$12.$ You plan to purchase a $$300,000$ house using a $15-$year mortgage obtained from your local bank. The mortgage rate offered to you is $3$ percent. You will make a down payment of $25$ 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 $50$th payment.

c$.$ Calculate the amount of interest and, separately, principal paid in the $150$th payment.