You plan to purchase a $$350,000$ house using a $15-$year mortgage obtained from your bank. The mortgage rate offered to you is $5\mathrm{.}50$ percent. You will make a down payment of $20$ percent of the purchase price.

a$.$ Calculate your monthly payments on this mortgage.

b$.(1)$ Construct the amortization schedule for the mortgage.

b$.(2)$ How much total interest is paid on this mortgage?