PSLE Mathematics Learning Guide · Guide 46
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GST and annual-interest problems are percentage problems with named contexts. The labels may sound financial, but the mathematical control remains the same: identify the base quantity, identify the stated percentage rate, calculate the percentage amount, then decide whether that amount is added to or compared with the base.
This guide does not assume a real-world tax rate or model a particular bank product. Use the rate and rules stated in the question. The worked examples deliberately use invented rates so the mathematics remains separate from changing policy or commercial terms.
This guide builds one habit: write “percentage of what?” before multiplying, keep the percentage amount separate from the final total, and reverse from the final percentage state only when the problem gives enough information.
Guide 21 develops percentage change and discount more broadly. This page owns two narrower applications—GST and annual interest—without replacing that general percentage owner.
The MOE Primary Mathematics syllabus updated October 2025 provides curriculum context. All examples here are original eduKate teaching material.
GST amount is a percentage of the price base named by the problem
A problem states that an item costs $80 before GST and GST is 10%.
GST amount = 10% of $80 = $8.
Price including GST = $80 + $8 = $88.
The 10% applies to the stated pre-GST price. It does not apply to the already increased $88.
Convert the final state into a percentage of the base
If GST is 10% of the pre-GST price, the final price is:
100% + 10% = 110% of the pre-GST price.
Therefore an $80 pre-GST price can also be calculated as:
110% × $80 = 1.10 × $80 = $88.
Both methods are equivalent.
Reverse from an including-GST price carefully
A problem states that a price including 10% GST is $132. Find the pre-GST price.
$132 represents 110% of the pre-GST price.
Pre-GST price = 132 ÷ 1.10 = $120.
Check: 10% of 120 = 12, and 120 + 12 = 132.
Subtracting 10% of 132 would be wrong because the 10% was defined from the smaller pre-GST base, not from the final $132.
Find the taxable base before finding the percentage when the problem requires a total
Three identical items cost $25 each before GST. A stated GST rate is 8%.
Pre-GST total = 3 × 25 = $75.
GST = 8% of 75 = $6.
Final total = $81.
Another valid method calculates the GST on one item and multiplies by three, provided the same rate applies uniformly and there is no rounding issue introduced by the question.
When several percentage steps occur, track the state in order
An item costs $200. A stated 20% discount is applied, then 10% GST is applied to the discounted price.
After discount: 80% of 200 = $160.
GST = 10% of $160 = $16.
Final price = $176.
The GST base is $160 in this problem because the question states it applies after the discount. Do not add 20% and 10% to create a single 30% change.
Annual interest is also a percentage of a stated base
A school-style problem says $500 earns simple annual interest at 4% for one year.
Interest for one year = 4% of $500 = $20.
Amount after one year = $500 + $20 = $520.
Here $500 is the principal—the base amount on which the stated annual rate is calculated.
Follow the interest model stated in the problem
If a problem explicitly uses simple annual interest of 4% on an unchanged $500 principal for three years:
Interest per year = $20.
Three-year interest = 3 × $20 = $60.
Final amount = $560.
This is a simplified mathematical model. Real financial products may calculate interest differently. Use the problem’s stated rule rather than importing an external banking assumption.
Do not silently compound a simple-interest question
If the question says simple annual interest remains based on the original principal, Year 2 interest is still a percentage of the original principal.
For $1000 at simple 5% annually:
interest each year = $50.
After two years, total interest = $100 and final amount = $1100.
Calculating 5% of $1050 in Year 2 would introduce compounding that the stated model did not request.
Recover the principal from one year’s interest
A problem says one year’s interest is $36 at 6% simple annual interest. Find the principal.
6% of principal = $36.
1% = 36 ÷ 6 = $6.
100% = $600.
Principal = $600.
Check: 6% of 600 = 36.
Recover the rate when principal and interest are known
A one-year simple-interest problem gives principal $800 and interest $40.
Rate = 40/800 × 100% = 5%.
The denominator is the principal because the interest is being compared with its base.
Keep three quantities separate
For an interest problem, distinguish:
- principal — original base amount;
- interest — percentage amount earned under the stated model;
- final amount — principal plus interest.
For a GST problem, distinguish:
- pre-GST price — base;
- GST amount — percentage amount;
- including-GST price — base plus GST.
Many errors come from calculating one of these correctly and reporting it as another.
Main worked workshop: sixteen original percentage-application problems
1.
An item costs $60 before a stated 5% GST. Find GST.
