent.

Change one condition: If another payment of $130.00 were included, the full total would rise to $1,270.00 and the count become 7.

132. Find how many instalments are stated · 15

Question: The fictional full plan total is $780.00, with a deposit of $420.00 and equal payments of $45.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($780.00−$420.00)/$45.00 = $360.00/$45.00=8 payments. The amount $360.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$45.00+$420.00=$780.00. The terms and units are consistent.

Change one condition: If another payment of $45.00 were included, the full total would rise to $825.00 and the count become 9.

133. Find how many instalments are stated · 16

Question: The fictional full plan total is $1,200.00, with a deposit of $480.00 and equal payments of $80.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,200.00−$480.00)/$80.00 = $720.00/$80.00=9 payments. The amount $720.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$80.00+$480.00=$1,200.00. The terms and units are consistent.

Change one condition: If another payment of $80.00 were included, the full total would rise to $1,280.00 and the count become 10.

134. Find how many instalments are stated · 17

Question: The fictional full plan total is $1,230.00, with a deposit of $80.00 and equal payments of $115.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,230.00−$80.00)/$115.00 = $1,150.00/$115.00=10 payments. The amount $1,150.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$115.00+$80.00=$1,230.00. The terms and units are consistent.

Change one condition: If another payment of $115.00 were included, the full total would rise to $1,345.00 and the count become 11.

135. Find how many instalments are stated · 18

Question: The fictional full plan total is $1,940.00, with a deposit of $140.00 and equal payments of $150.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,940.00−$140.00)/$150.00 = $1,800.00/$150.00=12 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$150.00+$140.00=$1,940.00. The terms and units are consistent.

Change one condition: If another payment of $150.00 were included, the full total would rise to $2,090.00 and the count become 13.

136. Find how many instalments are stated · 19

Question: The fictional full plan total is $1,175.00, with a deposit of $200.00 and equal payments of $65.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,175.00−$200.00)/$65.00 = $975.00/$65.00=15 payments. The amount $975.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$65.00+$200.00=$1,175.00. The terms and units are consistent.

Change one condition: If another payment of $65.00 were included, the full total would rise to $1,240.00 and the count become 16.

137. Find how many instalments are stated · 20

Question: The fictional full plan total is $2,060.00, with a deposit of $260.00 and equal payments of $100.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,060.00−$260.00)/$100.00 = $1,800.00/$100.00=18 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$100.00+$260.00=$2,060.00. The terms and units are consistent.

Change one condition: If another payment of $100.00 were included, the full total would rise to $2,160.00 and the count become 19.

138. Find how many instalments are stated · 21

Question: The fictional full plan total is $3,020.00, with a deposit of $320.00 and equal payments of $135.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($3,020.00−$320.00)/$135.00 = $2,700.00/$135.00=20 payments. The amount $2,700.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$135.00+$320.00=$3,020.00. The terms and units are consistent.

Change one condition: If another payment of $135.00 were included, the full total would rise to $3,155.00 and the count become 21.

139. Find how many instalments are stated · 22

Question: The fictional full plan total is $1,580.00, with a deposit of $380.00 and equal payments of $50.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,580.00−$380.00)/$50.00 = $1,200.00/$50.00=24 payments. The amount $1,200.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$50.00+$380.00=$1,580.00. The terms and units are consistent.

Change one condition: If another payment of $50.00 were included, the full total would rise to $1,630.00 and the count become 25.

140. Find how many instalments are stated · 23

Question: The fictional full plan total is $695.00, with a deposit of $440.00 and equal payments of $85.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($695.00−$440.00)/$85.00 = $255.00/$85.00=3 payments. The amount $255.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$85.00+$440.00=$695.00. The terms and units are consistent.

Change one condition: If another payment of $85.00 were included, the full total would rise to $780.00 and the count become 4.

141. Find how many instalments are stated · 24

Question: The fictional full plan total is $520.00, with a deposit of $40.00 and equal payments of $120.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($520.00−$40.00)/$120.00 = $480.00/$120.00=4 payments. The amount $480.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$120.00+$40.00=$520.00. The terms and units are consistent.

Change one condition: If another payment of $120.00 were included, the full total would rise to $640.00 and the count become 5.

142. Find how many instalments are stated · 25

Question: The fictional full plan total is $310.00, with a deposit of $100.00 and equal payments of $35.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($310.00−$100.00)/$35.00 = $210.00/$35.00=6 payments. The amount $210.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$35.00+$100.00=$310.00. The terms and units are consistent.

Change one condition: If another payment of $35.00 were included, the full total would rise to $345.00 and the count become 7.

143. Find how many instalments are stated · 26

Question: The fictional full plan total is $720.00, with a deposit of $160.00 and equal payments of $70.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($720.00−$160.00)/$70.00 = $560.00/$70.00=8 payments. The amount $560.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 8×$70.00+$160.00=$720.00. The terms and units are consistent.

Change one condition: If another payment of $70.00 were included, the full total would rise to $790.00 and the count become 9.

144. Find how many instalments are stated · 27

Question: The fictional full plan total is $1,165.00, with a deposit of $220.00 and equal payments of $105.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,165.00−$220.00)/$105.00 = $945.00/$105.00=9 payments. The amount $945.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 9×$105.00+$220.00=$1,165.00. The terms and units are consistent.

Change one condition: If another payment of $105.00 were included, the full total would rise to $1,270.00 and the count become 10.

145. Find how many instalments are stated · 28

Question: The fictional full plan total is $1,680.00, with a deposit of $280.00 and equal payments of $140.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,680.00−$280.00)/$140.00 = $1,400.00/$140.00=10 payments. The amount $1,400.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 10×$140.00+$280.00=$1,680.00. The terms and units are consistent.

Change one condition: If another payment of $140.00 were included, the full total would rise to $1,820.00 and the count become 11.

146. Find how many instalments are stated · 29

Question: The fictional full plan total is $1,000.00, with a deposit of $340.00 and equal payments of $55.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,000.00−$340.00)/$55.00 = $660.00/$55.00=12 payments. The amount $660.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 12×$55.00+$340.00=$1,000.00. The terms and units are consistent.

