Question

You are 44 years old today and want to plan for retirement at age 65. You want to set aside an equal amount every year from now to retirement. You expect to live to age 96 and want to withdraw a fixed amount each year during retirement that at age 65 will have the same purchasing power as $94,725 has today. You plan on withdrawing the money starting the day you retire. You have not saved any money for retirement. Inflation is assumed to be 4.0% in the future. You expect to earn an 8.5% return on your investments in the future. How much do you need to save each year until retirement to meet your goal?

Answer 1

Let's consider the time period from today (when you are 44 years old) till the retirement (when you are 65 years old).

n = 65 - 44 = 21 years

inflation, i = 4%

Fixed amount that will be withdrawn each year post retirement = $ 94,725 x (1 + i)ⁿ = $ 94,725 x (1 + 4%)²¹ = $  215,856.31

Let's now look at the post retirement period beginning with your retirement (when you are 65 years old) till you are 96 years old.

Withdrawal takes place at the beginning of the period.

Annuity, A = $ 215,856.31 , r = 8.5%, t = 96 - 65 = 31 years

Hence, PV of immediate annuities when you are 65 years old = PV (Rate, Period, PMT, FV, Type) = PV (8.5%, 31, -215856.31, 0, 1) = $2,535,630.31

So, this is the kitty size required at the time of retirement. In order to build this kitty, let's say you need to save and amount S each year until retirement to meet your goal.

Hence, FV of S over n = 21 years and r = 8.5% should result in $2,535,630.31

Hence, S = PMT (Rate, Period, PV, FV) = PMT (8.5%, 21, 0, -2535630.31) = $ 47,404.65

Hence, you need to save an amount = S = $47,404.65 every year.