Suppose you borrow $$245,000\mathrm{.}00$ by taking out a $15$ year fixed rate mortgage with a monthly payment of $$1,986\mathrm{.}59.$ You made a down payment of $$47,900\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 $$1,461\mathrm{.}65$ and a down payment of $$47,900\mathrm{.}00.$ Round your answer to the nearest cent.