Change one condition: If another payment of $55.00 were included, the full total would rise to $1,055.00 and the count become 13.

147. Find how many instalments are stated · 30

Question: The fictional full plan total is $1,750.00, with a deposit of $400.00 and equal payments of $90.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,750.00−$400.00)/$90.00 = $1,350.00/$90.00=15 payments. The amount $1,350.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 15×$90.00+$400.00=$1,750.00. The terms and units are consistent.

Change one condition: If another payment of $90.00 were included, the full total would rise to $1,840.00 and the count become 16.

148. Find how many instalments are stated · 31

Question: The fictional full plan total is $2,710.00, with a deposit of $460.00 and equal payments of $125.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($2,710.00−$460.00)/$125.00 = $2,250.00/$125.00=18 payments. The amount $2,250.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 18×$125.00+$460.00=$2,710.00. The terms and units are consistent.

Change one condition: If another payment of $125.00 were included, the full total would rise to $2,835.00 and the count become 19.

149. Find how many instalments are stated · 32

Question: The fictional full plan total is $860.00, with a deposit of $60.00 and equal payments of $40.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($860.00−$60.00)/$40.00 = $800.00/$40.00=20 payments. The amount $800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 20×$40.00+$60.00=$860.00. The terms and units are consistent.

Change one condition: If another payment of $40.00 were included, the full total would rise to $900.00 and the count become 21.

150. Find how many instalments are stated · 33

Question: The fictional full plan total is $1,920.00, with a deposit of $120.00 and equal payments of $75.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($1,920.00−$120.00)/$75.00 = $1,800.00/$75.00=24 payments. The amount $1,800.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 24×$75.00+$120.00=$1,920.00. The terms and units are consistent.

Change one condition: If another payment of $75.00 were included, the full total would rise to $1,995.00 and the count become 25.

151. Find how many instalments are stated · 34

Question: The fictional full plan total is $510.00, with a deposit of $180.00 and equal payments of $110.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($510.00−$180.00)/$110.00 = $330.00/$110.00=3 payments. The amount $330.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 3×$110.00+$180.00=$510.00. The terms and units are consistent.

Change one condition: If another payment of $110.00 were included, the full total would rise to $620.00 and the count become 4.

152. Find how many instalments are stated · 35

Question: The fictional full plan total is $820.00, with a deposit of $240.00 and equal payments of $145.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($820.00−$240.00)/$145.00 = $580.00/$145.00=4 payments. The amount $580.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 4×$145.00+$240.00=$820.00. The terms and units are consistent.

Change one condition: If another payment of $145.00 were included, the full total would rise to $965.00 and the count become 5.

153. Find how many instalments are stated · 36

Question: The fictional full plan total is $660.00, with a deposit of $300.00 and equal payments of $60.00 per month. How many monthly payments are included?

Worked answer: Number of payments = ($660.00−$300.00)/$60.00 = $360.00/$60.00=6 payments. The amount $360.00 is the repeated subtotal, not the complete total.

Reverse-check: Reconstruct 6×$60.00+$300.00=$660.00. The terms and units are consistent.

Change one condition: If another payment of $60.00 were included, the full total would rise to $720.00 and the count become 7.

Compare two different payment plans

154. Compare deposits, terms and stated fees · 1

Worked answer: Plan A =$20.00+4×$30.00+$0.00=$140.00. Plan B =$10.00+6×$30.00+$0.00=$190.00. Plan A is lower by $50.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $50.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $160.00; recompute which full total is lower.

155. Compare deposits, terms and stated fees · 2

Worked answer: Plan A =$50.00+6×$65.00+$10.00=$450.00. Plan B =$60.00+9×$85.00+$20.00=$845.00. Plan A is lower by $395.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $395.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $470.00; recompute which full total is lower.

156. Compare deposits, terms and stated fees · 3

Worked answer: Plan A =$80.00+8×$100.00+$20.00=$900.00. Plan B =$110.00+12×$140.00+$40.00=$1,830.00. Plan A is lower by $930.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $930.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $920.00; recompute which full total is lower.

157. Compare deposits, terms and stated fees · 4

Worked answer: Plan A =$110.00+10×$135.00+$30.00=$1,490.00. Plan B =$160.00+15×$50.00+$10.00=$920.00. Plan B is lower by $570.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $570.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,510.00; recompute which full total is lower.

158. Compare deposits, terms and stated fees · 5

Worked answer: Plan A =$140.00+12×$45.00+$40.00=$720.00. Plan B =$210.00+18×$105.00+$30.00=$2,130.00. Plan A is lower by $1,410.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,410.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $740.00; recompute which full total is lower.

159. Compare deposits, terms and stated fees · 6

Worked answer: Plan A =$170.00+18×$80.00+$0.00=$1,610.00. Plan B =$30.00+24×$160.00+$0.00=$3,870.00. Plan A is lower by $2,260.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $2,260.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,630.00; recompute which full total is lower.

160. Compare deposits, terms and stated fees · 7

Worked answer: Plan A =$200.00+4×$115.00+$10.00=$670.00. Plan B =$80.00+6×$70.00+$20.00=$520.00. Plan B is lower by $150.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $150.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $690.00; recompute which full total is lower.

161. Compare deposits, terms and stated fees · 8

Worked answer: Plan A =$20.00+6×$150.00+$20.00=$940.00. Plan B =$130.00+9×$125.00+$40.00=$1,295.00. Plan A is lower by $355.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $355.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $960.00; recompute which full total is lower.

162. Compare deposits, terms and stated fees · 9

Worked answer: Plan A =$50.00+8×$60.00+$30.00=$560.00. Plan B =$180.00+12×$35.00+$10.00=$610.00. Plan A is lower by $50.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $50.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $580.00; recompute which full total is lower.

163. Compare deposits, terms and stated fees · 10

Worked answer: Plan A =$80.00+10×$95.00+$40.00=$1,070.00. Plan B =$230.00+15×$90.00+$30.00=$1,610.00. Plan A is lower by $540.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $540.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,090.00; recompute which full total is lower.

164. Compare deposits, terms and stated fees · 11

Worked answer: Plan A =$110.00+12×$130.00+$0.00=$1,670.00. Plan B =$50.00+18×$145.00+$0.00=$2,660.00. Plan A is lower by $990.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $990.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,690.00; recompute which full total is lower.

165. Compare deposits, terms and stated fees · 12

Worked answer: Plan A =$140.00+18×$40.00+$10.00=$870.00. Plan B =$100.00+24×$55.00+$20.00=$1,440.00. Plan A is lower by $570.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $570.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $890.00; recompute which full total is lower.

166. Compare deposits, terms and stated fees · 13

Worked answer: Plan A =$170.00+4×$75.00+$20.00=$490.00. Plan B =$150.00+6×$110.00+$40.00=$850.00. Plan A is lower by $360.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $360.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $510.00; recompute which full total is lower.

167. Compare deposits, terms and stated fees · 14

Worked answer: Plan A =$200.00+6×$110.00+$30.00=$890.00. Plan B =$200.00+9×$165.00+$10.00=$1,695.00. Plan A is lower by $805.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $805.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $910.00; recompute which full total is lower.

168. Compare deposits, terms and stated fees · 15

Worked answer: Plan A =$20.00+8×$145.00+$40.00=$1,220.00. Plan B =$20.00+12×$75.00+$30.00=$950.00. Plan B is lower by $270.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $270.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,240.00; recompute which full total is lower.

169. Compare deposits, terms and stated fees · 16

Worked answer: Plan A =$50.00+10×$55.00+$0.00=$600.00. Plan B =$70.00+15×$130.00+$0.00=$2,020.00. Plan A is lower by $1,420.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,420.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $620.00; recompute which full total is lower.

170. Compare deposits, terms and stated fees · 17

Worked answer: Plan A =$80.00+12×$90.00+$10.00=$1,170.00. Plan B =$120.00+18×$40.00+$20.00=$860.00. Plan B is lower by $310.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $310.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,190.00; recompute which full total is lower.

171. Compare deposits, terms and stated fees · 18

Worked answer: Plan A =$110.00+18×$125.00+$20.00=$2,380.00. Plan B =$170.00+24×$95.00+$40.00=$2,490.00. Plan A is lower by $110.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $110.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $2,400.00; recompute which full total is lower.

172. Compare deposits, terms and stated fees · 19

Worked answer: Plan A =$140.00+4×$35.00+$30.00=$310.00. Plan B =$220.00+6×$150.00+$10.00=$1,130.00. Plan A is lower by $820.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $820.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $330.00; recompute which full total is lower.

173. Compare deposits, terms and stated fees · 20

Worked answer: Plan A =$170.00+6×$70.00+$40.00=$630.00. Plan B =$40.00+9×$60.00+$30.00=$610.00. Plan B is lower by $20.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $20.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $650.00; recompute which full total is lower.

174. Compare deposits, terms and stated fees · 21

Worked answer: Plan A =$200.00+8×$105.00+$0.00=$1,040.00. Plan B =$90.00+12×$115.00+$0.00=$1,470.00. Plan A is lower by $430.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $430.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,060.00; recompute which full total is lower.

175. Compare deposits, terms and stated fees · 22

Worked answer: Plan A =$20.00+10×$140.00+$10.00=$1,430.00. Plan B =$140.00+15×$170.00+$20.00=$2,710.00. Plan A is lower by $1,280.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,280.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,450.00; recompute which full total is lower.

176. Compare deposits, terms and stated fees · 23

Worked answer: Plan A =$50.00+12×$50.00+$20.00=$670.00. Plan B =$190.00+18×$80.00+$40.00=$1,670.00. Plan A is lower by $1,000.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,000.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $690.00; recompute which full total is lower.

177. Compare deposits, terms and stated fees · 24

Worked answer: Plan A =$80.00+18×$85.00+$30.00=$1,640.00. Plan B =$10.00+24×$135.00+$10.00=$3,260.00. Plan A is lower by $1,620.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,620.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,660.00; recompute which full total is lower.

178. Compare deposits, terms and stated fees · 25

Worked answer: Plan A =$110.00+4×$120.00+$40.00=$630.00. Plan B =$60.00+6×$45.00+$30.00=$360.00. Plan B is lower by $270.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $270.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $650.00; recompute which full total is lower.

179. Compare deposits, terms and stated fees · 26

Worked answer: Plan A =$140.00+6×$30.00+$0.00=$320.00. Plan B =$110.00+9×$100.00+$0.00=$1,010.00. Plan A is lower by $690.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $690.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $340.00; recompute which full total is lower.

180. Compare deposits, terms and stated fees · 27

Worked answer: Plan A =$170.00+8×$65.00+$10.00=$700.00. Plan B =$160.00+12×$155.00+$20.00=$2,040.00. Plan A is lower by $1,340.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,340.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $720.00; recompute which full total is lower.

181. Compare deposits, terms and stated fees · 28

Worked answer: Plan A =$200.00+10×$100.00+$20.00=$1,220.00. Plan B =$210.00+15×$65.00+$40.00=$1,225.00. Plan A is lower by $5.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $5.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,240.00; recompute which full total is lower.

182. Compare deposits, terms and stated fees · 29

Worked answer: Plan A =$20.00+12×$135.00+$30.00=$1,670.00. Plan B =$30.00+18×$120.00+$10.00=$2,200.00. Plan A is lower by $530.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $530.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,690.00; recompute which full total is lower.

183. Compare deposits, terms and stated fees · 30

Worked answer: Plan A =$50.00+18×$45.00+$40.00=$900.00. Plan B =$80.00+24×$30.00+$30.00=$830.00. Plan B is lower by $70.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $70.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $920.00; recompute which full total is lower.

