Question

You just turned 26. Happy birthday! Now that you’re old, you want to be responsible and start a retirement fund. You plan to invest $445 every month for the next 39 years. You expect to earn a 7.9% annual return until you retire. Once you retire, you will shift your savings into safer investments that you expect will earn 4.8% per year. You plan to make monthly withdrawals for 21 years of retirement (and don't want to have any money left at the end). Under this plan, how much money will you withdraw from your retirement account each month? (NOTE: Round your answer to the nearest cent)

Answer 1

First, we calculate the value of the account at retirement.

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $445

r = periodic rate of interest. This is (7.9%/12). We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 39 * 12 = 468

Future value of annuity = $445 * [(1 + (7.9%/12))⁴⁶⁸ - 1] / (7.9%/12)

Future value of annuity = $1,389,843.60

Next, we calculate the monthly withdrawal during retirement.

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

where P = periodic payment. We need to calculate this.

r = interest rate per period. This is (4.8%/12). We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 21 * 12 = 252

$1,389,843.60 = P * [1 - (1 + (4.8%/12))^-252] / (4.8%/12)

P =  $1,389,843.60 * (4.8%/12) / [1 - (1 + (4.8%/12))^-252]

P =  $8,764.34

You will withdraw  $8,764.34 each month