Question

21. our older brother turned 35 today, and he is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year.

Group of answer choices

$68,179

$71,588

$64,932

$61,686

$58,601

Answer 1

Using the formula for FV of annual annuity,

Future value of annuity (FV) = Periodic Payment (P) x [(1+r) ⁿ - 1 /r]

r = Rate per period = 7.5 %

n = Numbers of periods = 30

FV = 7,000 x [(1 + 0.075)³⁰ – 1/0.075]

     = 7,000 x [(1.075)³⁰ – 1/0.075]

     = 7,000 x [(8.754955 – 1)/0.075]

    = 7,000 x (7.754955/0.075)  

   = 7,000 x 103.3994

    = 723,795.82

This fund of $ 723,795.82 will facilitate cash flow for next 25 years. So considering this amount as PV at the time of retirement, we can calculate future cash flow as:

PV (at the time of retirement) = P x [1-(1+r)^-n/r]               

$ 723,795.82 = P x [1-(1+0.075)^-25/0.075]

                        = P x [1-(1.075)^-25/0.075]

                       = P x [(1-0.163979)/0.075]

                       = P x (0.836021/0.075)

                       = P x 11.14695

P = $ 723,795.82/11.14695 = $ 64,932.21

Elder brother can spend $ 64,932 per year after retirement.