Which of the following statements regarding a $15-$year $(180-$month$)$ $$125,000,$ fixed$-$rate mortgage is CORRECT? $($Ignore taxes and transactions costs.$)$

a$.$ The proportion of the monthly payment that goes towards repayment of principal will be lower $10$ years from now than it will be the first year.

b$.$ Interest payments on the mortgage will decrease steadily over time, but the total amount of each payment will remain constant.

c$.$ The remaining balance after three years will be $$125,000$ less one third of the interest paid during the first three years.

d$.$ The outstanding balance declines at a slower rate in the later years of the loan's life.

e$.$ Because it is a fixed$-$rate mortgage, the monthly loan payments are not constant.