Question

you have $400,000 saved for retirement. your account earns 2% interest. how much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years? round your answer to the nearest dollar.

Explanation:

Step1: Convert annual - interest rate to monthly rate

The annual interest rate $r = 2\%=0.02$, so the monthly interest rate $i=\frac{0.02}{12}$. The number of periods $n = 20\times12=240$ months, and the present - value $PV = 400000$.

Step2: Use the present - value of an ordinary annuity formula

The formula for the present - value of an ordinary annuity is $PV = PMT\times\frac{1-(1 + i)^{-n}}{i}$, where $PMT$ is the monthly payment. We need to solve for $PMT$. Rearranging the formula gives $PMT=\frac{PV\times i}{1-(1 + i)^{-n}}$.
Substitute $PV = 400000$, $i=\frac{0.02}{12}$, and $n = 240$ into the formula:
\[

$$\begin{align*} PMT&=\frac{400000\times\frac{0.02}{12}}{1-(1+\frac{0.02}{12})^{-240}}\\ \end{align*}$$

\]
First, calculate $(1+\frac{0.02}{12})^{-240}\approx0.67032$. Then $1-(1+\frac{0.02}{12})^{-240}=1 - 0.67032 = 0.32968$. And $400000\times\frac{0.02}{12}\approx666.67$. So $PMT=\frac{666.67}{0.32968}\approx2022$.

Answer:

$2022$