Compounded Interest Example.

Consider the situation of a person depositing $100 into a bank that pays 5% interest, compounded
semiannually. How much would be in the savings account at the end of one year?

Five percent interest, compounded semiannually, means that the bank pays 21/2% every 6 months. Thus, the initial amount P =$100 would be credited with 0.025(100) =$2.50 interest at the end of 6 months, or

The $102.50 is left in the savings account; at the end of the second 6-month period, the interest earned is 0.025(102.50) = $2.56, for a total in the account at the end of one year of 102.50 + 2.56 = $105.06, or