A fully amortizing mortgage loan is made for $$101,000$ at $6$ percent interest for $20$ years.

Required:

a$.$ Calculate the monthly payment for a CPM loan.

b$.$ What will the total of payments be for the entire $20-$year period? Of this total, how much will be the interest?

c$.$ Assume the loan is repaid at the end of eight years. What will be the outstanding balance? How much total interest will have been collected by then?

d$.$ The borrower now chooses to reduce the loan balance by $$5,100$ at the end of year $8.$

$(1)$ What will be the new loan maturity assuming that loan payments are not reduced?

$(2)$ Assume the loan maturity will not be reduced. What will the new payments be$?$