Question

Suppose you want to have $700,000 for retirement in 30 years. Your account earns 9% interest. How much would you need to deposit in the account each month?$____________

Answer 1

Step 1

State the formula for the Future Value.

`\begin{gathered} Fv=((d(1+(r)/(m))^(mt)-1)))/((r)/(m)) \\ \end{gathered}`

where;

`\begin{gathered} Fv=\text{ \$700000} \\ r=(9)/(100)=0.09 \end{gathered}`
`\begin{gathered} m=12 \\ d=? \\ t=30\text{years} \end{gathered}`

Step 2

Find how much you need to deposit in the account each month

`\begin{gathered} Fv=((d(1+(r)/(m))^(mt)-1)))/((r)/(m)) \\ 700000=((d(1+(0.09)/(12))^(12*30)-1)))/((0.09)/(12)) \end{gathered}`
`\begin{gathered} 700000((0.09)/(12))=(d(1.0075)^(360)-1) \\ 5250=(d(14.73057612-1) \\ \end{gathered}`
`\begin{gathered} 5250=13.73057612d \\ (13.73057612d)/(13.73057612)=(5250)/(13.73057612) \\ d=\text{ \$}382.3583187 \\ d\approx\text{ \$}382.36 \end{gathered}`

Hence, approximately $382.36 need to be deposited in the account each month