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3.2a · Maths for Personal Finance · Sub-skill
Simple vs compound interest — how money grows over time, and the formulas AQA expects you to use.
Build it up, step by step
Click each step below to reveal it — work through them in order the first time round.
Simple interest is paid only on the original amount (the principal) each year — the interest itself doesn't earn more interest. Simple interest = $\frac{P \times r \times t}{100}$, where $P$ is the principal, $r$ is the interest rate per year (%), and $t$ is the number of years.
Compound interest is paid on the principal plus any interest already earned, so the amount grows faster each year. After $t$ years: Total = $P\left(1+\frac{r}{100}\right)^t$. This is a multiplier method — e.g. 3% growth means multiplying by 1.03 each year.
Over 1 year, simple and compound interest give the same amount. After that, compound interest always earns more (or, for a loan, costs more) than simple interest at the same rate, because it builds on itself. The longer the time period, the bigger the gap.
You can also use the multiplier method for repeated percentage decreases (e.g. depreciation of a car), using $\left(1-\frac{r}{100}\right)^t$. You can also rearrange the compound interest formula to find $P$, $r$ or $t$ if you know the other values — e.g. finding how many years it takes an investment to double.
£4,000 is invested for 3 years at 2.5% p.a. compound interest. Find the total value after 3 years, and compare it to simple interest at the same rate.
Compound: 4000×(1.025)3 = 4000×1.076890625 = £4,307.56 (2dp)
Simple: 4000 + (4000×0.025×3) = 4000+300 = £4,300
Compound interest earns £7.56 more than simple interest over the 3 years.
Test yourself
Aisha invests £2,500 in a savings account paying 3% per year compound interest.
(a) Calculate the value of her investment after 4 years, to the nearest penny.
(b) A different account pays 3% simple interest instead. Calculate how much more Aisha would have after 4 years with the compound interest account compared to the simple interest account. [5 marks]
(a) 2500×(1.03)4 = 2500×1.12550881 = £2,813.77 (2dp).
(b) Simple interest total = 2500 + (2500×0.03×4) = 2500+300 = £2,800. Difference = 2813.77 − 2800 = £13.77 more with compound interest.
Practice
Five short questions on interest. Work through them, then reveal the mark scheme to check.