Question

Steve Weatherspoon, a super salesman contemplating retirement on his fifty-fifth birthday, decides to create a fund on an 12% basis that will enable him to withdraw $18,180 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.

(a)

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How much must the balance of the fund equal on June 30, 2023, in order for Steve 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

$

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(b)

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What are each of Steve’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.)

Steve’s contributions to the fund

$

Answer 1

a.

withdrawal per year (P) =18180

annual rate (i) =12%

number of withdrawal from June 30, 2024 to 2027 (n) =4

Withdrawal is made at end, so it is ordianry annuity Present value of annuity formula will be used to find the value of fund needed at June 30, 2023

PV of annuity formula = P*(1-(1/(1+i)^n))/i

=18180*(1-(1/(1+12%)^4))/12%

=55219.01112

So the balance of the fund mus tbe equal on June 30, 2023 to $55219.01

b

future value required to be saved is PV of withdrawal made that is =55219.01

number of deposit made (2020-2023) n =4

annual interest rate (i) =12%

Amount required to save each period Formula = Future value*i/(((1+i)^n)-1)

55219.01*12%/(((1+12%)^4)-1)

=11553.71843

so amount required to be saved each year is $11553.72