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

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