Thinking Mathematically (6th Edition)

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

Chapter 8 - Personal Finance - Chapter Summary, Review, and Test - Review Exercises - Page 572: 71

Answer

See below

Work Step by Step

(a) The total amounts to \[\$130888\]approximately and the total number of days billing period 30 days. $\begin{align} & \text{Average daily balance}=\frac{\text{Sum of unpaid balance for each day billing period}}{\text{No}\text{. of days in the billing period}} \\ & =\frac{\$130,888}{30}\\&=\$4362.93\\&\simeq\$4363\end{align}$ (b) The rate of interest is $1.1percent$per month, Compute the interest to be paid on December 1 as follows: \[\begin{align} & I=Prt \\ & =\text{ }\!\!\$\!\!\text{4363}\!\!\times\!\!\text{0}\text{.011}\!\!\times\!\!\text{1}\\&=\frac{\text{}\!\!\$\!\!\text{4363}\!\!\times\!\!\text{1}\text{.1}\!\!\times\!\!\text{1}}{\text{100}}\\&=\text{}\!\!\$\!\!\text{47}\text{.99}\\&\simeq\$\text{48}\end{align}\] Hence, the amount of interest is\[\$48\]. (c) Compute the balance due on December 1 as shown below; \[\begin{align} & \text{Balance due}=\text{Unpaid balance on November 30}+\text{Interest} \\ & =\$4,485+\$48\\&=\$4,533\end{align}\] (d) The Balance due exceeds the amount$\$360$. Therefore, the customers must pay a minimum of $\frac{1}{36}$ balance due. Compute the monthly payment as follows: \[\begin{align} & \text{Minimum}\,\text{Monthly}\,\,\text{Payment}=\,\text{Balance}\,\text{due}\,\text{ }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{36}} \\ & =\,\$\,4533\,\times\frac{1}{36}\\&=\,\$\,125.9\\&\simeq\,\text{}\!\!\$\!\!\text{}\,\text{126}\,\text{approximately}\end{align}\] Hence, the minimum monthly payment due by December 9 is\[\$97\].
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