Answer to Question #181059 in Economics for Cally

Question

Kizito is currently 25 years old. He intends opening and contributing to a retirement savings account. His goal is to be a millionaire after retirement. Assuming the retirement age is 60 years and he makes an annual contribution of GHS15,000 into that account. (i) Would he meet his retirement goal assuming his account will generate an annual rate of interest equal to 5%? (ii) Suppose that he would like to retire as soon as possible with GHS1,000,000 in his account. Assuming that nothing else associated with his situation changes, what is the earliest age at which he can retire?

Answer 1

(i) The future value of this annuity is:

$F = (P * ((1 + I)^N - 1))/I = (15,000×(1.05^{35} - 1))/0.05 = 1,354,804.61.$

So, he will meet his retirement goal.

(ii) $n = ln(1 + 1,000,000×0.05/15,000) /ln(1.05) = 30.05$

years.