Compound interest — growth and decay with percentages
How do you calculate compound interest?
Compound interest means the interest is added to the account each year, and the next year's interest is worked out on the new, larger amount. That is why the amount grows by the same multiplier every year rather than by the same number of pounds. The same idea, with a multiplier below 1, describes depreciation — a car losing value year after year.
Worked examples, step by step
£5000 is invested at 5% compound interest per year. How much is in the account after 3 years?
- The multiplier for a 5% rise is 1.05, applied once for each of the 3 years
- Amount = 5000 × 1.05 × 1.05 × 1.05 = 5000 × 1.05³
- 1.05³ = 1.157625, so the amount is 5000 × 1.157625 = 5788.125
- Answer: £5788.13 (to the nearest penny)
What would the same £5000 earn at 5% simple interest over 3 years, and how much more does compound interest give?
- Simple interest pays 5% of the ORIGINAL amount each year: 5% of 5000 = £250 per year
- Over 3 years: 3 × 250 = £750, so the total is 5000 + 750 = £5750
- Compound interest gave £5788.13, which is 5788.13 − 5750 = £38.13 more
- Answer: compound interest earns £38.13 more, because the second and third years' interest is worked out on a larger amount
A car bought for £12 000 loses 15% of its value every year. What is it worth after 3 years, to the nearest pound?
- Losing 15% is a multiplier of 0.85 per year
- Value = 12 000 × 0.85³
- 0.85³ = 0.614125, so the value is 12 000 × 0.614125 = 7369.5
- Answer: £7370 (to the nearest pound)
£2000 is invested at 10% compound interest. After how many whole years will it first exceed £3000?
- Multiply by 1.1 year by year: after 1 year 2200, after 2 years 2420, after 3 years 2662, after 4 years 2928.20
- After 5 years: 2928.20 × 1.1 = 3221.02, which is more than 3000
- Answer: after 5 years
Now try it yourself
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest pays the same amount every year, worked out on the original sum. Compound interest is worked out on the current balance, including the interest already added, so the amount grows faster each year. After the first year the two are no longer the same.
What is the compound interest formula?
Amount = P × (1 + r)ⁿ, where P is the starting amount, r is the annual rate as a decimal and n is the number of years. For 4% over 5 years the multiplier is 1.04⁵. The GCSE exam does not give you this formula — you need to know it.
How does depreciation work?
Exactly like compound interest but with a multiplier below 1. A 15% loss each year is a multiplier of 0.85, so after n years the value is P × 0.85ⁿ. This is the standard GCSE question about cars, phones and machinery.
Can I use a calculator for this?
In the exam these questions appear on Papers 2 and 3, the calculator papers, so yes — use the power button rather than multiplying year by year. Round only at the end, to the nearest penny or pound as the question says.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: