Question

You know you will have $500,000 in your account when you retire. You want to be able to take monthly withdrawals from the account for a total of 30 years. Your retirement account earns 8% interest. How much will you be able to withdraw each month?

Answer 1

$\displaystyle P = \frac{w(1-(1+\frac{r}{k})^{-kt}}{\frac{r}{k}}\\ \text{where P = balance at the beginning of the period}\\ \text{w = regular withdrawal rate}\\ \text{r = annual interest rate}\\ \text{k = no of compounding periods in one year}\\ \therefore 500000 = \frac{w(1-(1+\frac{0.08}{12})^{-360}}{\frac{0.08}{12}}\\ \implies w = \$3667.03$