Compound interest and depreciation

A multiplier and a power

Compound interest is interest added to the money each year, so the next year's interest is worked out on the new, bigger amount (interest on the interest).

The multiplier for an increase of r% is 1 + r/100: for 3% it is 1.03, for 5.6% it is 1.056.

3% compound interest a year: each year × 1.03. After 5 years: × 1.03⁵.

1. £2000 at 3% for 5 years
2. 2000 × 1.03⁵ = 2318.548...
3. = £2318.55

Depreciation means losing value. The multiplier for a decrease of r% is 1 − r/100: losing 15% a year leaves 85%, so × 0.85 each year, and after 4 years × 0.85⁴. Multiplying by 0.15 would give the part lost, not the value left.

Reading it backwards: in V = 800 × 1.07ⁿ the multiplier 1.07 is 107%, an increase of 7% a year. A multiplier above 1 is an increase; below 1 is a decrease (0.92 is a decrease of 8%).

Simple interest is the same amount every year, worked out on the starting amount only. £2000 at 3% simple interest earns 3% of £2000 = £60 a year, so after 5 years it is worth 2000 + 5 × 60 = £2300, less than the £2318.55 from compound interest.

The interest earned is the final value minus the amount put in: £2318.55 − £2000 = £318.55.