Mr$.$ Qualify is applying for a $$101,400$ GPM loan for $25$ years at an interest rate of $9$ percent. Payments would be designed so as to graduate at the rate of $7\mathrm{.}7$ percent for three years beginning with payments in the second year.

Required:

a$.$ What would the monthly payments be for Mr$.$ Qualify in each of the first five years of the loan?

b$.$ What would the loan balance be on the GPM at the end of year $3?$

c$.$ If the lender charged $4$ points at origination, what would be the effective interest rate on this loan after five years?