A family wants to purchase a house that costs $$135,000.$ They plan to take out a $$125,000$ mortgage on the house and put $$10,000$ as a down payment. The bank informs them that with a $15-$year mortgage their monthly payment would be $$731\mathrm{.}85$ and with a $30-$year mortgage their monthly payment would be $$588\mathrm{.}41.$ Determine the amount they would save on the cost 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?

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