Question

You want to be able to withdraw $30,000 from your account each year for 25 years after you retire.You expect to retire in 15 years.If your account earns 9% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?

Answer 1

In order to withdraw $30,000 per year for 25 years, you need to have:

$\ 30000\/\text{year}\times25\text{ years}=\ 750,000$

This will be the future value.

To figure the annual deposit, which plus annual interest would amount to $750,000, it is necessary to use the formula:

$\begin{gathered} \text{Future Value}=P(\frac{(1+r)^t-1}{r}) \\ \text{Where P is the principal, which is the annual deposit.} \\ r\text{ is the rate of interest.} \end{gathered}$

Substitute Future Value=$750,000, r=9%=0.09 and t=15 into the formula:

$\begin{gathered} 750000=P(\frac{(1+0.09)^{15}-1}{0.09}) \\ \Rightarrow750000=P(\frac{(1.09)^{15}-1}{0.09}) \\ \Rightarrow750000=P(29.361) \\ \Rightarrow P=\frac{750000}{29.361}\approx\ 25,544 \end{gathered}$

Hence, the annual deposit until retirement to achieve the goal is about $25,544.