Answer
See below
Work Step by Step
(a)
Calculation of future value of amount can be done with the mentioned formula:
\[A=P\times {{\left( 1+\frac{r}{n} \right)}^{nt}}\]
Where A denotes the Future value of the amount, 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 Future value by substituting the values in the formula as mentioned below:
\[\begin{align}
& A=P\times {{\left( 1+\frac{r}{n} \right)}^{nt}} \\
& =\$30,000\times{{\left(1+\frac{0.025}{4}\right)}^{4\times10}}\\&=\$30,000\times{{\left(1+0.00625\right)}^{40}}\\&=\$38,490.80\end{align}\]
Hence, the future value of the amount is \[\$38,490.80\]
(b)
Computation of the interest amount can be done by deducting the Principal amount (P) from the future value (A) of the loan. Compute the interest amount as mentioned below:
\[\begin{align}
& \text{Interest amount}=A-P \\
& =\$38,490.80-\$30,000\\&=\$8,490.80\end{align}\]
Hence, the interest amount is\[\$8,490.80\].
