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 $8\mathrm{.}00\%.$ You will make a down payment of $20\%$ of the purchase price.

$(3$ points$)$ Calculate your monthly payments on this mortgage.

$(4$ points$)$ Calculate the amount of interest and, separately, the principal paid in the $127$th payment.

$(4$ points$)$ Calculate the amount of interest and separately, the principal paid in the $159$th payment.

$(3$ points$)$ Calculate the amount of interest paid over the life of this mortgage.