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\[9.5%\], n is number of payments in a year which is\[12\], and \[t\]is time period that is\[3\text{ years}\].
Compute the amount that the credit card holder must pay each month using the equation as shown below:
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{1-{{\left( 1+\frac{r}{n} \right)}^{-nt}}} \\
& =\frac{\$3,600\left(\frac{0.095}{12}\right)}{1-{{\left(1+\frac{0.095}{12}\right)}^{-12\times3}}}\\&=\frac{\$3,600\left(0.007917\right)}{1-{{\left(1+0.007917\right)}^{-12\times3}}}\\&=\frac{\$3,600\left(0.007917\right)}{1-{{\left(1.007917\right)}^{-36}}}\end{align}\]
\[\begin{align}
& PMT=\frac{\$28.5012}{0.24715}\\&=\$115\end{align}\]
(b)
Firstly, compute the total amount paid in the form of payment made each month using the equation as shown below:
\[\begin{align}
& \text{Total payments}=\text{Amount}\times \text{time period}\times \text{Number of payments in a year} \\
& =\$115\times3\times12\\&=\$4,140\end{align}\]
Compute the amount of total interest using the equation as shown below:
\[\begin{align}
& \text{Interest}=\text{Total payments}-\text{Balance amount} \\
& =\$4,140-3,600\\&=\$540\end{align}\]
