Answer
See below
Work Step by Step
(a)
Calculation of future value of amount can be done by using 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:
\[\begin{align}
& A=P\times {{\left( 1+\frac{r}{n} \right)}^{nt}} \\
& =\$2,500\times{{\left(1+\frac{0.04}{12}\right)}^{12\times20}}\\&=\$2,500\times{{\left(1+0.00333\right)}^{240}}\\&=\$5,556.46\end{align}\]
Hence, the future value of the amount is \[\$5,556.46\]
(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:
\[\begin{align}
& \text{Interest amount}=A-P \\
& =\$5,556.46-\$2,500\\&=\$3,056.46\end{align}\]
Hence, the interest amount is \[\$3,056.46\]
