Question

You have $500,000 saved for retirement. Your account earns 8% interest. How much will you be able to pullout each month, if you want to be able to take withdrawals for 15 years?$

Answer 1

The rule of the payout annuity is

$P=\frac{d(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}}$

P is the initial amount

d is regular withdrawals

r is the annual rate in decimal

n is the number of periods in a year

t is the time

Since you have $500 000 saved, then

P = 500000

Since the interest is 8%, then

r = 8/100 = 0.08

Since the time is 15 years, then

t = 15

Since you want the monthly amount, then

n = 12

Substitute them in the rule to find d

$\begin{gathered} 500000=\frac{d(1-(1+\frac{0.08}{12})^{-12(15)})}{\frac{0.08}{12}} \\ 500000(\frac{0.08}{12})=d(1-(\frac{151}{150})^{-180}) \\ \frac{10000}{3}=d(1-(\frac{151}{150})^{-180}) \\ \frac{\frac{10000}{3}}{(1-(\frac{151}{150})^{-180})}=d \\ 4778.260422=d \end{gathered}$

Then you will be able to pull $4778.260422 each month