Step 1

Future value is calculate by using this formula:

\(\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{{{n}}}\)

r is interest rate and n is time period.

Step 2

a) Present value \(\displaystyle=\${5000}\)

Time period \(\displaystyle={3}\) year

- Future value at \(\displaystyle{4}\%\) interest rate

\(\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{{{t}}}\)

\(\displaystyle{F}{V}={5000}{\left({1}+{0.04}\right)}^{{{3}}}\)

\(\displaystyle=\${5624.32}\)

- Future value at \(\displaystyle{5}\%\) interest rate

\(\displaystyle{F}{V}={5000}{\left({1}+{0.05}\right)}^{{{3}}}\)

\(\displaystyle=\${5788.13}\)

- Future value at \(\displaystyle{7.25}\%\) interest rate

\(\displaystyle{F}{V}={5000}{\left({1}+{0.0725}\right)}^{{{3}}}\)

\(\displaystyle=\${6168.25}\)

- Future value at \(\displaystyle{10}\%\) interest rate

\(\displaystyle{F}{V}={5000}{\left({1}+{0.10}\right)}^{{{3}}}\)

\(\displaystyle=\${6655}\)

Future value is calculate by using this formula:

\(\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{{{n}}}\)

r is interest rate and n is time period.

Step 2

a) Present value \(\displaystyle=\${5000}\)

Time period \(\displaystyle={3}\) year

- Future value at \(\displaystyle{4}\%\) interest rate

\(\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{{{t}}}\)

\(\displaystyle{F}{V}={5000}{\left({1}+{0.04}\right)}^{{{3}}}\)

\(\displaystyle=\${5624.32}\)

- Future value at \(\displaystyle{5}\%\) interest rate

\(\displaystyle{F}{V}={5000}{\left({1}+{0.05}\right)}^{{{3}}}\)

\(\displaystyle=\${5788.13}\)

- Future value at \(\displaystyle{7.25}\%\) interest rate

\(\displaystyle{F}{V}={5000}{\left({1}+{0.0725}\right)}^{{{3}}}\)

\(\displaystyle=\${6168.25}\)

- Future value at \(\displaystyle{10}\%\) interest rate

\(\displaystyle{F}{V}={5000}{\left({1}+{0.10}\right)}^{{{3}}}\)

\(\displaystyle=\${6655}\)