184. Compare deposits, terms and stated fees · 31

Worked answer: Plan A =$80.00+4×$80.00+$0.00=$400.00. Plan B =$130.00+6×$85.00+$0.00=$640.00. Plan A is lower by $240.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $240.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $420.00; recompute which full total is lower.

185. Compare deposits, terms and stated fees · 32

Worked answer: Plan A =$110.00+6×$115.00+$10.00=$810.00. Plan B =$180.00+9×$140.00+$20.00=$1,460.00. Plan A is lower by $650.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $650.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $830.00; recompute which full total is lower.

186. Compare deposits, terms and stated fees · 33

Worked answer: Plan A =$140.00+8×$150.00+$20.00=$1,360.00. Plan B =$230.00+12×$50.00+$40.00=$870.00. Plan B is lower by $490.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $490.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,380.00; recompute which full total is lower.

187. Compare deposits, terms and stated fees · 34

Worked answer: Plan A =$170.00+10×$60.00+$30.00=$800.00. Plan B =$50.00+15×$105.00+$10.00=$1,635.00. Plan A is lower by $835.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $835.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $820.00; recompute which full total is lower.

188. Compare deposits, terms and stated fees · 35

Worked answer: Plan A =$200.00+12×$95.00+$40.00=$1,380.00. Plan B =$100.00+18×$160.00+$30.00=$3,010.00. Plan A is lower by $1,630.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $1,630.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,400.00; recompute which full total is lower.

189. Compare deposits, terms and stated fees · 36

Worked answer: Plan A =$20.00+18×$130.00+$0.00=$2,360.00. Plan B =$150.00+24×$70.00+$0.00=$1,830.00. Plan B is lower by $530.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $530.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $2,380.00; recompute which full total is lower.

190. Compare deposits, terms and stated fees · 37

Worked answer: Plan A =$50.00+4×$40.00+$10.00=$220.00. Plan B =$200.00+6×$125.00+$20.00=$970.00. Plan A is lower by $750.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $750.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $240.00; recompute which full total is lower.

191. Compare deposits, terms and stated fees · 38

Worked answer: Plan A =$80.00+6×$75.00+$20.00=$550.00. Plan B =$20.00+9×$35.00+$40.00=$375.00. Plan B is lower by $175.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $175.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $570.00; recompute which full total is lower.

192. Compare deposits, terms and stated fees · 39

Worked answer: Plan A =$110.00+8×$110.00+$30.00=$1,020.00. Plan B =$70.00+12×$90.00+$10.00=$1,160.00. Plan A is lower by $140.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $140.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,040.00; recompute which full total is lower.

193. Compare deposits, terms and stated fees · 40

Worked answer: Plan A =$140.00+10×$145.00+$40.00=$1,630.00. Plan B =$120.00+15×$145.00+$30.00=$2,325.00. Plan A is lower by $695.00.

Reverse-check: Add each plan’s monthly subtotal, deposit and fee again; subtract totals to verify their difference $695.00. The comparison is conditional on these fictional complete figures.

Change one condition: Add an extra once-only $20.00 charge to Plan A while keeping all B amounts fixed. The new A total becomes $1,650.00; recompute which full total is lower.

Make a household budget arithmetic check

194. A monthly residual is not a whole-plan total · 1

Reverse-check: Reconstruct monthly income: $350.00+$30.00+($820.00)=$1,200.00. Also verify 6×$30.00+$20.00=$200.00.

195. A monthly residual is not a whole-plan total · 2

Reverse-check: Reconstruct monthly income: $600.00+$140.00+($760.00)=$1,500.00. Also verify 9×$140.00+$160.00=$1,420.00.

196. A monthly residual is not a whole-plan total · 3

Reverse-check: Reconstruct monthly income: $850.00+$40.00+($910.00)=$1,800.00. Also verify 12×$40.00+$40.00=$520.00.

197. A monthly residual is not a whole-plan total · 4

Reverse-check: Reconstruct monthly income: $1,100.00+$150.00+($850.00)=$2,100.00. Also verify 15×$150.00+$180.00=$2,430.00.

198. A monthly residual is not a whole-plan total · 5

Reverse-check: Reconstruct monthly income: $1,350.00+$50.00+($1,000.00)=$2,400.00. Also verify 18×$50.00+$60.00=$960.00.

199. A monthly residual is not a whole-plan total · 6

Reverse-check: Reconstruct monthly income: $450.00+$160.00+($2,090.00)=$2,700.00. Also verify 21×$160.00+$200.00=$3,560.00.

200. A monthly residual is not a whole-plan total · 7

Reverse-check: Reconstruct monthly income: $700.00+$60.00+($2,240.00)=$3,000.00. Also verify 24×$60.00+$80.00=$1,520.00.

201. A monthly residual is not a whole-plan total · 8

Reverse-check: Reconstruct monthly income: $950.00+$170.00+($2,180.00)=$3,300.00. Also verify 8×$170.00+$220.00=$1,580.00.

202. A monthly residual is not a whole-plan total · 9

Reverse-check: Reconstruct monthly income: $1,200.00+$70.00+($2,330.00)=$3,600.00. Also verify 11×$70.00+$100.00=$870.00.

203. A monthly residual is not a whole-plan total · 10

Reverse-check: Reconstruct monthly income: $1,450.00+$180.00+($2,270.00)=$3,900.00. Also verify 14×$180.00+$240.00=$2,760.00.

204. A monthly residual is not a whole-plan total · 11

Reverse-check: Reconstruct monthly income: $550.00+$80.00+($3,570.00)=$4,200.00. Also verify 17×$80.00+$120.00=$1,480.00.

205. A monthly residual is not a whole-plan total · 12

Reverse-check: Reconstruct monthly income: $800.00+$190.00+($310.00)=$1,300.00. Also verify 20×$190.00+$260.00=$4,060.00.

206. A monthly residual is not a whole-plan total · 13

Reverse-check: Reconstruct monthly income: $1,050.00+$90.00+($460.00)=$1,600.00. Also verify 23×$90.00+$140.00=$2,210.00.

