Your friend is purchasing a house for $$182,000$ using a $30-$year mortgage at $4\%$ APR.

a$)$ If they make a $20\%$ down payment, how much will they be borrowing for their mortgage? $2$ points

b$)$ The monthly mortgage payment is found to be $$695\mathrm{.}12.$ If your friend accepts this loan, how much will they pay in total over the lifetime of the loan? $2$ point

c$)$ How much interest would be paid over the life of the loan? $2$ point