Answer: $3.
2.
Using Problem 1, find including-GST price.
Answer: $63.
3.
An item costs $250 before a stated 8% GST. Find final price.
Answer: $270.
4.
A final price of $220 includes stated 10% GST. Find pre-GST price.
Answer: $200.
5.
Four items cost $30 each before stated 5% GST. Find total including GST.
Answer: base $120; GST $6; final $126.
6.
A $150 item is discounted 20%, then stated 5% GST applies to the discounted price.
Answer: $150→$120→$126.
7.
Simple annual interest: $400 at 3% for one year. Interest?
Answer: $12.
8.
Using Problem 7, final amount?
Answer: $412.
9.
Simple annual interest: $900 at 4% for two years, based on original principal each year.
Answer: $36 per year; $72 total interest; final $972.
10.
One-year interest is $45 at 5%. Find principal.
Answer: $900.
11.
Principal $750 earns $30 simple interest in one year. Find rate.
Answer: 4%.
12.
A learner says 10% GST on a $90 pre-GST price gives final price $99, then adds another 10% because “GST is 10%”.
Repair: GST is added once under the stated problem. Final is $99.
13.
A learner reverses $132 including 10% GST by calculating 132 − 13.20.
Repair: $132 is 110%; divide by 1.10 to get $120.
14.
A learner calculates Year 2 simple interest using the Year 1 final amount.
Repair: if the problem states simple interest on original principal, the base stays unchanged.
15.
A $500 principal earns $75 simple interest over three years. Find annual interest amount and annual rate.
Reasoning: $25/year; 25/500=5% per year.
16.
A stated 12% GST amount is $24. Find the pre-GST base.
Answer: $200.
A percentage-application decision card
| Known | Required | Relationship |
|---|---|---|
| base + rate | percentage amount | rate × base |
| base + rate | final after addition | (100% + rate) × base |
| final + rate | base | final ÷ final percentage state |
| principal + interest | rate | interest ÷ principal × 100% |
| rate + interest | principal | interest ÷ rate-as-decimal |
Handle money rounding only as the task directs
Some percentage calculations may produce more than two decimal places. Follow the problem’s stated rounding instruction or school convention for that task.
Do not round an intermediate value early unless required. Early rounding can change a later total.
Guide 16 develops exact-versus-estimated and rounding control more broadly.
Common GST and interest errors
Error 1: apply the percentage to the wrong base.
Error 2: report the GST or interest amount when the question asks for final amount.
Error 3: reverse a percentage addition by subtracting the same percentage from the final amount.
Error 4: combine successive percentage changes by simply adding rates when the bases change.
Error 5: introduce compound interest when the problem states a simple-interest model.
Independent transfer check
- $140 before stated 5% GST. Find GST and final price.
- $324 includes stated 8% GST. Find pre-GST price.
- A $250 item is discounted 20%, then stated 6% GST applies. Find final price.
- $600 at simple 5% annual interest for one year. Find interest and final amount.
- $600 at simple 5% annual interest for four years, based on original principal each year. Find total interest.
- One year’s interest is $42 at 7%. Find principal.
- Principal is $1200 and one-year simple interest is $72. Find annual rate.
- Explain why a final price including 10% GST represents 110% of the pre-GST price, not 90%.
Independent-check answers
1. GST $7; final $147.
2. 324 ÷ 1.08 = $300.
3. $250→$200→$212.
4. $30 interest; $630 final.
5. $120.
6. $600.
7. 6%.
8. The original base is 100%; adding 10% makes the final state 110%.
Parent and tutor guide
Ask the learner to label every money value as base, percentage amount or final amount. Do not allow an unlabeled dollar answer in practice until the state distinction is secure.
For reverse problems, write the final percentage state first. “Including 8% means 108%.” Then solve from that relationship rather than memorising a reverse formula.
For annual interest, underline the model word in the problem. If it says simple interest on the original principal, keep that base fixed across years.
The learner’s final card
Percentage of what? Is this the percentage amount or the final total? What percentage of the original does the final state represent? For annual interest, does the problem keep the original principal as the base?
Continue through Batch 12
Use Guide 45: Division as Fraction or Decimal Quotients. Continue with Guide 47: Unit Cubes and Isometric Solids and Guide 48: Rectangular Tank Liquid Levels.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
All rates and financial scenarios in this guide are invented teaching examples. They do not state current tax policy, bank rates or product terms. Follow the rate and interest model explicitly given in the learner’s actual mathematics question.