207. A monthly residual is not a whole-plan total · 14

Reverse-check: Reconstruct monthly income: $1,300.00+$200.00+($400.00)=$1,900.00. Also verify 7×$200.00+$20.00=$1,420.00.

208. A monthly residual is not a whole-plan total · 15

Reverse-check: Reconstruct monthly income: $400.00+$100.00+($1,700.00)=$2,200.00. Also verify 10×$100.00+$160.00=$1,160.00.

209. A monthly residual is not a whole-plan total · 16

Reverse-check: Reconstruct monthly income: $650.00+$210.00+($1,640.00)=$2,500.00. Also verify 13×$210.00+$40.00=$2,770.00.

210. A monthly residual is not a whole-plan total · 17

Reverse-check: Reconstruct monthly income: $900.00+$110.00+($1,790.00)=$2,800.00. Also verify 16×$110.00+$180.00=$1,940.00.

211. A monthly residual is not a whole-plan total · 18

Reverse-check: Reconstruct monthly income: $1,150.00+$220.00+($1,730.00)=$3,100.00. Also verify 19×$220.00+$60.00=$4,240.00.

212. A monthly residual is not a whole-plan total · 19

Reverse-check: Reconstruct monthly income: $1,400.00+$120.00+($1,880.00)=$3,400.00. Also verify 22×$120.00+$200.00=$2,840.00.

213. A monthly residual is not a whole-plan total · 20

Reverse-check: Reconstruct monthly income: $500.00+$230.00+($2,970.00)=$3,700.00. Also verify 6×$230.00+$80.00=$1,460.00.

214. A monthly residual is not a whole-plan total · 21

Reverse-check: Reconstruct monthly income: $750.00+$130.00+($3,120.00)=$4,000.00. Also verify 9×$130.00+$220.00=$1,390.00.

215. A monthly residual is not a whole-plan total · 22

Reverse-check: Reconstruct monthly income: $1,000.00+$30.00+($3,270.00)=$4,300.00. Also verify 12×$30.00+$100.00=$460.00.

216. A monthly residual is not a whole-plan total · 23

Reverse-check: Reconstruct monthly income: $1,250.00+$140.00+($10.00)=$1,400.00. Also verify 15×$140.00+$240.00=$2,340.00.

217. A monthly residual is not a whole-plan total · 24

Reverse-check: Reconstruct monthly income: $350.00+$40.00+($1,310.00)=$1,700.00. Also verify 18×$40.00+$120.00=$840.00.

218. A monthly residual is not a whole-plan total · 25

Reverse-check: Reconstruct monthly income: $600.00+$150.00+($1,250.00)=$2,000.00. Also verify 21×$150.00+$260.00=$3,410.00.

219. A monthly residual is not a whole-plan total · 26

Reverse-check: Reconstruct monthly income: $850.00+$50.00+($1,400.00)=$2,300.00. Also verify 24×$50.00+$140.00=$1,340.00.

220. A monthly residual is not a whole-plan total · 27

Reverse-check: Reconstruct monthly income: $1,100.00+$160.00+($1,340.00)=$2,600.00. Also verify 8×$160.00+$20.00=$1,300.00.

221. A monthly residual is not a whole-plan total · 28

Reverse-check: Reconstruct monthly income: $1,350.00+$60.00+($1,490.00)=$2,900.00. Also verify 11×$60.00+$160.00=$820.00.

222. A monthly residual is not a whole-plan total · 29

Reverse-check: Reconstruct monthly income: $450.00+$170.00+($2,580.00)=$3,200.00. Also verify 14×$170.00+$40.00=$2,420.00.

223. A monthly residual is not a whole-plan total · 30

Reverse-check: Reconstruct monthly income: $700.00+$70.00+($2,730.00)=$3,500.00. Also verify 17×$70.00+$180.00=$1,370.00.

224. A monthly residual is not a whole-plan total · 31

Reverse-check: Reconstruct monthly income: $950.00+$180.00+($2,670.00)=$3,800.00. Also verify 20×$180.00+$60.00=$3,660.00.

225. A monthly residual is not a whole-plan total · 32

Reverse-check: Reconstruct monthly income: $1,200.00+$80.00+($2,820.00)=$4,100.00. Also verify 23×$80.00+$200.00=$2,040.00.

226. A monthly residual is not a whole-plan total · 33

Reverse-check: Reconstruct monthly income: $1,450.00+$190.00+(−$440.00)=$1,200.00. Also verify 7×$190.00+$80.00=$1,410.00.

227. A monthly residual is not a whole-plan total · 34

Reverse-check: Reconstruct monthly income: $550.00+$90.00+($860.00)=$1,500.00. Also verify 10×$90.00+$220.00=$1,120.00.

228. A monthly residual is not a whole-plan total · 35

Reverse-check: Reconstruct monthly income: $800.00+$200.00+($800.00)=$1,800.00. Also verify 13×$200.00+$100.00=$2,700.00.

229. A monthly residual is not a whole-plan total · 36

Reverse-check: Reconstruct monthly income: $1,050.00+$100.00+($950.00)=$2,100.00. Also verify 16×$100.00+$240.00=$1,840.00.

230. A monthly residual is not a whole-plan total · 37

Reverse-check: Reconstruct monthly income: $1,300.00+$210.00+($890.00)=$2,400.00. Also verify 19×$210.00+$120.00=$4,110.00.

Identify missing or misleading plan terms

231. Deposit is not the full purchase total

Question: An advertisement mentions a fictional $100 deposit but gives no term or monthly charge. Can a full total be found?

Worked answer: No. The payment count and amount remain unknown.

Common first error: Calling the deposit the final price ignores further payments.

Reverse-check: Name missing terms.

232. Small monthly versus total cost

Question: Compare $20 each month for 36 months against $35 for 18 months, no other costs.

Worked answer: First $720, second $630. Larger monthly payment has lower full total.

Common first error: Monthly amounts are not directly comparable as complete costs.

