Question

You have $500,000 saved for retirement. Your account earns 8% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

Answer 1

This is an example of a Payout Annuity problem.

The Payout Annuity formula is given to be:

$P_O=\frac{d(1-(1+\frac{r}{k})^{-Nk}}{(\frac{r}{k})}$

where

P0 is the balance in the account at the beginning

d is the regular withdrawal

r is the annual interest rate

k is the number of compounding periods in one year

N is the number of years we plan to take withdrawals.

From the question, we have the following parameters:

$\begin{gathered} P_O=500,000 \\ r=\frac{8}{100}=0.08 \\ k=12 \\ N=20 \\ d=\text{?} \end{gathered}$

Since we are to find the value of d, we can adjust the formula such that d is the subject:

$d=\frac{P_O(\frac{r}{k})}{1-(1+\frac{r}{k})^{-Nk}}$

We can now substitute the values and solve as shown below:

$d=\frac{500000(\frac{0.08}{12})}{1-(1+\frac{0.08}{12})^{-20\times12}}=4182.20$

Therefore, you will be able to pull out $4,182.20 monthly.