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=(d(1-(1+(r)/(k))^(-Nk))/(((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=(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=(P_O((r)/(k)))/(1-(1+(r)/(k))^(-Nk))`

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

`d=(500000((0.08)/(12)))/(1-(1+(0.08)/(12))^(-20*12))=4182.20`

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