## What Is Compound Interest?

Compound interest occurs when a value goes up by the same percentage every year (or month, week, whatever – but usually year). This is sometimes called ‘appreciation’. If a value goes down by the same percentage every year, it’s called ‘depreciation’.

Note that although the *perentage* change each year is the same, the *actual* change is not.

An example question:

`A house is worth £500,000 today. If its value goes up by 4% a year, what will it be worth in 3 years time? Give your answer to the nearest thousand pounds.`

The easiest way to do these questions is change the new percentage to a decimal them multiply the original number by this to the power of the number of years. So:

`Increase of 4% => 104% = 1.04`

500,000 x 1.04^{3} = 562432 = £562,000 to the nearest £1000

An example where the value is going down:

`An industrial machine cost £60,000. If it's value falls by 7% a year, what will it be worth after 3 years? Give your answer to the nearest pound.`

Fall of 7% => 93% = 0.93

60000 x 0.93^{3} = 48261.42 = £48261 to the nearest pound

Make sure you read the question carefully and do any rounding asked for – there’s a mark for it.

One thing to watch out for is that sometimes the question doesn’t ask for the new amount but for the amount of change. Here there’s one extra step, you need to find the difference between the new value and the original. An easy step to do, but also easy to miss. For example:

`A painting is bought for £350. If it's value goes up by 11% a year, how much more will it be worth in three years time? Give your answer to the nearest pound.`

Increase of 11% = 111% = 1.11

350 x 1.11^{3} = 478.67085

478.67085 - 350 = 128.67085 = Increase of £129 to the nearest pound