How to Learn Mortgage Interest Calculations Quickly and Correctly

How does a bank calculate the interest on a home loan, and why can your monthly mortgage payment stay the same even though the interest portion changes? The key is to distinguish the outstanding principal, the interest rate and the period for which interest is charged. In this eduKateSG Quick Notes lesson, we will use an imaginary S$300,000 mortgage to explain monthly reducing-balance interest, compare it with an illustrative daily-accrual calculation and show how an interest-rate change affects what you owe. You can learn the core mathematics without applying for a mortgage.

Start with principal: calculate interest on the applicable outstanding loan balance, not automatically the original loan amount.
Read the rate: 3% per annum means an annual rate, not a 3% monthly charge.
Read the period: interest calculations can use monthly-rest or a contractually specified daily basis.
Separate payment parts: an instalment can include both interest expense and repayment of principal.
Check the reset: floating interest and some promotional periods can change the rate.
Trust the contract: the bank’s precise day-count rules, fees and repayment schedule govern actual amounts.

Teaching paragraph 1 — calculate the first month’s interest. Imagine a fictional S$300,000 home loan, a constant annual rate of 3% and a conventional monthly-rest calculation. Convert 3% to the decimal 0.03, divide by twelve and multiply by the balance: S$300,000 × 0.03 ÷ 12 = S$750. That is the interest for one modelled month. If the instalment for this fictional 25-year mortgage is about S$1,422.63, the remaining S$672.63 of the instalment reduces principal. The next balance is approximately S$299,327.37. The critical idea is that the same payment has two different jobs.

Teaching paragraph 2 — calculate interest on the new balance. Under the same simplified monthly-rest assumptions, the next month’s interest uses the smaller balance: S$299,327.37 × 0.03 ÷ 12 ≈ S$748.32. The interest portion is now about S$1.68 less than the previous month; consequently, approximately S$674.32 of the unchanged monthly instalment goes toward principal. This is why a standard amortising mortgage gradually changes the composition of each repayment. If you keep charging 3% on the original S$300,000 every year, you are doing a different calculation and will misread a reducing-balance mortgage.

Teaching paragraph 3 — recognise the limits of the shortcut. The Singapore MoneySense home-loan guide identifies monthly reducing, or monthly rest, as a common approach. But an actual mortgage can use contractually defined calendar-day accrual, disbursement dates, rate resets, irregular first payment periods or charges. For example, under a purely illustrative actual/365 simple daily interest calculation, S$300,000 at 3% for 31 days produces approximately S$764.38 before repayment, compared with S$739.73 for 30 days. These are teaching examples of a daily-basis method, not alternative guaranteed DBS, OCBC, HDB or other bank bills. Read the loan’s interest clause and rely on the lender’s actual statement for an exact charge.

The Four Inputs in an Interest Calculation

For the basic monthly-rest classroom model, write monthly interest = principal × annual decimal rate ÷ 12. For a simple daily-accrual illustration using a 365-day basis, write interest = principal × annual decimal rate × number of days ÷ 365. The second formula assumes the balance and rate remain unchanged during those days. Real lenders may use a different day-count convention, leap-year basis or daily-balance changes, so these formulas are not universal payment instructions.

Always label units. A figure of 3% p.a. is per year, even when a monthly payment is due. The symbol % means divide by 100; 3% is 0.03, not the whole number 3.

Principal (P): the applicable amount outstanding during the interest period.
Annual rate (r): the stated percentage per annum, converted to a decimal for calculations.
Time: one month, a number of calendar days, or another contractual calculation interval.
Method: monthly rest, daily accrual, or a specified alternative under the agreement.

Worked Example: Two Consecutive Months

Assume S$300,000 borrowed at an unchanging 3% annual rate, a 25-year fully amortising term and a monthly-rest model. The calculated monthly instalment is about S$1,422.63. First period: interest S$750.00; principal paid S$672.63; balance approximately S$299,327.37. Second period: interest approximately S$748.32; principal paid approximately S$674.32; balance approximately S$298,653.05.

Notice the pattern: total monthly payment remains broadly unchanged, but interest declines as the principal declines. Rounded instalments in actual bank statements can produce minor rounding differences. The full mortgage schedule may also include a different first repayment date or rate resets that make this simple pattern less regular.

An accurate learner should be able to explain the running balance without using complicated algebra: old principal − principal repaid = new principal. That new principal is the starting point for the next appropriate interest calculation.

Daily Accrual Versus Monthly Rest

Some mortgage documents describe interest in terms of the actual number of days elapsed. A daily calculation is sensitive to the precise disbursement, repayment and settlement dates and may use a particular convention for leap years. Monthly rest is a common method that calculates using the outstanding principal at an agreed periodic rest. These terms describe calculation conventions, not two universally interchangeable products.

For a fictional S$300,000 balance at 3% using an assumed 365-day basis, 30 days of simple accrual comes to about S$739.73, while 31 days produces about S$764.38. This does not mean a real bank changes your scheduled monthly instalment to exactly those amounts; scheduled instalments also contain principal, and bank methods may differ. The loan agreement is the document to consult.

