Percentage change
- Percentage change = change ÷ original amount × 100. Always divide by the original amount, not the new one.
- A shop buys a jacket for £40 and sells it for £50. The profit is £10, so the percentage profit is 10 ÷ 40 × 100 = 25%.
- A price falls from £80 to £68. The decrease is £12, and 12 ÷ 80 × 100 = 15%.
Simple interest
- Simple interest is the same amount every year, worked out on the original amount only.
- £400 at 5% simple interest for 3 years earns 400 × 0.05 × 3 = £60.
Compound interest
- Compound interest is added to the total each year, so the next year's interest is worked out on a bigger amount.
- Amount = original × multiplierⁿ, where n is the number of years. £400 at 5% compound interest for 3 years: 400 × 1.05³ = £463.05.
- Over the same time, compound interest earns more than simple interest: £63.05 compared with £60.
Depreciation and repeated changes
- Depreciation is a loss in value. A £15 000 car that depreciates by 20% a year is worth 15 000 × 0.8² = £9600 after 2 years.
- Repeated percentage changes multiply: a 10% increase then a 10% decrease is 1.1 × 0.9 = 0.99, which is a 1% decrease overall.
Key terms
- Percentage change
- Change ÷ original amount × 100.
- Profit
- The amount gained when something is sold for more than it cost.
- Loss
- The amount lost when something is sold for less than it cost.
- Simple interest
- Interest that is the same amount each year, based on the original amount.
- Compound interest
- Interest added to the total each year, so interest is also earned on interest.
- Depreciation
- A decrease in value over time.
- Per annum
- Per year.
Practise Percentage change, interest and depreciation: 12 questions