Question

John 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, John intends to make equal contributions on June 30 of each of the years 2020–2023.

How much must the balance of the fund equal on June 30, 2023, in order for John 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.) Balance of the fund equal on June 30, 2023 $___

What are each of John’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.) John’s contributions to the fund $______

Answer 1

Solution:

Pmt	16830	Payments of a fixed amount
i	9.00%	Interest Rate
n	4	no of payment period

Present Value of an Annuity
Formula
Present Value = PMT[1-1/(1+i)^n]/i
1+i	1.0900
(1+i)^n	1.4116
1/(1+i)^n	0.7084
1-1/(1+i)^n	0.2916
[1-1/(1+i)^n / i]	3.23972
Present Value	$54,524.49
Balance of the fund equal on June 30, 2023 = $54524

2.

Future Value of an Annuity
Formula
PMT = Future Value / [ (1+i)^n - 1] / i
Future Value	54524	Future Value
i	9.00%	Interest Rate
n	4	no of payment period
1+i	1.0900
(1+i)^n	1.4116
(1+i)^n - 1	0.4116
[ (1+i)^n - 1] / i	4.5731
Future Value	$11,922.69

John’s contributions to the fund $ $11923