E6-8 (Computations for a Retirement Fund) Clarence Weatherspoon, a super salesma

Question

E6-8 (Computations for a Retirement Fund)

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 20, 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.

(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?

Explanation / Answer

Part 1 Calculation of balance of fund for clarence weatherspoon on june 30, 2020

Present value of an ordinary annuity for 4 period @ 8% for yearly withdrawal of $20000 (Calculation in simple steps)

Ordinary Annuity [1/(1+n/100)]

(n = rate of interest 8%)

Amount

(Drawings *annuity)

0.9259

[1/(1/1.08)]

0.8573

[1/(1/1.08*1/08)]

0.7938

[1/(1/1.08*1.08*1.08)]

0.7351

[1/(1.08*1.08*1.08*1.08)]

Part 2 Calculation of each of clarence contribution to the fund

Future value of annuity = [(1+n)t - 1]/n

Where 'n' is Interest rate i.e. 8% and 't' is number of payments i.e. 4 period

Future value of annuity = [(1+0.08)4-1]/0.08 = 4.506112

Amount of each of four contribution = $66242/4.506112 = $14701

Year Drawings

Ordinary Annuity [1/(1+n/100)]

(n = rate of interest 8%)

Amount

(Drawings *annuity)

1 $20000

0.9259

[1/(1/1.08)]

$18518 2 $20000

0.8573

[1/(1/1.08*1/08)]

$17146 3 $20000

0.7938

[1/(1/1.08*1.08*1.08)]

$15876 4 $20000

0.7351

[1/(1.08*1.08*1.08*1.08)]

$14702 Total total annuity = 3.3121 $66242

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