Simple interest adds the same amount every year, a fixed percentage of the original sum. Compound interest is added to the balance each year, so the following year's interest is calculated on a bigger amount. Repeated percentage change, including depreciation, is worked out by multiplying by a multiplier once for each period, and different rates in different years simply use different multipliers.
Interest and repeated change
- Simple interest per year = rate × original amount
- Simple interest total = yearly interest × number of years
- Compound: final amount = original × multiplierⁿ
- Different rates: multiply by each year's multiplier in turn
Simple interest
Simple interest pays the same amount every year, because it is always a percentage of the original amount. £2400 at 4% simple interest earns £96 each year, so over 3 years it earns £288 and grows to £2688.
Compound interest
With compound interest, the interest is added on each year, and the next year earns interest on the new total. Instead of working year by year, multiply by the multiplier once for each year: £2400 at 4% for 3 years becomes 2400 × 1.04³ = £2699.67.
Comparing simple and compound interest
Over one year the two give the same result, but after that compound interest pulls ahead, because interest earns interest. In the example above, compound interest earns £11.67 more after 3 years. The gap grows larger the longer the money is invested.
Depreciation and decay
Depreciation is compound decay. A car losing 20% of its value each year keeps 80%, so its value is multiplied by 0.8 each year. A car worth £12 000 is worth 12 000 × 0.8² = £7680 after 2 years.
Different rates in different years
If the rate changes, multiply by each year's multiplier in turn. £5000 growing by 3% in year 1 and 5% in year 2 becomes 5000 × 1.03 × 1.05 = £5407.50. Comparing investments often means working out each option fully, because a higher rate of simple interest can beat a lower rate of compound interest over a few years.
Worked examples
Example 1. £2400 is invested at 4% simple interest. Work out the total value after 3 years.
- Interest each year: 4% of 2400 = 96.
- Over 3 years: 3 × 96 = 288.
Answer: £2688.
Example 2. £2400 is invested at 4% compound interest. Work out its value after 3 years.
- Multiplier 1.04.
- 2400 × 1.04³ = 2400 × 1.124864 = 2699.6736.
Answer: £2699.67.
Example 3. A car worth £12 000 depreciates by 20% each year. Work out its value after 2 years.
- Multiplier 0.8.
- 12 000 × 0.8².
Answer: £7680.
Example 4. £5000 grows by 3% in the first year and 5% in the second year. Work out its value after 2 years.
- Multiply by each year's multiplier: 5000 × 1.03 × 1.05.
Answer: £5407.50.
Example 5. Account A pays 6% simple interest and account B pays 5% compound interest. Which gives more on £1000 after 4 years?
- A: 4 × £60 = £240 interest, total £1240.
- B: 1000 × 1.05⁴ = £1215.51.
Answer: Account A, by £24.49.
Common mistakes
- Using simple interest for a compound question. Compound interest uses a power of the multiplier.
- Adding the percentages for different years. 3% then 5% is × 1.03 × 1.05, not × 1.08.
- Using 0.2 for a 20% depreciation. The multiplier is 0.8.
- Confusing interest with final value. Interest = final value − original amount.
- Rounding during the calculation. Round only the final money answer.
How growth and decay are examined
Interest, depreciation and repeated percentage change are among the most frequent real-life questions on Edexcel GCSE (1MA1) and International GCSE (4MA1) papers, at both tiers. You may be asked to:
- work out simple interest over several years
- work out compound interest or depreciation
- compare simple and compound interest, or two investments
- apply different percentage changes in different years
The growth and decay worksheet includes answers, and new questions can be generated in the proportion revision engine.
For more on money contexts, see compound interest and depreciation; for populations and science, see compound growth and decay.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is always calculated on the original amount; compound interest is calculated on the growing balance.
Which earns more, simple or compound interest?
At the same rate, compound interest earns more after the first year.
How do you apply two different percentage increases?
Multiply by each multiplier in turn, for example × 1.03 × 1.05.