Question

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

a.	$452,206.46
b.	$548,677.17
c.	$602,941.94
d.	$657,206.71
e.	$494,412.39

Answer 1

- Your sister is planning to save $65,000 per year for 30 years with first deposit to be made one year from today.

Calculating the Future Value when she turns 65 at retirement date:-

Where, C= Periodic Deposit = $65,000

r = Periodic Interest rate = 7.5%

n= no of periods = 30 years

Future Value at retirement = $6,720,961.16

Now, from this account balance she will withdraw per year at the end of each year.

Calculating the Periodic withdrawal using PV of ordinary annuity formula:-

Where, C= Periodic Withdrawal

r = Periodic Interest rate = 7.5%

n= no of periods = 25 years

Present Value = $6,720,961.16

C = $602,941.94

So, the amount she can spend each year after she retires is $602,941.94

Option C

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