# Answered Essay: Clarence Weatherspoon, a super salesman contemplating retirement on his fifty-fifth birthday, decides to create a fund on an 8%

Exercise 6-8 (Part Level Submission)

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 \$30,400 per year on June 30, beginning in 2018 and continuing through 2021. To develop this fund, Clarence intends to make equal contributions on June 30 of each of the years 2014–2017.

(a)

(Use the table below.)

How much must the balance of the fund equal on June 30, 2017, in order for Clarence Weatherspoon 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, 2017 \$
 Attempts: 1 of 3 used

(b)

(Use the table below.)

What are each of Clarence’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.)

 Clarence’s contributions to the fund \$

a)

Annual withdrawals from 2018 to 2021 = \$30,400

Number of withdrawals = 4

Annual interest rate = 8%

Fund balance on June 30, 2017 = Present value of annual withdrawals

Present value of annuity of uniform amount = Uniform amount*{1-(1+r)-n}/r

Fund balance on June 30, 2017 = \$30,400*(1-1.08-4)/0.08 = \$100,688.66

b)

Number of contributions = 4

Future value of contribution = \$100,688.66

Future value of annuity of \$1 = {(1+r)n-1}/r

\$100,688.66 = Annual contributions*(1.084-1)/0.08

Annual contributions = \$100,688.66/4.50611 = \$22,344.91

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