Answer
See below
Work Step by Step
(a)
Here, P is the balance amount, that is, \[\$4,200\], r is the rate of interest,that is,number of payments in a year, and \[t\]is time period, that is, \[2\text{ years}\].
Compute the amount that the credit cardholder must pay each month using the equation as shown below:
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{1-{{\left( 1+\frac{r}{n} \right)}^{-nt}}} \\
& =\frac{\$4200\left(\frac{0.18}{12}\right)}{1-{{\left(1+\frac{0.18}{12}\right)}^{-12\times2}}}\\&=\frac{\$4200\left(0.015\right)}{1-{{\left(1+0.015\right)}^{-12\times2}}}\\&=\frac{\$4200\left(0.015\right)}{1-{{\left(1.015\right)}^{-24}}}\end{align}\]
\[\begin{align}
& PMT=\frac{\$63}{0.300456}\\&=\$210\end{align}\]
Hence, the amount that the credit cardholder will pay at the end of each month is \[\$210.\]
(b)
First, compute the total amount paid in the form of payment made each month using the equation as shown below:
\[\begin{align}
& \text{Total payments}=\text{Amount}\times \text{time period}\times \text{Number of payments in a year} \\
& =\$210\times2\times12\\&=\$5,040\end{align}\]
Compute the amount of total interest using the equation as shown below:
\[\begin{align}
& \text{Interest}=\text{Total payments}-\text{Balance amount} \\
& \text{= }\!\!\$\!\!\text{5040}-\text{4200}\\&=\$840\end{align}\]
Hence, the amount that the credit holder will pay as interest is \[\$840\].
