Ratio, proportion and rates of change
Compound interest
Work out compound interest and the amount it grows to, and use the same idea for growth and depreciation.
With simple interest, every year earns the same amount, because the interest is always worked out on the sum you started with. With compound interest, each year's interest is added on before the next year begins — so the second year earns interest on the first year's interest too. Over two or three years the difference looks small. Over twenty it is enormous.
The shortcut
At a rate of R per cent, one year multiplies the amount by (1 + R/100). So after n years the amount is P × (1 + R/100) raised to the power n, and the compound interest is that amount minus P. Compounded half-yearly, halve the rate and double the number of periods. Depreciation is the same formula with a minus: value × (1 - R/100) each year.
Worked example
Find the compound interest on £4000 at 10 per cent per year for 2 years.
Year one: 10 per cent of 4000 is 400, so the amount becomes 4400.
Nothing new yet — this first year is identical to simple interest.
Try it together
Now let us find the amount when £6000 is invested at 5 per cent per year, compounded yearly, for 2 years.
Year by year is the safest way while the idea is new. Find the interest, add it on, and repeat with the new amount.
1.What is 5 per cent of 6000?
Have a go
Have a go on your own: find the compound interest on £10000 at 10 per cent per year for 2 years. Give just the number.
Hint: Find the amount after two years first, then take the sum you started with away from it.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.