You plan to purchase an $$80,000$ house using a $15-$year mortgage obtained from your local bank. The mortgage rate offered to you is $8\mathrm{.}00$ percent. You will make a down payment of $20$ percent of the purchase price.$$a$.$ Calculate your monthly payments on this mortgage.b$.$ Calculate the amount of interest and, separately, principal paid in the $127$th payment.c$.$ Calculate the amount of interest and, separately, principal paid in the $159$th payment.d$.$ Calculate the amount of interest paid over the life of this mortgage.$$