You plan to purchase a $$150,000$ house using a $15-$year mortgage obtained from your local credit union. The mortgage rate offered to you is $6\mathrm{.}25$ percent. You will make a down payment of $10$ 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 $20$th payment.

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

d$.$ Calculate the amount of interest paid over the life of this mortgage.

$($For all requirements, do not round intermediate calculations. Round your answers to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$