Reverse-check: 20×36=720 and 35×18=630.

233. Cash price and total plan price differ

Question: Cash $500, fictional plan $575. Difference?

Worked answer: $75 more by plan under specified terms.

Common first error: Using the cash price as though it were the monthly payment total.

Reverse-check: 575−500=75.

234. One-time fees count once

Question: Deposit 80 plus six payments of 45. Total?

Worked answer: $350.

Common first error: 80×6 repeats deposit wrongly.

Reverse-check: 80+270=350.

235. A fractional payment count is a warning

Question: Total $275, deposit $50, equal monthly payments $40. How many complete payments?

Worked answer: (275−50)/40=5.625, incompatible with an integer count of complete equal payments under the stated conditions.

Common first error: Rounding to six changes total.

Reverse-check: Six payments would total $290.

236. Deposit creates upfront cash requirement

Question: Can a small monthly amount prove a $150 deposit can be paid today?

Worked answer: No. Immediate cash availability is a separate fact not supplied.

Common first error: Monthly surplus alone doesn’t establish available deposit.

Reverse-check: State payment timing.

237. Unstated fees must not be invented

Question: The fictional problem says no other fees. Should the student add a guessed $30 late charge?

Worked answer: No. Compute only stated terms.

Common first error: Adding invented charges violates the model.

Reverse-check: Read the precise assumptions.

238. Zero interest is not zero extra fees

Question: A fictional offer advertises zero interest but has a $50 stated one-off fee. Can the fee be ignored?

Worked answer: No. The full arithmetic cost includes any stated fee.

Common first error: A marketing phrase does not override stated amounts.

Reverse-check: Add fee once.

239. Percent difference cash baseline

Question: Cash price $400, plan total $460. Percent higher relative to cash?

Worked answer: $60/$400=15%.

Common first error: Using the plan total as base answers another question.

Reverse-check: 400×1.15=460.

240. A negative difference can occur

Question: Cash $500, invented plan $470. Difference plan minus cash?

Worked answer: −$30.

Common first error: Assuming every hypothetical plan must cost more is false.

Reverse-check: 470−500=−30.

241. Overpayment is not APR

Question: Total plan exceeds cash by $100. Does this reveal effective yearly interest rate?

Worked answer: No. Timing, financed principal and charges matter.

Common first error: Percentage overpayment is not automatically annualised cost.

Reverse-check: Identify cash flows and dates.

242. Exact due dates need a start date

Question: Ten monthly payments listed, no first due date. Can their calendar dates be known?

Worked answer: No. Actual dates require the starting date and terms.

Common first error: Inventing dates from count alone is invalid.

Reverse-check: Request payment schedule.

243. A positive residual is not guaranteed saving

Question: Monthly budget has $500 available and payment $480. Is $20 guaranteed saved?

Worked answer: No. It is only the residual before all other needs.

Common first error: Limited budget categories may omit expenses.

Reverse-check: 500−480=20 mathematically.

244. Deposit as share of cash price

Question: Deposit $120 and cash quote $800. What percent is deposit of cash?

Worked answer: 15%.

Common first error: The base is $800, not $120.

Reverse-check: 120/800=0.15.

245. Change deposit with unchanged total

Question: Total $600 over ten monthly payments; deposit rises $100 to $150. Find new monthly amount.

Worked answer: (600−150)/10=$45.

Common first error: Treating monthly amount as unchanged would increase total.

Reverse-check: 150+450=600.

246. Payment frequency matters

Question: $60 every two months for twelve months, with a payment after each period. Total?

Worked answer: Six payments, $360.

Common first error: Twelve payments assumes monthly frequency not given.

Reverse-check: 12/2=6.

247. Annual fee is once per year

Question: One $24 annual fee and 12 monthly $10 payments. Total one year?

Worked answer: $144.

Common first error: 24×12 charges annual fee each month.

Reverse-check: 24+120=144.

248. Identical full totals with different timing

Question: A: $100+6×$50, B: $40+12×$30. Compare totals.

Worked answer: Both $400, though payment timing differs.

Common first error: Equal total does not imply identical monthly burden.

Reverse-check: 100+300=40+360.

249. Instalment minus cash

Question: Cash $560; plan $100+12×$40. Difference?

Worked answer: Plan $580, $20 above cash.

Common first error: Comparing $40 with $560 ignores term and deposit.

Reverse-check: 100+480=580.

250. Deposit discount changes the deposit

Question: Deposit $100 is discounted 20%, monthly charges unchanged. Total reduction?

Worked answer: $20.

Common first error: Applying 20% to entire plan changes percentage base.

Reverse-check: 0.2×100=20.

251. No deposit plan

Question: Zero deposit and eight $65 payments. Total?

Worked answer: $520.

Common first error: Adding an imaginary deposit changes the question.

Reverse-check: 8×65=520.

252. Label monthly count and monetary amount

Question: A calculation gives 6 payments of $40. Which value is dollars and which a count?

Worked answer: $40 is money per payment; six is the number of payments; total $240.

Common first error: Switching units can make a seemingly correct answer unclear.

Reverse-check: 6×$40=$240.

253. Negative budget residual

Question: Income $1000, commitments $900, plan payment $150. Residual?

Worked answer: −$50 in simplified monthly budget.

Common first error: A negative residual cannot be called an available surplus.

Reverse-check: 1000−900−150=−50.

254. Decimal-dollar payments

Question: Deposit $25.50 and three $19.95 payments. Full total?

Worked answer: $85.35.

Common first error: Rounding each before multiplication changes pennies.

Reverse-check: 25.50+59.85=85.35.

255. Recover monthly from total

Question: Total $900 includes deposit $180 and 12 equal monthly payments. Find each.

Worked answer: $60.

Common first error: $900/12 includes deposit incorrectly.

Reverse-check: 180+12×60=900.

256. Actual terms need current verification

Question: Can one select a real finance provider solely from two made-up classroom totals?

Worked answer: No. It is a numerical illustration, not a real-world recommendation.

