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:

$P_0=\frac{d(1-(1+\frac{r}{k})^{-N\cdot k}}{(\frac{r}{k})}$

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:

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

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