Effect of Repayments
See how repayments change a loan for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-03). On a reducing balance loan, anything that makes the balance smaller sooner means less interest is charged, so the loan is repaid faster and costs less — even though the interest rate stays the same.
You will see what happens to the length and total cost of a loan when you pay more often, pay extra each period or make a one-off lump-sum payment, using tables and graphs of the balance owing — useful advice for anyone paying off a car or personal loan.
Theory
The effect of repayments on a loan is part of the Depreciation and loans topic in Year 12 Standard 1 (NSW). Paying more, paying earlier or paying more often lowers the balance of a reducing-balance loan sooner, so less interest is charged and the loan is repaid in less time — the interest rate itself does not change.
On a reducing-balance loan, each month the interest is the rate times the opening balance, and the closing balance is opening \(+\) interest \(-\) repayment. Anything that makes the balance smaller sooner means less interest is charged in every later month.
A higher regular repayment takes more off each month. An extra repayment is subtracted with the usual repayment that month. A lump sum at the start is taken off before the first month's interest is charged — the earlier a lump sum is paid, the more interest it saves. More frequent repayments, such as half the monthly amount every fortnight, give \(26\) payments a year (\(13\) months' worth).
The effect: the loan is repaid sooner and less total interest is paid, while the interest rate stays the same. In this Year 12 Standard 1 (NSW) topic you calculate and explain these effects.
Every month of a reducing-balance loan follows the same two steps:
In a month with an extra payment, subtract the total paid. A lump sum at the start comes off first:
| Repayment plan | Payments a year | Paid in a year |
|---|---|---|
| $600 a month | 12 | $7200 |
| $300 a fortnight | 26 | $7800 |
How to work out the effect of a repayment change
- Start the month: take off any lump sum paid at the start, then find interest \(=\) rate \(\times\) opening balance.
- Subtract the total paid that month: the usual repayment plus any extra payment.
- Compare the closing balance, or the next month's interest, with and without the change.
- Explain the effect: a smaller balance means less interest, so the loan is repaid sooner — the rate is unchanged.
The interest is the same; only the amount subtracted changes.
| \(\text{Interest}\) | \(=\) | \(0.01 \times 14000 = 140\) |
| \(\text{\$600 repayment: Closing}\) | \(=\) | \(14000 + 140 - 600 = 13540\) |
| \(\text{\$900 repayment: Closing}\) | \(=\) | \(14000 + 140 - 900 = 13240\) |
The \(\$900\) repayment leaves \(\$13\,240\) owing, \(\$300\) less than \(\$13\,540\), so the loan will be repaid sooner with less interest.
In month \(1\), subtract \(650+1500=2150\).
| \(\text{Interest (m1)}\) | \(=\) | \(0.01 \times 16000 = 160\) |
| \(\text{Closing (m1)}\) | \(=\) | \(16000 + 160 - 2150 = 14010\) |
| \(\text{Interest (m2)}\) | \(=\) | \(0.01 \times 14010 = 140.10\) |
Without the extra: closing \(=16000+160-650=15510\), so the month-\(2\) interest would be \(0.01\times15510=155.10\).
Month-\(2\) interest is \(\$140.10\), which is \(\$15\) less — and the saving continues every month.
Take off the lump sum first, then charge interest on the reduced balance.
| \(\text{Opening}\) | \(=\) | \(11000 - 2500 = 8500\) |
| \(\text{Interest}\) | \(=\) | \(0.015 \times 8500 = 127.50\) |
| \(\text{Closing}\) | \(=\) | \(8500 + 127.50 - 500\) |
| \(\) | \(=\) | \(8127.50\) |
The closing balance is \(\$8127.50\).
There are \(12\) months but \(26\) fortnights in a year.
| \(\text{Monthly}\) | \(=\) | \(12 \times 800 = 9600\) |
| \(\text{Fortnightly}\) | \(=\) | \(26 \times 400 = 10400\) |
| \(\text{Extra}\) | \(=\) | \(10400 - 9600 = 800\) |
She repays \(\$800\) more each year, and the balance is reduced more often, so the loan is repaid sooner with less total interest.
Common pitfalls
Frequently asked questions
Does paying more off a loan reduce the interest?
Yes. Paying more lowers the balance owing, and interest is worked out on that balance, so every later month's interest is smaller. The interest rate stays the same, but the total interest paid goes down and the loan is repaid sooner.
Is it better to pay a loan fortnightly or monthly?
Paying half the monthly amount every fortnight gives 26 payments a year, which is the same as 13 monthly payments instead of 12. The balance is reduced more often and by more each year, so the loan is repaid sooner with less interest.
What does a lump sum payment do to a loan?
A lump sum is taken straight off the balance owing. If it is paid at the start, it comes off before the first month's interest is charged, so every month's interest is lower. The earlier it is paid, the more interest it saves.
How much interest do you save with a higher repayment?
It depends on the loan. For a $10000 loan at 1 percent per month, repaying $800 a month instead of $500 clears the loan in 14 months instead of 23, and the total interest falls from about $1213 to about $737.
Does an extra repayment change the interest rate?
No. The interest rate stays the same. An extra repayment lowers the balance that the rate is applied to, which is why the interest charged each month becomes smaller.