You take a $15-$year mortgage that requires annual payments. The mortgage payment is $$25,000.$

You will make your first payment to the bank in one year. The interest rate is $7\%$ per year.

a$.$ How much do you receive from the bank today?

b$.$ What is the loan balance after $5$ years $($ie immediately after you make the $5$th payment$)?$

c$.$ How much of your first payment is interest, and how much is repayment of principal?

d$.$ How much of your last payment is interest, and how much is repayment of principal?