Question

Your sister turned 35 today, and she is planning to save $7,500 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that will provide a return of 8.0% 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 beginning of her first retirement year. Enter your answer rounded to two decimal places.

Answer 1

First we will find the future value of the payments made for 30 years

Future value annuity = p * [ ( 1+r)ⁿ - 1 ] / r

Future value annuity = 7500 * [ ( 1 + 0.08)³⁰ - 1 ] / 0.08

Future value annuity = 7500 *9.062657 / 0.08

Future value annuity = 849624.08

This amount she will have at the end of 30 years in her retirement account.

Now she will withdraw them at the beginning of the next year for next 25 years. Therefore, we will use the formula for present value annuity due.

P = PV [ r / 1 - ( 1 + r)^-n ] * 1 / (1 + r)

P = 849624.08 * [ 0.08 / 1 - ( 1+0.08)^-25 ] * 1 / ( 1+ 0.08)

P = 849624.08 * [ 0.08 / 1 - 0.146018 ] * 1 / 1.08

P = 849624.08 * [ 0.08 / 0.853982 ] * 0.925926

P = $73696.06

So, she can make a withdrawal of $73696.06 for 25 years at the beginning of each year.