interest

In finance, a sum of money paid by a borrower to a lender in return for the loan, usually expressed as a percentage per annum. Simple interest is interest calculated as a straight percentage of the amount loaned or invested. In compound interest, the interest earned over a period of time (for example, per annum) is added to the investment, so that at the end of the next period interest is paid on that total.

A sum of £100 invested at 10% per annum simple interest for five years earns £10 a year, giving a total of £50 interest (and at the end of the period the investor receives a total of £150). The same sum of £100 invested for five years at 10% compound interest earns a total of £61.05 interest (with £161.05 returned at the end of the period). Generally, for a sum S invested at x% simple interest for y years, the total amount returned is S+xyS/100. If it is invested at x% compound interest for y years, the total amount returned is S[(100 +x)/100]^y.