A family wants to purchase a house that costs $$140,000.$ They plan to take out a $$100,000$ mortgage on the house and put $$40,000$ as a down payment. The bank informs them that $w$ a $15-$year mortgage their monthly payment would be $$789\mathrm{.}47$ and with a $30-$year mortgage their monthly payment would be $$546\mathrm{.}08.$ Determine the amount they would save on the cos of the house if they selected the $15-$year mortgage rather than the $30-$year mortgage.

How much would they save if they selected the $15-$year mortgage?