A couple who wants to purchase a home with a price of $$250,000$ has $$50,000$ 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? $($Do not round until the final answer. Then round to the nearest hundredth as needed.$)$

Your answer

b$.$ How much interest will they pay over the life of the loan? $($Do not round until the final answer. Then round to the nearest hundredth as needed.$)$

Your answer