We are to find the future value
The future value can be calculated using
[tex]FV=PV(1+\frac{r}{100\alpha})^{n\alpha}[/tex]From the given information
PV = $4013
r = 4.1
n = 9 years
Since the investment is compounded quarterly then
α = 4
By substituting these values we get
[tex]FV=\text{ \$4013(1 }+\frac{4.1}{100(4)})^{9(4)}[/tex]Simplifying the equation we get
[tex]\begin{gathered} FV=\text{ \$}4013(1\text{ }+\frac{4.1}{400})^{36} \\ FV=\text{ \$}4013(1\text{ }+0.01025)^{36} \\ FV=\text{ \$}4013(1.01025)^{36} \\ FV=\text{ \$}4013(1.44436) \\ FV=\text{\$}5793.17 \end{gathered}[/tex]Therefore,
The Future Value is $5793.17
