You don’t need a degree in finance to understand how your loan repayment is calculated. The maths behind every level-repayment loan — home loans, vehicle finance, personal loans — is one formula, and this guide walks through it with a complete worked example.
The three inputs
Every loan repayment depends on three numbers:
- Principal (P) — the amount you borrow.
- Interest rate — your annual rate, e.g. 10% p.a.
- Term — how many months you’ll repay over.
Step 1: Convert the annual rate to monthly
Interest is quoted per year, but loans charge monthly. Divide the annual rate by 12.
A 10% p.a. loan → 10 ÷ 12 = 0.8333% per month. As a decimal for the formula: 0.008333.
Step 2: Count the months
A 5-year loan → 5 × 12 = 60 months.
Step 3: Apply the formula
The standard amortisation formula for a level monthly payment is:
Monthly payment = P × r ÷ (1 − (1 + r)^−n)
where P is the principal, r is the monthly rate as a decimal, and n is the number of months.
Worked example: R100,000 at 10% over 5 years
- P = 100,000
- r = 0.10 ÷ 12 = 0.008333
- n = 60
Monthly payment = 100,000 × 0.008333 ÷ (1 − 1.008333^−60) = R2,124.70
| Result | Amount |
|---|---|
| Monthly repayment | R2,124.70 |
| Total repaid (60 × R2,124.70) | R127,482.00 |
| Total interest | R27,482.00 |
A useful sanity check: with a positive interest rate and no fees or balloon payment, the monthly payment is greater than the zero-interest amount of principal divided by months (R1,666.67 here). At zero interest, they are equal. Do not estimate a short loan by adding a full month’s interest to every payment: interest falls as the balance is repaid.
Step 4: Understand what the payment does
Each month, interest is charged on the current balance, and the rest of the payment reduces the principal:
- Month 1: interest = 100,000 × 0.008333 = R833.33; principal = 2,124.70 − 833.33 = R1,291.37; new balance R98,708.63.
- Month 2: interest is now charged on the smaller balance: 98,708.63 × 0.008333 = R822.57, so R1,302.13 goes to principal.
The payment never changes, but the split does — more principal each month, less interest. By the end, the balance reaches exactly zero.
How to check a lender’s quote
Your lender’s written quote shows the same three numbers (amount, rate, term) plus anything the formula can’t see: initiation fees, monthly service fees and credit insurance. To check the quote:
- Run the loan repayment calculator with the quoted amount, rate and term.
- Compare the result to the quote’s interest-and-principal line.
- Add the fee lines separately — the difference between your number and theirs should be exactly the fees.
If the quote’s repayment is higher than the formula says and the difference isn’t the fees, ask the lender to explain — under the National Credit Act, every charge must be itemised in the agreement.
When the formula doesn’t apply
- Variable rates — “prime plus” loans move when the repo rate moves, so the payment changes even though the formula stays the same.
- Balloon payments — some vehicle finance deals defer a big portion of the principal to the end, which lowers monthly payments but leaves you with a large final payment.
- Interest-only periods — rare, but some agreements charge interest for a period with no principal being paid.
For each of these, ask for the full repayment schedule in writing before you sign. The calculator gives a mathematical estimate and shows the first year’s schedule. To understand the rate itself, read how loan interest works.