A couple who wants to purchase a home with a price of $$360,000$ has $$100,000$ for a down payment. If they can get a $30-$year mortgage at $6\%$ per year on the unpaid balance, find each of the following.

$($a$)$ What will be their monthly payments?

$($b$)$ What is the total amount they will pay before they own the house outright?

$($c$)$ How much interest will they pay over the life of the loan?