Question

Steve Weatherspoon, a super salesman contemplating retirement on his fifty-fifth birthday, decides to create a fund on an 10% basis that will enable him to withdraw $21,040 per year on June 30, beginning in 2024 and continuing through 2027. To develop this fund, Steve 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 Steve to satisfy his objective? Balance of the fund equal on June 30, 2023? What are each of Steve's contributions to the funds?

Answer 1

Steve wants to withdraw $21040 per year for four years starting June 30 2024 and ending on June 30 2027.

Therefore Value of the fund as on June 30 2023 should be = Present value of the annuity of $21040 discounted at 10% for four years. This can be calculated using the below formula:

[4-(4+5)-) 11- (1 + r)-n LT P = Periodic Payment r=rate per period n = number of periods

Value of the fund as on June 30 2023 = = $66693.97

210401-11-0.10)- 010

b) To develop this fund Steve wants to contribute to the fund each year for four years starting from June 30 2020 till June 30 2023.

Therefore each year contribution should be such that the future value of the annuity =   $66693.97

This can be calculated using the formula:

  

F=p(1+r)" – 1

where

F = Future Value of the annuity at the end of the period

P = Periodic contribution required

r = rate per period

n = number of periods

- 1 66693.97 = p' (1+0.10) 0.10

P = $14370.6

Therefore annual contribution would be $14370.6