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

Sagot :

Step 1

State the formula for the Future Value.

[tex]\begin{gathered} Fv=\frac{(d(1+\frac{r}{m})^{mt}-1))}{\frac{r}{m}} \\ \end{gathered}[/tex]

where;

[tex]\begin{gathered} Fv=\text{ \$700000} \\ r=\frac{9}{100}=0.09 \end{gathered}[/tex][tex]\begin{gathered} m=12 \\ d=? \\ t=30\text{years} \end{gathered}[/tex]

Step 2

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

[tex]\begin{gathered} Fv=\frac{(d(1+\frac{r}{m})^{mt}-1))}{\frac{r}{m}} \\ 700000=\frac{(d(1+\frac{0.09}{12})^{12\times30}-1))}{\frac{0.09}{12}} \end{gathered}[/tex][tex]\begin{gathered} 700000(\frac{0.09}{12})=(d(1.0075)^{360}-1) \\ 5250=(d(14.73057612-1) \\ \end{gathered}[/tex][tex]\begin{gathered} 5250=13.73057612d \\ \frac{13.73057612d}{13.73057612}=\frac{5250}{13.73057612} \\ d=\text{ \$}382.3583187 \\ d\approx\text{ \$}382.36 \end{gathered}[/tex]

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

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