HC$10$

$1.$You and your spouse have found your dream home. The selling price is $$220,000$; you will put $$50,000$ down and obtain a $30-$year fixed$-$rate mortgage at $12\%$ compounded monthly for the balance a$)$ Assume that monthly payments begin in one month. What will each payment be$?$ b$)$ How much interest will you pay in dollars$)$ over the lifetime of the loan? $($Assume you make each of the required $360$ payments on time.$)$ c$)$ Although you will get a $30-$year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in $20$ years?