Your sister turned 35 today, and she is planning to save $5,000 per year for retirement, with the first deposit to be made 1 year from today. She will invest in a mutual fund that will provide a return of 8% 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 in each year after she retires? Her first withdrawal will be made at the END of her first retirement year.

Question

Quizplus · Accepted Answer

First, we need to calculate the amount that will be saved by your sister by the time she retires. She will make deposits for a total of 30 years (since she plans to retire 30 years from today), and the investment will earn a return of 8% per year. We can use the formula for future value of an annuity:

FV = PMT x (((1 + r)^n - 1) / r)

Where:

PMT = Payment per year = $5,000
r = Annual interest rate = 8%
n = Number of years = 30

FV = $5,000 x (((1 + 0.08)^30 - 1) / 0.08) = $547,992.36

So, your sister will have $547,992.36 saved by the time she retires.

Next, we need to calculate the amount that she can withdraw each year in retirement, assuming that she wants to make the money last for 25 years (until age 90) and earn a return of 8%. We can use the formula for present value of an annuity:

PV = (PMT x (1 - (1 + r)^-n)) / r

Where:

PMT = Payment per year = Unknown
r = Annual interest rate = 8%
n = Number of years = 25

PV = $547,992.36 (this is the amount that she has saved)

$547,992.36 = (PMT x (1 - (1 + 0.08)^-25)) / 0.08

PMT = $53,060.72

So, your sister can withdraw $53,060.72 per year in retirement, assuming that she wants to make the money last for 25 years (until age 90) and earn a return of 8%.

Therefore, the answer is choice letter C, $53,061.

Your Sister Turned 35 Today, and She Is Planning to Save