Common first error: Terms, fees and conditions may differ.

Reverse-check: Check current written terms.

257. Identical monthly, different deposit

Question: Two plans both pay $30/month over 12 months; deposits $50 and $100. Compare totals.

Worked answer: $410 versus $460.

Common first error: Same monthly number does not mean same overall total.

Reverse-check: 360+50 vs 360+100.

258. Longer term with unchanged monthly cost

Question: Deposit $100 and payment $40, terms 12 and 18 months. Compare totals.

Worked answer: $580 versus $820, difference $240.

Common first error: More payments at same amount increase total.

Reverse-check: 40×6=240 extra.

259. Currency units must match

Question: Deposit quoted SGD and payments in another currency, no FX rate. Can exact SGD total be found?

Worked answer: No. A conversion rate is necessary.

Common first error: Adding numbers in different currencies is invalid.

Reverse-check: Identify missing exchange information.

260. Cash price does not determine monthly schedule

Question: Only cash price $1000 is given. Can monthly instalment be calculated?

Worked answer: No. Term, deposit and charges are unspecified.

Common first error: Assuming twelve months invents data.

Reverse-check: Request schedule.

261. Final balloon payment counts

Question: Ten payments $30 plus final separately stated $100 balloon. Full total?

Worked answer: $400.

Common first error: Omitting final special charge understates total.

Reverse-check: 300+100=400.

262. Ignore tax only if stated

Question: A fictional Maths question says ignore tax. Add an estimated local sales tax?

Worked answer: No. Follow the written assumption.

Common first error: Invented tax changes the scenario.

Reverse-check: Use stated costs.

263. APR cannot be inferred from simple overpayment

Question: Plan total is 12% higher than cash. Is annual percentage rate 12%?

Worked answer: Not necessarily. Time, principal and payments matter.

Common first error: Equating simple total comparison with annual rate is wrong.

Reverse-check: Define difference separately.

264. Equal dollar totals but different cash flows

Question: Is $500 cash at once identical in timing to ten monthly $50 payments?

Worked answer: No. Arithmetic totals match but timing differs.

Common first error: A total-only comparison omits timing.

Reverse-check: State totals and dates separately.

265. Advertised starting price can be incomplete

Question: A headline says ‘from $20/month’ but no term. Does it fix the full total?

Worked answer: No. Payment count and fees remain missing.

Common first error: Multiplying by a guessed term invents terms.

Reverse-check: Request complete schedule.

266. Rounding payments changes exact totals

Question: Six $49.99 instalments total what?

Worked answer: $299.94.

Common first error: Rounding to $50 before multiplying inflates six cents.

Reverse-check: 6×49.99=299.94.

267. Full total is not the same as affordability

Question: Two plans total $500 and $480. Which has lower numerical cost?

Worked answer: The $480 plan, by $20; this does not prove personal affordability.

Common first error: Conflating a numeric comparison with a personal finance decision is wrong.

Reverse-check: 480<500.

268. Missing contract details

Question: No cancellation rule is given. Can the pupil calculate a cancellation fee?

Worked answer: No. Missing rules prevent that calculation.

Common first error: Assuming imaginary penalties is not valid.

Reverse-check: Ask for written terms.

269. The question’s percentage base matters

Question: Plan total $600 vs cash $250. Total as % of cash?

Worked answer: 240%.

Common first error: Assuming every percentage must be under 100 is wrong for comparing different quantities.

Reverse-check: 600/250=2.4.

270. A deposit could be handled differently in contracts

Question: Can a maths solution assume an unstated deposit is refundable?

Worked answer: No. A specific real agreement would need terms; these examples treat deposits as paid within total.

Common first error: Assuming refund changes arithmetic.

Reverse-check: State whether refundable.

271. Monthly cost versus total fee

Question: Two offers with $20 and $30 monthly, missing lengths. Is the cheaper total known?

Worked answer: No. Counts of payments are missing.

Common first error: Smaller monthly does not determine full total.

Reverse-check: Give possible terms that reverse comparison.

272. Multiple payment schedules

Question: A fee $50 once plus two semiannual payments $100. Total?

Worked answer: $250.

Common first error: Calling them monthly changes frequency.

Reverse-check: 50+200=250.

273. Cash savings are not automatically profit

Question: Income $3000, known expenses $2500. Is $500 certain savings?

Worked answer: No. It is a limited residual before omitted needs.

Common first error: Incomplete budget doesn’t establish exact savings.

Reverse-check: Name assumptions.

274. Fictional amounts are not commercial quotes

Question: Are the article’s examples real deals?

Worked answer: No. They are invented G1 Mathematics problems.

Common first error: Treating a classroom payment as an offer misinforms.

Reverse-check: Check real sources separately.

275. A deposit changes the upfront burden

Question: Why might two equal-total plans feel different?

Worked answer: Their deposits and payment timing may differ.

Common first error: Full total alone does not describe the schedule.

Reverse-check: List upfront and repeated amounts.

276. One-time fees must appear once

Question: Deposit $50, 5 monthly $100, admin fee $20 once. Total?

Worked answer: $570.

Common first error: Multiplying admin fee by five is wrong.

Reverse-check: 50+500+20=570.

277. Student focus is interpretation, not real financing

Question: What should a learner explain after comparing schedules?

Worked answer: Which full total is lower under the stated amounts and which assumptions limit the comparison.

Common first error: Claims about real providers, credit eligibility or suitability exceed the classroom data.

Reverse-check: State conditional result.

278. A total overpayment may be negative in a fictional example

Question: Cash $800, plan $750. Is total difference negative?

Worked answer: Yes, −$50 plan-minus-cash.

Common first error: There is no rule that all imaginary instalment totals must exceed cash.

Reverse-check: 750−800=−50.

279. Count payments rather than visual calendar boxes

Question: A schedule has monthly payments from month 1 through month 12 inclusive. How many?

Worked answer: Twelve payments.

Common first error: Counting 11 gaps instead of 12 named months is wrong.

