The rule of the payout annuity is
[tex]P=\frac{d(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}}[/tex]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
[tex]\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}[/tex]Then you will be able to pull $4778.260422 each month
