An amount of money was invested for 8 years. It earned compound interest at 2.5% per year. After 8 years the total value of the investment was £11,696.67. Work out the total interest earned.

I would make sure the student new the difference between simple and compound interest to begin with. I would then explain the formula for compound interest and how it works normally. The formula is p(1+m)^n  where p is the initial amount, m is the multiplier (or the decimal version of our percentage/interest) and n is the number of years. Usually, when we substitute in p, m and n we would find the amount of money after n years. However, in this example, we know the mulipltier (0.025) (n.b. time would be taken to convert percentages into decimals if students were struggling with this) and we know the number of years (8) but we do not know the initial amount.

The question is asking us to work out the interest earned. So in order to work this out we need to know how much we had originally and then from there we can work out how much this has increased by to give us the total of £11,696.67. So we are going to need to use algebra skills/ rearranging formula skills to help us.                                                         P(1 + 0.025)^8 = 11,696.67.  

P x 1.025^8 = 11,696.67 

P = 11,696.67 / 1.025^8 

P = 11,696.67 / 1.2184 = 9,600 

So if we started with £9600 and finished with £11696.67 then our total interest earned is £11696,67 - £9600 = £2,096.67