GCSE Compound Interest — Examiner's Guide | The Maths and Science Tutor

Compound interest is one of those GCSE topics that everybody thinks they understand until they hit a question that asks for a value after the interest has been added five times. The good news: there's a single formula that handles every variation — and an even faster shortcut once you understand what's happening underneath. This guide walks through both, plus the depreciation flavour that comes up on most papers.

Simple vs compound interest

Both add a percentage to a starting amount each year. The difference is what happens in year two.

Simple interest — the percentage is always calculated on the original amount. The interest stays the same each year.
Compound interest — the percentage is calculated on the current amount, including any interest already added. The interest grows each year.

The compound interest formula

Final amount = P × (1 + r/100)ⁿ

Where:

P = the principal (starting amount)
r = the interest rate as a percentage per year
n = the number of years

The multiplier method — much faster

The bit in the bracket, (1 + r/100), is called the multiplier. Calculate it once, then raise it to the power n. This is much quicker than doing the year-by-year calculation by hand.

Worked example 1

£2,000 is invested at 4% compound interest per year. What is it worth after 5 years?

Multiplier: 1 + 4/100 = 1.04

Final = 2000 × 1.04⁵

= 2000 × 1.21665…

= £2,433.31 (to nearest penny)

Examiner's note: The question often asks for "the interest earned", not "the final amount". Read carefully. The interest is the final amount minus the principal. Here that's £433.31, not £2,433.31.

Depreciation

Depreciation is compound interest in reverse — the value goes down by a percentage each year. The formula is the same but with subtraction in the bracket:

Final value = P × (1 − r/100)ⁿ

Worked example 2

A car worth £18,000 depreciates by 15% per year. What's it worth after 3 years?

Multiplier: 1 − 15/100 = 0.85

Final = 18000 × 0.85³

= 18000 × 0.614125

= £11,054.25

Different rates in different years

If the rate changes between years, multiply the year-by-year multipliers together.

Worked example 3

£5,000 is invested. Year 1: 3% interest. Year 2: 5% interest. Year 3: 4% interest. Final value?

5000 × 1.03 × 1.05 × 1.04

= 5000 × 1.124796 = £5,623.98

The mistakes that cost the most marks

Mistake 1 — Confusing simple and compound. If the question doesn't say "simple", assume compound. "Interest is added each year" usually means compound.

Mistake 2 — Calculating interest instead of final amount, or vice versa. Always finish by reading the question again to see which one was asked for.

Mistake 3 — Wrong multiplier for depreciation. 15% depreciation gives a multiplier of 0.85 (= 1 − 0.15), not 0.15 or 1.15.

Mistake 4 — Rounding to the nearest pound when the question wants pence. Money answers are nearly always to two decimal places.

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Compound Interest — An Examiner's Guide