Given, Present value, interest rate and time in quarterly are

\(\displaystyle{P}{V}=\${56780}\)

\(\displaystyle{r}={2.8}\%\ \text{quarterly}\ ={0.028}\)

\(\displaystyle{t}={23}\) quarterly

Part (a): The formula for Future value and interest are

\(\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{t}{\quad\text{and}\quad}{I}{F}{V}-{P}{V}\)

\(\displaystyle{P}{V}=\) Present value

\(\displaystyle{F}{V}=\) Future value

\(\displaystyle{I}=\) Interest

\(\displaystyle{r}=\) rate quarterly

\(\displaystyle{t}=\) time in quarterly

The Amount is

\(\displaystyle{F}{V}=\${56780}{\left({1}+{0.028}\right)}^{23}\)

\(\displaystyle=\${56780}{\left({1.028}\right)}^{23}\)

\(\displaystyle=\${56780}{\left({1.88730303}\right)}\)

\(\displaystyle=\${107161.066}\)

\(\displaystyle{I}=\${107161.066}-{56780}\)

\(\displaystyle=\${50381.066}\)

Part (b): The formula for Future value and interest are

\(\displaystyle{F}{V}={P}{V}\cdot{e}^{n}{\quad\text{and}\quad}{I}={F}{V}-{P}{V}\)

\(\displaystyle{P}{V}=\) Present value

\(\displaystyle{F}{V}=\) Future value

\(\displaystyle{I}=\) Interest

\(\displaystyle{r}=\) rate

\(\displaystyle{t}=\) time in years

The amount is

\(\displaystyle{F}{V}=\${56780}\cdot{e}^{{{0.028}{\left({15}\right)}}}\)

\(\displaystyle=\${56780}\cdot{\left({1.521961556}\right)}\)

\(\displaystyle=\${86416.97713}\)

\(\displaystyle{I}=\${86416.97713}-{56780}\)

\(\displaystyle=\${29636.97713}\)

\(\displaystyle{P}{V}=\${56780}\)

\(\displaystyle{r}={2.8}\%\ \text{quarterly}\ ={0.028}\)

\(\displaystyle{t}={23}\) quarterly

Part (a): The formula for Future value and interest are

\(\displaystyle{F}{V}={P}{V}{\left({1}+{r}\right)}^{t}{\quad\text{and}\quad}{I}{F}{V}-{P}{V}\)

\(\displaystyle{P}{V}=\) Present value

\(\displaystyle{F}{V}=\) Future value

\(\displaystyle{I}=\) Interest

\(\displaystyle{r}=\) rate quarterly

\(\displaystyle{t}=\) time in quarterly

The Amount is

\(\displaystyle{F}{V}=\${56780}{\left({1}+{0.028}\right)}^{23}\)

\(\displaystyle=\${56780}{\left({1.028}\right)}^{23}\)

\(\displaystyle=\${56780}{\left({1.88730303}\right)}\)

\(\displaystyle=\${107161.066}\)

\(\displaystyle{I}=\${107161.066}-{56780}\)

\(\displaystyle=\${50381.066}\)

Part (b): The formula for Future value and interest are

\(\displaystyle{F}{V}={P}{V}\cdot{e}^{n}{\quad\text{and}\quad}{I}={F}{V}-{P}{V}\)

\(\displaystyle{P}{V}=\) Present value

\(\displaystyle{F}{V}=\) Future value

\(\displaystyle{I}=\) Interest

\(\displaystyle{r}=\) rate

\(\displaystyle{t}=\) time in years

The amount is

\(\displaystyle{F}{V}=\${56780}\cdot{e}^{{{0.028}{\left({15}\right)}}}\)

\(\displaystyle=\${56780}\cdot{\left({1.521961556}\right)}\)

\(\displaystyle=\${86416.97713}\)

\(\displaystyle{I}=\${86416.97713}-{56780}\)

\(\displaystyle=\${29636.97713}\)