The price of a home is $$150,000.$ The bank requires a $15\%$ down payment. The buyer is offered two mortgage options: $15-$year fixed at $8\mathrm{.}5\%$ or $30-$year fixed at $8\mathrm{.}5\%.$ Calculate the amount of interest paid for each option. How much does the buyer save in interest with the $15-$year option? Use the following formula to determine the regular payment amount.

$PMT=\frac{P(\frac{r}{n})}{[1-(1+\frac{r}{n}{)}^{-nt}]}$

Find the monthly payment for the $15-$year option.

s $($Round to the nearest dollar as needed.$)$