Question

8. You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar.Regular withdrawal:$300Interest rate:4%FrequencyweeklyTime:17 yearsAccount balance: $

Answer 1

To solve this question, we can just use the Payout Annuity Formula. This formula is given by

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

Where P is the balance in the account at the beginning (starting amount, or principal).

d is the regular withdrawal (the amount you take out each year, each month, etc.)

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.

From the text, we have

$\begin{gathered} d=300 \\ r=0.04 \\ k=52 \\ N=17 \end{gathered}$

k equals to 52 because we have 52 weeks in a year.

Plugging those values in our formula, we have

$P_0=\frac{300(1-(1+\frac{0.04}{52})^{-17\times52})}{(\frac{0.04}{52})}=192367.717778\approx192368$

We would need an account balance of $192368.