You put £800 in a bank account, which earns you 3.5% compound interest per year. How much interest would you have earned after seven years?

We start with £800 in the bank. As we are earning compound interest, it means that each year we get 3.5% of the original £800, plus 3.5% of any interest that has already been earned. So, at the end of the year, you will have

1.035 x (however much money was in the account at the start of the year).

Let's start with year 1. You have £800 at the start, and at the end you have 

£800 x 1.035 = £828.

Now let's think about year 2. You start with £828, and end with

£828 x 1.035 = £856.98

We can also write it like this:

Money at end of year 2 = £828 x 1.035 = £800 x 1.035 x 1.035

Do you see how for each year we earn interest, we just multiply the original £800 by another 1.035?

So, after n years, the total in the account is:

£800 x 1.035ⁿ

This makes it easy to work out the total after 7 years, which is just:

£800 x 1.035⁷ =  £1017.82 (rounded to the nearest penny)

To find the interest earned, just subtract the original amount (in this case £800), and we get our answer:

£1017.82 - £800 = £217.82 interest