Compound interest, and why GCSE students lose marks on it
Compound interest is one of the few GCSE topics with an obvious use outside the exam, which makes it a good one to teach with a calculator in front of you. It is also a reliable source of lost marks, and the reasons are predictable.
The two ways students get it wrong
Repeated simple interest. Calculating the interest once and multiplying by the number of years. That is simple interest, and it undershoots, because it ignores the interest earning interest.
The wrong multiplier. A 5 per cent increase is × 1.05, not × 0.05 and not × 5. Getting to the multiplier is the whole skill, and it is where the marks go.
| Change | Multiplier | Over n years |
|---|---|---|
| 5% increase | × 1.05 | × 1.05n |
| 5% decrease | × 0.95 | × 0.95n |
| 12% increase | × 1.12 | × 1.12n |
| 30% decrease | × 0.70 | × 0.70n |
Once the multiplier is secure, compound growth, depreciation and population change are all the same question wearing different clothes.
Where it appears on the paper
Compound interest sits on both Foundation and Higher tiers. On Foundation it usually arrives as a straightforward savings or depreciation question. On Higher it tends to be reversed: given the final amount, find the original, or find the rate, or find how many years it took.
Reverse questions are where confident students still stall, because dividing by the multiplier feels wrong when the instinct is to subtract a percentage. Our reverse percentages lesson teaches it with a bar model, which makes the division obvious rather than a rule to remember.
Using the calculator as a teaching tool
Predict, then check. Ask your child what they think £1,000 at 5 per cent becomes after ten years before running it. Almost everyone guesses too low, and the gap between the guess and the answer is the lesson.
Then try the comparisons that make the idea stick: the same money at 3 per cent for twenty years against 6 per cent for ten, or what happens to a car losing 15 per cent a year. Depreciation lands harder than savings with most teenagers.
The bit worth knowing beyond the exam
Compound growth is the reason small differences in rate matter enormously over long periods, and the reason debt at a high rate is so difficult to escape. It is genuinely one of the most useful ideas in the whole maths curriculum.
It also makes a good answer to "when will I ever use this", which is worth having ready. Our piece on what a maths grade is worth makes the same argument with different numbers.
Questions parents ask
Is this on Foundation tier?
Yes, compound interest appears on both tiers. Foundation questions are usually direct, Higher questions are more often reversed.
Either way the multiplier method is the same.
Should my child memorise the formula?
Understanding the multiplier is more robust than memorising a formula, because it transfers to depreciation, growth and reverse questions without any extra learning.
A student who understands why it is 1.05 to the power n rarely needs to recall a formula at all.
Where to go next
For repeated percentage change without the monthly payments, the growth and decay calculator shows the multiplier and the power at every step. The rest of the set lives on the maths calculators page.