Question

You have $ 567,625 saved for retirement. Your account earns 4.8 % interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 19 years?

Answer 1

The payout annuity formula is the following:

`P_0=(d(1-(1+(r)/(k))^(-N\cdot k))/(((r)/(k)))`

Where:

Po is starting amount in the account

d is the regular withdrawal

r is the annual interest rate (in decimal form)

k is the number of compounding periods in one year

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

The given information is:

Po=$567,625

r=4.8%/100%=0.048

k=12 since we are withdrawing monthly

N=19 years.

By replacing this information in the formula, we can solve for d as follows:

`\begin{gathered} 567,625=(d(1-(1+(0.048)/(12))^(-19\cdot12)))/(((0.048)/(12))) \\ 567,625=(d(1-(1+0.004)^(-228)))/((0.004)) \\ 567,625=(d(1-(1.004)^(-228)))/((0.004)) \\ 567,625=(d(1-0.4025))/((0.004)) \\ 567,625=(d(0.5975))/((0.004)) \\ 567,625\cdot(0.004)=d(0.5975) \\ 2270.5=d(0.5975) \\ d=(2270.5)/(0.5975) \\ d=3799.69 \end{gathered}`

Answer: you will be able to pull out each month $3799.69 for 19 years