Question

Henry Weatherspoon, a super salesman contemplating retirement on his fifty-fifth birthday, decides to create a fund on an 9% basis that will enable him to withdraw $16,830 per year on June 30, beginning in 2024 and continuing through 2027. To develop this fund, Henry intends to make equal contributions on June 30 of each of the years 2020–2023.

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How much must the balance of the fund equal on June 30, 2023, in order for Henry to satisfy his objective? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

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What are each of Henry’s contributions to the fund? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Henry’s contributions to the fund

$

show work and explain

Answer 1

a) Annual withdrawal from 2024 to 2027 = $ 16,830
Number of withdrawal = 4
Annual Interest rate = 9%
Fund balance on June 30th 2023 = Present value of annual withdrawal
= Uniform withdrawal x (1 - (1 + r)^-n)/r
= 16,830 x (1 - (1.09)⁻⁴)/0.09
= $54,524
b) Number of contribution = 4
Future value of contribution = $54,524
Future Value of annuity of $1 = Annual Contribution x ((1 + r)ⁿ - 1)/r
$54,524 = Annual Contribution x (1.09⁴ - 1)/0.09
Annual Contribution = $54,524/4.57312
= $11,922