Answer
See below
Work Step by Step
(a)
Here, \[P\]is the balance amount which is\[\$3,600\], \[r\]is rate of interest which is\[16.5%\], \[n\]is number of payments in a year which is\[12\], and \[t\]is time period that is\[1\text{ year}\].
Compute the amount that the credit card holder must pay each month using the equation as shown below:
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{1-{{\left( 1+\frac{r}{n} \right)}^{-nt}}} \\
& =\frac{\$3,600\left(\frac{0.165}{12}\right)}{1-{{\left(1+\frac{0.165}{12}\right)}^{-12\times1}}}\\&=\frac{\$3,600\left(0.01375\right)}{1-{{\left(1+0.01375\right)}^{-12\times1}}}\\&=\frac{\$3,600\left(0.01375\right)}{1-{{\left(1.01375\right)}^{-12}}}\end{align}\]
\[\begin{align}
& PMT=\frac{\$49.5}{0.151153}\\&=\$328\end{align}\]
Now, compute the excess amount per month using the equation as shown below:
\[\begin{align}
& \text{Excess amount per month}=\text{New PMT}-\text{Old PMT} \\
& =\$328-\$177\\&=\$151\end{align}\]
(b)
Firstly, compute the total amount paid in the form of payment made each month using the equation as shown below:
\[\begin{align}
& \text{Total payments}=\text{Amount}\times \text{time period}\times \text{Number of payments in a year} \\
& =\$328\times1\times12\\&=\$3,936\end{align}\]
Compute the amount of total interest using the equation as shown below:
\[\begin{align}
& \text{Interest}=\text{Total payments}-\text{Balance amount} \\
& \text{= }\!\!\$\!\!\text{3,936}-3,600\\&=\$336\end{align}\]
Now, compute the less amount that the credit card holder will have to pay using the equation as shown below:
\[\begin{align}
& \text{Amount}=\text{Old interest}-\text{New interest} \\
& =\$648-\$336\\&=\$312\end{align}\]
