Answer
See below
Work Step by Step
(a)
Annual fuel expense can be computed by dividing the Annual miles driven by miles per gallon and multiplying the result to the price per gallon.
Compute the annual fuel expenses for Hybrid car using the equation as shown below:
\[\begin{align}
& \text{Annual fuel expense}=\frac{\text{Annual miles driven}}{\text{miles per gallon}}\times \text{price per gallon} \\
& =\frac{36,000}{40}\times \$3.60\\&=\$3,240\end{align}\]
Compute the annual fuel expenses for Hybrid car using the equation as shown below:
\[\begin{align}
& \text{Annual fuel expense}=\frac{\text{Annual miles driven}}{\text{miles per gallon}}\times \text{price per gallon} \\
& =\frac{36,000}{12}\times \$3.60\\&=\$10,800\end{align}\]
The savings in annual fuel expense can be computed by subtracting the annual fuel expense of hybrid car from the annual fuel expense of SUV car.
\[\begin{align}
& \text{Savings in annual fuel expense}=\text{Annual fuel expense of SUV car} \\
& -\text{Annual fuel expense of Hybrid car} \\
& =\$10,800-\$3,240\\&=\$7,560\end{align}\]
(b)
Calculation of the value of an annuity can be done by using formula:
\[A=\frac{P\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]}{\left( \frac{r}{n} \right)}\]
Where A denotes the annuity value of the annuity, P denotes the Principal amount, r denotes the rate of interest, t denotes the number of years and n denotes the number of times compounding is done in a year.
Compute the annuity value by substituting the values in the formula as mentioned below:
\[\begin{align}
& A=\frac{P\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]}{\left( \frac{r}{n} \right)} \\
& =\frac{\$630\left[{{\left(1+\frac{0.052}{12}\right)}^{12\times6}}-1\right]}{\left(\frac{0.052}{12}\right)}\\&=\frac{\$630\left[{{\left(1+0.0043\right)}^{72}}-1\right]}{\left(0.0043\right)}\\&=\$53,099\end{align}\]
Hence, the value of the annuity at the end of 6 years is \[\$53,099\].
