If I put £500 in the bank with an annual interest rate of 3% how much money will I have earned in 2 years?

Too calculate this we need to increase to total amount of money in the bank by 3% year on year for 6 years.

Year 0   £500

Year 1   £500 x 1.03 = £515

Year 2   £515 x 1.03 = £530.45

Notice we use the running total and increase that by 3% per year.

This can also be represented as £500 x 1.03 x 1.03 or £500 x 1.03^2.

To work out how much we have earned, it is then a simple matter of subtracting £500 from £530.45 leaving us with £30.45.

You will earn £30.45 in 2 years.