Answer
See below
Work Step by Step
(a)
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 value of deposit by substituting the values in the formula -
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{\left[ 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right]} \\
& =\frac{\$15,000\left(\frac{0.072}{12}\right)}{\left[1-{{\left(1+\frac{0.072}{12}\right)}^{-12\times3}}\right]}\end{align}\]
Solve and simplify the equation as follows:
\[\begin{align}
& PMT=\frac{\$15,000\times0.006}{1-{{\left(1+0.0006\right)}^{-36}}}\\&=\frac{\$15,000\times0.006}{1-{{\left(1.0006\right)}^{-36}}}\\&=\frac{\$90}{0.193744}\\&=\$465\end{align}\]
Computation of the interest amount can be done by deducting the amount of the loan from the total of monthly payments.
Compute the amount of interest using the equation as shown below:
\[\begin{align}
& \text{Interest amount}=\text{Total of Monthly payments}-\text{Amount of the loan} \\
& =\left( \$465\times36\right)-\$15,000\\&=\$1,740\end{align}\]
(b)
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 value of deposit by substituting the values in the formula as mentioned below:
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{\left[ 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right]} \\
& =\frac{\$15,000\left(\frac{0.081}{12}\right)}{\left[1-{{\left(1+\frac{0.081}{12}\right)}^{-12\times5}}\right]}\end{align}\]
Simplify and solve the equation as follows:
\[\begin{align}
& PMT=\frac{\$15,000\left(0.00675\right)}{\left[1-{{\left(1+0.00675\right)}^{-60}}\right]}\\&=\frac{\$10,125}{0.3321155}\\&=\$305\end{align}\]
Computation of the interest amount can be done by deducting the amount of the loan from the total of monthly payments. Compute the amount of interest using the equation as shown below:
\[\begin{align}
& \text{Interest amount}=\text{Total of Monthly payments}-\text{Amount of the loan} \\
& =\left( \$305\times60\right)-\$15,000\\&=\$3,300\end{align}\]
