Answer
See below
Work Step by Step
(a)
Here, P is the balance amount which is\[\$4,200\],r is rate of interest which is\[10.5%\], and n is a number of payments in a year which is\[12\], and t is time period that is \[3\]years.
Compute the amount that the credit card holder must pay each month using the equation as shown below:
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{1-{{\left( 1+\frac{r}{n} \right)}^{-nt}}} \\
& =\frac{\$4,200\left(\frac{0.105}{12}\right)}{1-{{\left(1+\frac{0.105}{12}\right)}^{-12\times3}}}\\&=\frac{\$4,200\left(0.00875\right)}{1-{{\left(1+0.00875\right)}^{-12\times3}}}\\&=\frac{\$4,200\left(0.00875\right)}{1-{{\left(1.00875\right)}^{-36}}}\end{align}\]
\[\begin{align}
& PMT=\frac{\$36.75}{0.269211}\\&=\$137\end{align}\]
(b)
Firstly, compute the total amount paid in the form of payment made each month using the equation as shown below:
\[\begin{align}
& \text{Total payments}=\text{Amount}\times \text{time period}\times \text{Number of payments in a year} \\
& =\$137\times3\times12\\&=\$4,932\end{align}\]
Compute the amount of total interest using the equation as shown below:
\[\begin{align}
& \text{Interest}=\text{Total payments}-\text{Balance amount} \\
& =\$4,932-4,200\\&=\$732\end{align}\]
