In life interest comes into play in many different areas of our life whether it be interest on a loan or interest added on to our savings. There are two forms of interest simple and compound. For this question we are going to work out compound interest.

Compound interest is when interest is added on to the principle amount and from then on the new interest also gains interest. As you can see the interest is compounded over time so that the principle amount increases by a larger percentage year upon year.

Now let's work on a question!

Susan takes a loan from the bank of £500, she is told that the compound interest on the loan is 5% a year for 4 years. If she pays her loan at the end of the 4 year period how much compound interest will Susan pay back?

Principle amount: £500

Interest in the first year = £500 x 1.05 = £525 (£25 interest)

Principle amount after first year: £525

Interest in the second year = £525 x 1.05 = £551.25 (£26.25 interest)

Principle amount after second year: £551.25

Interest in the third year = £551.25 x 1.05 = £578.81 (£27.56 interest) 27.56

Principle amount after the third year: £578.81 

Interest in the fourth year = £578.81 x 1.05 = £607.75 (£28.94 interest)

Principle amount at the end of the fourth year: £607.75

Ok so we can now see the total amount of how much Susan will pay back after the 4 year period, to find the total compound interest that Susan will pay back we must simply subtract the principal amount that Susan was loaned from the principle amount at the end of the fourth year:

£607.75 - £500 = £107.75

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