Question

You want to be able to withdraw $30,000 each year for 30 years from your account earning 7% interest. How much do you need in the account atthe beginning, to the nearest dollar?

Answer 1

Given:

The amount to be withdrawn each year is $30000.

number of years n = 30

interest rate is 7%.

The amount that should ne need in the beginning is calculated by using payout annuity formula.

$\begin{gathered} P_0=\frac{d(1-(1+\frac{r}{k})^{-nk})}{\frac{r}{k}} \\ d=30000 \\ r=7\text{ \%} \\ k=1 \\ n=30 \\ P_0=\frac{30000(1-(1+\frac{7}{100})^{-30})}{\frac{7}{100}} \\ =\frac{30000(1-(1.07)^{-30})}{0.07} \\ =\frac{30000\times0.8686}{0.07} \\ =372271.2355 \end{gathered}$

Answer : The amount needed in the account at the beginning is $372271.2