Question

Brad and Kelly just had a daughter, Katie. They establish an account, to accumulate money for her college education, in which they would like to have $100,000 after 17 years. If the account pays 4% interest per year compounded quarterly, and they make deposits at the end of every quarter, how large must each deposit be for them to reach their goal? Please show the formula used

Answer 1

The formula for computing the future value (F) of an annuity is F = (P/r)[ (1+r)ⁿ-1] where P is the periodic payment, r is the rate of interest per period and n is the number of periods.

Here, F = $ 100000, n = 17*4 = 68 and r = 4/400 = 0.01. Hence, 100000 = (P/0.01)[(1.01)⁶⁸ -1] = 100P(1.967222202-1) = 100P*0. 967222202 so that P = 100000/(100*0.967222202) = 1033.89 ( on rounding off to 2 decimal places).

Thus, Brad and Kelly need to deposit $ 1033.89 at the end of each quarter to reach their goal of having $ 100000 after 17 years.