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 $\$518,011.20$ .