Reverse-check: List months 1–12.

280. Budget questions can use exact cents

Question: Monthly net $1200.50 and stated expense $300.25. Residual?

Worked answer: $900.25 before all other needs.

Common first error: Dropping cents prematurely changes exact sum.

Reverse-check: 1200.50−300.25=900.25.

281. The payee and payer roles differ

Question: Is ‘amount received’ always identical to ‘amount paid by buyer’ in an unstated financing model?

Worked answer: Not necessarily; fees and counterparties may change cash flows. State the perspective.

Common first error: Inventing a one-to-one transfer assumption may be misleading.

Reverse-check: Identify whose total is requested.

282. Compare actual unit of rate

Question: Monthly amount $25 per month, 12 months. What is the repeated total?

Worked answer: $300.

Common first error: Leaving rate at $25 without multiplying count misses duration.

Reverse-check: 25×12=300.

How a three-pupil Maths tutorial could teach full-cost thinking

10 minutes: identify deposit, per-period charge, number of periods and any one-time fee.
20 minutes: build a payment schedule as blocks and a one-variable equation.
25 minutes: solve full totals and reverse questions individually.
15 minutes: compare two fictional complete schedules.
10 minutes: spot one missing term or unjustified inference.
10 minutes: reverse-check the total and choose a short delayed retest.

Five manageable parent practice sessions

Day one: add one deposit to a multiplied number of monthly payments.
Day two: compare a plan’s full total against a supplied cash price.
Day three: find the unknown monthly payment from the complete sum.
Day four: compare two made-up terms, including one stated once-only fee.
Day five: explain why ‘lowest monthly payment’ and ‘lowest full cost’ do not mean the same thing.

Frequently asked questions

How do I find total paid?

Add the deposit once, every scheduled periodic payment and any other separately stated amount under the specified terms.

Is a lower monthly payment always cheaper?

No. The number of payments, deposit and fees can alter the full total.

How do I find an unknown monthly payment?

Subtract once-only charges from the complete stated total and divide by the number of equal payments.

Does overpaying the cash price tell us APR?

No. Annualised financing rates require more detailed cash-flow and financing assumptions.

Are these genuine offers or personal advice?

No. Every plan in this guide is fictional and used only for mathematical literacy.

Are instalments mentioned in G1 Mathematics?

The 2027 K110 graduating syllabus names instalments as a possible household-finance context. Current year-level teaching depends on the school.

Official syllabus and accuracy notes

Take one school-style payment-schedule question to eduKate Singapore and ask the tutor to show how once-only and repeated terms lead to a complete total without misreading the monthly headline.

Secondary 2 G1 Mathematics Tutor Bukit Timah | Instalment Plans, Deposits and Total Cost

Official syllabus and accuracy notes

Official syllabus and accuracy notes

Frequently asked questions

How do I find total paid?

Is a lower monthly payment always cheaper?

How do I find an unknown monthly payment?

Does overpaying the cash price tell us APR?

Are these genuine offers or personal advice?

Are instalments mentioned in G1 Mathematics?

Other Secondary 2 G1 Mathematics resources

Official syllabus and accuracy notes

Frequently asked questions

How do I find total paid?

Is a lower monthly payment always cheaper?

How do I find an unknown monthly payment?

Does overpaying the cash price tell us APR?

Are these genuine offers or personal advice?

Are instalments mentioned in G1 Mathematics?

Other Secondary 2 G1 Mathematics resources

Official syllabus and accuracy notes

Five manageable parent practice sessions

Frequently asked questions

How do I find total paid?

Is a lower monthly payment always cheaper?

How do I find an unknown monthly payment?

Does overpaying the cash price tell us APR?

Are these genuine offers or personal advice?

Are instalments mentioned in G1 Mathematics?

Other Secondary 2 G1 Mathematics resources

Official syllabus and accuracy notes

Five manageable parent practice sessions

Frequently asked questions

How do I find total paid?

Is a lower monthly payment always cheaper?

How do I find an unknown monthly payment?

Does overpaying the cash price tell us APR?

Are these genuine offers or personal advice?

Are instalments mentioned in G1 Mathematics?

Other Secondary 2 G1 Mathematics resources

Official syllabus and accuracy notes

Which option has the lower full total?

A deposit has a different time role from a monthly fee

Lower total and easier cash flow are different questions

282 original instalment cost and comparison clinics

Complete a deposit-plus-payments total

1. One deposit and 3 repeated payments · 1

2. One deposit and 4 repeated payments · 2

3. One deposit and 6 repeated payments · 3

4. One deposit and 8 repeated payments · 4

5. One deposit and 10 repeated payments · 5

6. One deposit and 12 repeated payments · 6

7. One deposit and 15 repeated payments · 7

8. One deposit and 18 repeated payments · 8

9. One deposit and 24 repeated payments · 9

10. One deposit and 3 repeated payments · 10

11. One deposit and 4 repeated payments · 11

12. One deposit and 6 repeated payments · 12

13. One deposit and 8 repeated payments · 13

14. One deposit and 10 repeated payments · 14

15. One deposit and 12 repeated payments · 15

16. One deposit and 15 repeated payments · 16

17. One deposit and 18 repeated payments · 17

18. One deposit and 24 repeated payments · 18

19. One deposit and 3 repeated payments · 19

20. One deposit and 4 repeated payments · 20

21. One deposit and 6 repeated payments · 21

22. One deposit and 8 repeated payments · 22

23. One deposit and 10 repeated payments · 23

24. One deposit and 12 repeated payments · 24

25. One deposit and 15 repeated payments · 25

26. One deposit and 18 repeated payments · 26

27. One deposit and 24 repeated payments · 27

28. One deposit and 3 repeated payments · 28

29. One deposit and 4 repeated payments · 29

30. One deposit and 6 repeated payments · 30

31. One deposit and 8 repeated payments · 31

32. One deposit and 10 repeated payments · 32

33. One deposit and 12 repeated payments · 33

34. One deposit and 15 repeated payments · 34