What is compound interest and how do I calculate it?

Compound interest means, for example, the money you have put into a bank, earns interest each year, but you earn interest upon the interest that was already added last year i.e. you earn interest on the new amount of money you have in the bank, rather than the original amount that you put in. Whereas simple interest, just means you earn exactly the same amount of interest each year, because you're always earning interest on the original amount.

It may sound complicated, but don't worry! Its actually very simple with an explained example.

Say we put £500 in the bank, and we earn 2% compound interest.
This means for the first year we earn 500 x 0.02 = £10 interest.

If this was simple interest, then we would earn £10 each year to add to our savings. But because this is compund interest, in the second year, we now earn interest on the new amount that we have = £510. So now in the second year, we earn £510 x 0.02 = £10.20 interest. So in the third year what do we earn? You guessed it: (510 + 10.20) x 0.02 = £10.404  and so on.

So you can see that each year we earn a little bit more interest because we have a little bit more in the bank. You can see how much you have all together after earning the interest each year, by multiplying by (1 + r/100) instead of just r/100 as we have done above. e.g. After one year we will have 500 x 1.02 = £510

We have a simple formula we can use instead of calculating each year separately which can take a very long time.

N = Nx (1 + r/100)t

N = Our new amount that we have in the bank after t years 

N0 = The original amount we put in the bank (£500 in our example)

r/100 = the percentage change per year (2/100 in our example = 0.02)

t = number of years the money is earning interest for


So for our example if we want to know how much we will have after 8 years of 2% compound interest, we do:

N = 500 x (1 + 0.02)8

    = 500 x 1.028    

    = £585.83


So we have earned £85.83 in interest over the 8 years :)

Rocio F. GCSE Maths tutor

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