Question #246799

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?


1
Expert's answer
2021-10-12T09:03:24-0400

P=w(1(1+rk)ktrkwhere P = balance at the beginning of the periodw = regular withdrawal rater = annual interest ratek = no of compounding periods in one year500000=w(1(1+0.0812)3600.0812    w=$3667.03\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


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