The Green Mortgage Company has originated a pool containing $75$ ten$-$year fixed interest rate mortgages with an average balance of $$100,600$ each. All mortgages in the pool carry a coupon of $12$ percent. $($For simplicity, assume that all mortgage payments are made annually at $12\%$ interest.$)$ Green would now like to sell the pool to FNMA.

Required:

a$.$ Assuming a constant annual prepayment rate of $10$ percent $($for simplicity, assume that prepayments are based on the pool balance at the end of each year$),$ what will be the price that Gree should obtain on the date of issuance if market interest rates were $(1)11$ percent? $(2)12$ percent? $(3)9$ percent?

b$.$ Assume that five years have passed since the date in $($a$).$ What will the pool factor be$?$ If market interest rates are $12$ percent, what price can Green obtain then?

c$.$ Instead of selling the pool of mortgages in $($a$),$ Green decides to securitize the mortgages by issuing $100$ pass$-$through securities$.$ The coupon rate will be $11\mathrm{.}5$ percent and the servicing and guarantee fee will be $0\mathrm{.}5$ percent. However, the current market rate of return is now $9\mathrm{.}5$ percent. How much will Green obtain for this offering of MPTs$?$ What will each purchaser pay for an MPT security, assuming the same prepayment rate as in $($a$)?$

d$.$ Assume now that immediately after purchase in $($c$),$ interest rates fall to $8$ percent and that the prepayment rates are expected to accelerate to $20$ percent per year, beginning at the end of the first year. What will the MPT security be worth now?

Complete this question by entering your answers in the tabs below.

Assume that five years have passed since the date in $($a$).$ What will the pool factor be$?$ If market interest rates are $12$ percent, what price can Green obtain then? $($Do not round intermediate calculations. Round "Pool factor" answer to $4$ decimal places and other answer to the nearest whole dollar.$)$

$\backslash$table$[[$Pool factor,$0\mathrm{.}5905],[$Price of the pool after $5$ years,$]]$