A couple who wants to purchase a home with a price of $$270,000$ has $$50,000$ for a down payment. If they can get a $20-$year mortgage at $7\%$ 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?

$($a$)$ Their monthly payments would be approximately $

$($Do not round until the final answer. Then round to the nearest hundredth as needed.$)$

$($b$)$ They will pay a total amount of approximately $ before they own the house outright. $($Use the answer from part a to find this answer. Round to the nearest hundredth as needed.$)$

$($c$)$ The total interest is approximately $

$($Use the answer from part $b$ to find this answer. Round to the nearest hundredth as needed.$)$