Question

Clarence Weatherspoon, a super salesman contemplating retirement on his fifty-fifth birthday, decides to create a fund on an 8% basis that will enable him to withdraw $20,000 per year on June 30, beginning in 2021 and continuing through 2024. To develop this fund, Clarence intends to make equal contributions on June 30 of each of the years 2017–2020. Instructions

(a) How much must the balance of the fund equal on June 30, 2020, in order for Clarence to satisfy his objective?

(b) What are each of Clarence’s contributions to the fund?

Short answer

The fund balance of June 30, 2020, will be $66,242.6, and the annual contribution will be $14,701.

Step-by-step solution

Calculation of fund balance of June 30, 2020

$\begin{array}{rcl}\mathrm{Fund}\mathrm{balance}\mathrm{on}\mathrm{June}30,2020& =& \mathrm{Uniform}\mathrm{withdrawal}\times \mathrm{PV}\mathrm{factor}\mathrm{of}\mathrm{annuity}\\ & =& 20,000\times 3.31201\\ & =& \$66,242.6\end{array}$

Calculation of annual contribution

$\begin{array}{rcl}\mathrm{Annual}\mathrm{Contribution}& =& \frac{\mathrm{Fund}\mathrm{balance}\mathrm{on}\mathrm{june}30,220}{\mathrm{Future}\mathrm{value}\mathrm{factor}\mathrm{ordinary}\mathrm{annuity}}\\ & =& \frac{66,242.6}{4.50611}\\ & =& 14,701\end{array}$