Compound growth and decay

Simple interest is the same amount every year, worked out on the original amount only.

Simple interest = original amount × rate × number of years (learn this)

1. Work out the interest for one year.
2. Multiply by the number of years.
3. Add it to the original amount if asked for the total.

Example: £500 is invested at 4% simple interest for 3 years. Find the total.

1. One year: 4% of £500 = £20
2. Three years: 3 × 20 = £60
3. Total: 500 + 60 = £560

Compound interest is worked out on the amount at the end of each year, so the interest itself earns interest. Use the multiplier for one year, raised to the number of years:

Amount = original × multiplierⁿ, where n is the number of years. (The compound interest formula is on the formulae sheet.)

Example: £500 is invested at 4% compound interest for 3 years. Find the total.

1. Multiplier: 1.04
2. 500 × 1.04³ = 562.432
3. £562.43

This is more than the £560 from simple interest, because each year's interest is a bit bigger than the last.

Depreciation means losing value. For a percentage decrease each year, the multiplier is less than 1, but the method is the same.

1. Find the multiplier: 1 − the percentage as a decimal.
2. Multiply the original by the multiplier to the power of the number of years.

Example: a car worth £15 000 loses 15% of its value each year. What is it worth after 4 years?

1. Multiplier: 1 − 0.15 = 0.85
2. 15 000 × 0.85⁴ = 7830.09…
3. £7830.09

The same method works for growth and decay of anything that changes by the same percentage each time, such as a population or bacteria.

To find how many years it takes to reach an amount, try values of n until you pass it.

1. Write the amount after n years: original × multiplierⁿ.
2. Work it out for n = 1, 2, 3, … (or make a sensible guess first).
3. Stop at the first year that reaches the target.

Example: £2000 is invested at 6% compound interest. After how many whole years will it first be worth more than £2500?

1. Multiplier: 1.06
2. n = 3: 2000 × 1.06³ = £2382.03
3. n = 4: 2000 × 1.06⁴ = £2524.95
4. After 4 years

On a calculator, type 2000, press =, then × 1.06 = again and again, counting the presses.