Youve decided to buy a house that is valued at $$1$ million. You have $$250,000$ to use as a down payment on the house, and want your take out a mortgage for the remainder of the purchase price. Your bank has approved your $$750,000$ mortgage, and if offering a standard $30-$year mortgage at a $10\%$ fixed nominal interest rate $($APR$).$ Under this loan proposal, your mortgage payment will be $$6,581\mathrm{.}57$ per month.

It is likely that you wont like the prospect of paying more money each month, but if you do take out a $15-$year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a $30-$year mortgage instead of a $15-$year mortgage?

A$)$ $$1,267,781\mathrm{.}44$

B$)$ $$918,682\mathrm{.}20$

C$)$ $$1,175,913\mathrm{.}22$

D$)$ $$1,084,045\mathrm{.}00$