Question

You want to be able to withdraw $45,000 each year for 20 years. Your account earns 10% interest. How much do you need in your account at the beginning?

Answer 1

Step-by-step 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.

`P_0=(d\left(1-\lparen1+(r)/(k)\right)^(-Nk)\rparen)/((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. 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

`\begin{gathered} P_0=(45000\lparen1-\left(1+(10)/(100)\right)^(-20*1)))/((10)/(100)) \\ P_0=(45000\left(1-\left(1.1\right)^(-20)\right?)/(0.1) \\ P_0=383110.36738 \end{gathered}`

Answer: $383110.36738