Question

You want to be able to withdraw $45,000 each year for 25 years. Your account earns 10% interest. How much do you need in your account at the beginning?

Answer 1

Let's use the compound interest formula,

$A=P(1+\frac{r}{n})^{nt}$

where,

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

Given,

time or periods, t = 25 years

rate, r = 10% = 0.10

A = $45,000 * 25 = $1,125,000

n = 1 , Assuming that interest is compounded annually

Solution,

Let's replace the above,

$1125000=P(1+0.1)^{25}$

Solve for P

$\begin{gathered} P=\frac{1125000}{1.1^{25}} \\ \\ P=103833.00 \end{gathered}$

Answer: $103,833.00