Ask your lender: Is interest calculated daily or at monthly rest? What day-count denominator applies? When is an extra principal payment recognised? How is the first instalment handled? A precise question is more useful than guessing from the words ‘per annum’ alone.

What Happens When a Floating Rate Changes?

Suppose the same fictional S$300,000 balance had an annual rate of 3%, then the applicable rate became 4% at an allowed reset date, with the same balance held constant solely for this illustration. The one-month interest proxy changes from S$750 to S$1,000, an additional S$250 for that modelled period. This is an interest comparison, not the actual increase in instalment on a partially repaid mortgage.

In real life, the remaining principal and repayment term have changed by the time a later rate resets. The lender recalculates according to the contractual formula. Floating packages may use a compounded SORA benchmark plus a spread or another reference rate. Some bank packages change the margin when an introductory period ends. Find both the benchmark reset and the margin schedule, rather than assuming a headline rate is permanent.

The MoneySense SORA guide explains why compounded SORA averages overnight rates over a period, and MAS describes its benchmark administration. A daily published SORA value is not automatically the rate charged by your individual mortgage.

What Is Effective Interest Rate?

An effective interest rate (EIR) is a way to express borrowing cost on an annualised basis using the relevant cash flows and timing. A quoted nominal annual interest percentage is not the same concept as the EIR on every loan. Fees, how and when payments occur, and the interest calculation method can affect the comparison.

MoneySense’s Costs of Borrowing guide distinguishes flat-rate loans, monthly-rest interest and EIR. The ABS consumer guide to home loans discusses EIR and the need to review the residential property loan fact sheet.

Do not divide a single month’s interest by the original principal and label the result the whole mortgage’s EIR. Compare the actual schedule and disclosures using the same loan term and funding assumptions.

Interest Versus Principal: Why This Matters in Real Life

Suppose a household has spare cash and wants to make a S$10,000 extra capital payment. At a fictional 3% annual monthly-rest rate, reducing principal by S$10,000 lowers the immediate simple monthly interest proxy by S$25. That does not guarantee a fixed S$25 saving every future month. The lender may adjust the schedule, rate resets may occur and a prepayment penalty may apply. Check the real net effect before paying.

Interest: the cost of borrowing money during the applicable period.
Principal: the amount of debt you still owe.
Principal reduction: repayment that reduces the base on which future interest is calculated.
Extra prepayment: a contractually permitted additional principal reduction, potentially lowering future interest.
Rate rise: higher interest can reduce how much of a given instalment goes to principal or require a revised instalment.

How to Read a Bank Mortgage Statement

If the closing principal does not match a simple calculation, look for rounding, additional disbursements, interest adjustments, fees, payment date differences and the bank’s exact interest convention. A small discrepancy is a reason to ask a precise question, not evidence by itself of wrongdoing.

Find the opening principal balance and the period covered.
Identify the annual interest rate actually applied for that period.
Locate the amount charged as interest and any separate fees.
Find the total instalment paid and the portion applied to principal.
Check the closing principal and any prepayment or adjustment.
Read any pending rate reset, changed instalment or loan-package notice.

Try a Ten-Minute Mortgage Interest Lesson

Minutes 1–2: write ‘principal’, ‘annual rate’, ‘time’ and ‘method’ on a page.
Minutes 3–4: calculate S$300,000 × 3% ÷ 12.
Minutes 5–6: subtract the S$750 interest from the fictional S$1,422.63 instalment.
Minutes 7–8: calculate interest on the reduced S$299,327.37 balance.
Minute 9: explain how a 31-day daily-accrual example differs from monthly rest.
Minute 10: say why the bank’s actual rate, day-count rule and repayment schedule matter.

Check Your Understanding

Question 1: At 3% p.a. and a constant S$100,000 balance, what is the simplified monthly-rest interest? Answer: S$250.

Question 2: In the fictional S$300,000 example, how much of the first S$1,422.63 instalment reduces principal? Answer: About S$672.63.

Question 3: Does a floating loan’s reference rate necessarily stay constant for 25 years? Answer: No.

Question 4: Is a mortgage EIR always identical to the nominal annual rate? Answer: No. The method and timing of the cash flows matter.

Question 5: What is the correct source for a real interest charge? Answer: The actual bank contract, interest schedule and statement.

Common Mistakes and Quick Corrections

Multiplying the balance by 3 instead of by 0.03 for a 3% rate.
Using the original loan balance for every period after principal has been repaid.
Treating an interest-only number as the full mortgage instalment.
Assuming all banks use the same daily day-count calculation.
Using an example SORA rate as though it were the current published benchmark.
Treating introductory rates or monthly payments as guaranteed for the entire mortgage.
Comparing loans using nominal interest percentages alone.

Original Sources and Final Rule

Reliable sources: MoneySense: How Home Loans Work, MoneySense: Costs of Borrowing, MAS: SORA Interest Rate Benchmark and the ABS guide to home loans. All rates, balances and instalments in this lesson are hypothetical educational numbers, not loan quotes. Final rule: rate × actual balance × correct time, checked against the contract.