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The amount to be withdrawn each year is $30000.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=(d(1-(1+(r)/(k))^(-nk)))/((r)/(k)) \\ d=30000 \\ r=7\text{ \%} \\ k=1 \\ n=30 \\ P_0=(30000(1-(1+(7)/(100))^(-30)))/((7)/(100)) \\ =(30000(1-(1.07)^(-30)))/(0.07) \\ =(30000*0.8686)/(0.07) \\ =372271.2355 \end{gathered}`

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