Answer:

Compound interest is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on. A loan, for example, may have its interest compounded every month, in this case, a loan with $1000 principal and 1% interest per month would have a balance of $1010 at the end of the first month. Interest rates must be comparable in order to be useful, and in order to be comparable, the interest rate and the compounding frequency must be disclosed.

When $100 is invested in a bank or building society at 7% interest per year, it grown by $7 to $107 at the end of the first year. In the second year, interest is earned on the original $100 and on $7 interest. So at the end of the second year the investment grows by $7 + $0.49 to $114.49. (This is more rapidly calculated at $107 x 1.07.) At the end of the third year it will have grown to $114.49 x 1.07 = $122.50 to the nearest penny. When money grown in this way it is said to grow with compound interest.

An initial amount P invested at r% per year grows to P (1 + r/100)ⁿ at the end of n years.