Your sister turned 20 today, and she is planning to save $5,000 per year for ret
ID: 2730522 • Letter: Y
Question
Your sister turned 20 today, and she is planning to save $5,000 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% per year.
She plans to retire 40 years from today, when she turns 60, and she expects to live for 25 years after retirement, to age 85.
Under these assumptions, how much can she spend each year after she retires, if she can earn 9 % per year after retirement.
Her first withdrawal will be made at the end of her first retirement year.
Explanation / Answer
To answer this question, we first need to calculate the value of yearly deposits upon retirement. As she will make first deposit one year from today and last at the age of 60, total number of deposits will be 40 -1 = 39
Formula: FV = Pmt x ((1+r)n -1))/r)
FV = $5,000 x ((1+0.07)39 -1))/0.07) = $982,201.50
Now, she will start making withdrawals from this amount. This amount will act as an annuity for her and will earn 9% returns. So, the amount she will withdraw for 25 Years:
Pmt = Ar / (1-(1+r)-t)
The deposited amount is A, the interest rate per period is r, the number of periods is t, and P is the payment per period.
[($982,201.50 x 0.09) / (1-(1+0.09)-25)] = $94,496.71
So, She will be able to withdraw $94,496.71 every year for 25 years.
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