You accepted a new job with starting salary of $65,000 per year. The salary is expected to increase 4% each year. Now it is time to make a retirement plan for the next 39 years you expect to work. Your retirement fund has an annual interest rate of 5%, and You plan to deposit 6% of your annual salary into the account. (Hint: Be sure to move all values to the same point in time for equivalency.)

a. How much money will be in your retirement account at the end of 39 years? (Hint: this is a geometric gradient problem)
b. How much can you with draw from that account each year in retirement for 25 years. Assume you will withdraw the same amount each year. (Hint: this is uniform annuity problem)

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TomShelby TomShelby · Answer 1 · 2020-02-12T09:44:28+01:00

Answer:

Future value of the retirement account $814,470.21

The annual withdrawals will be in the order of $ 63,713.33

Explanation:

we go with the future value of a growing annuity:

[tex]\frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}[/tex]

g 0.04

r 0.05

C 65,000 x 6% savings = 3,900

n 39

[tex]\frac{1-(1+0.04)^{-n}\times (1+0.05)^{-39} }{r - g}[/tex]

FV 814,470.21

Present value of the retirement couta

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV 814,470.21

time 25

rate 0.06

[tex]814470.21474148 \div \frac{1-(1+0.06)^{-25} }{0.06} = C\\[/tex]

C $ 63,713.332