Suppose you borrow $$290,000\mathrm{.}00$ by taking out a $15$ year fixed rate mortgage with a monthly payment of $$1,972\mathrm{.}74.$ You made a down payment of $$50,700\mathrm{.}00.$

$($a$)$ Calculate the Total Cost of the home, including the down payment. Round your answer to the nearest cent.

Total Cost

$

$($b$)$ Calculate the Total Cost of the home, including the down payment, assuming instead a $30$ year fixed mortgage with a monthly payment of $$1,464\mathrm{.}18$ and a down payment of $$50,700\mathrm{.}00.$ Round your answer to the nearest cent.

$($c$)$ How do the totals compare for the $15$ and $30$ year loans?

Total Cost of home with $15$ year mortgage $$ Total Cost of home with $30$ year mortgage

Total Cost of home with $15$ year mortgage $>$ Total Cost of home with $30$ year mortgage