Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 8 - Personal Finance - 8.8 Credit Cards - Exercise Set 8.8 - Page 565: 10

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: \[\begin{align} & \text{Amount}=\text{Old interest}-\text{New interest} \\ & =\$648-\$336\\&=\$312\end{align}\]
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