Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-2 Multiplying and Dividing Rational Expressions - Practice and Problem-Solving Exercises - Page 663: 59

Answer

$\$518,011.20$

Work Step by Step

The total cost is $\$300,000$ and the downpayment is $\$60,000$. Therefore, the amount to mortgage, $A$, is $$ A=300,000-60,000=240,000 .$$ Using the given formula, $m=\frac{A\left(\frac{r}{12}\right)\left(1+\frac{r}{12}\right)^n}{\left(1+\frac{r}{12}\right)^n-1}$, with $r=6\%=0.06$ and $n=30(12)=360$, then $$\begin{aligned} m&=\frac{240\,000\left(\frac{0.06}{12}\right)\left(1+\frac{0.06}{12}\right)^{360}}{\left(1+\frac{0.06}{12}\right)^{360}-1} \\&\approx 1\, 438.92 .\end{aligned}$$ Therefore, the monthly amortization is approximately $\$1\, 438.92$. With a monthly amortization of approximately $\$1\,438.92$, the total amount that will be paid in $30$ years (i.e. $360$ months) is $$ 1\,438.92(360)=518\,011.20 .$$ Hence, the cost for the family to repay the $\$260,000$ mortgage in $30$ years is approximately $\$518,011.20$ .
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