Consider a GNMA mortgage pool with principal of $$20$ million. The maturity is $15$ years with a monthly mortgage payment of $12$ percent per year. Assume no prepayments.

a$.$ What is the monthly mortgage payment $(100$ percent amortizing$)$ on the pool of mortgages?

b$.$ if the GNMA insurance fee is $5$ basis points and the servicing fee is $45$ basis points, what is the yield on the GNMA pass$-$through?

c$.$ What is the monthly payment on the GNMA in part $($b$)?$

d$.$ Calculate the first monthly servicing fee paid to the originating FI's?

e$.$ Calculate the first monthly insurance fee paid to GNMA.