Question

You are going to save money for your son's education. You have decided to place $2,454 every half year at the end of the period into a saving account earning 7.47 percent per year, compounded semi-annually for the next 10 years. How much money will be in the account at the end of that time period?

Answer 1

Sol:

Semiannual Payment (P) = $2,454

Interest rate (r) = 7.47% annually, Semiannually = 7.47 / 2 = 3.735%

Periods (n) = 10 years, Semiannual = 10 x 2 = 20

To determine money in the account at the end of the time period we have to use future value (FV) of annuity formula:

Future value (FV) of annuity = P x (1 + r)^n - 1 / r

Future value (FV) of annuity = 2454 x (1 + 3.735%)^20 - 1 / 3.735%

Future value (FV) of annuity = 2454 x (1.03735)^20 - 1 / 0.03735

Future value (FV) of annuity = 2454 x (2.082122 - 1) / 0.03735

Future value (FV) of annuity = 2454 x (1.082122 / 0.03735)

Future value (FV) of annuity = 2454 x 28.972483 = $71,098.47

Therefore money in the account at the end of the time period will be $71,098.47.