Respuesta :
Explanation
In the question, we are given that the individual should be able to withdraw $45,000 each year for 20 years through his account that earns 10% interest.
To find the amount he would need at in the account at the beginning, we will use the Payout Annuity formula below.
[tex]P_0=\frac{d\left(1-\lparen1+\frac{r}{k}\right)^{-Nk}\rparen}{\frac{r}{k}}[/tex]
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. Example: 5% = 0.05)
k is the number of compounding periods in one year.
N is the number of years we plan to take withdrawals
[tex]\begin{gathered} P_0=\frac{45000\lparen1-\left(1+\frac{10}{100}\right)^{-20\times1})}{\frac{10}{100}} \\ P_0=\frac{45000\left(1-\left(1.1\right)^{-20}\right?}{0.1} \\ P_0=383110.36738 \end{gathered}[/tex]Answer: $383110.36738
