Consider a mortgage pool consisting of $1,00030-$year fixed$-$rate loans, each with a mortgage

rate of $8\mathrm{.}5\%$ and an original principal balance of $$300,000.$ Assume that no servicing fee is

charged and that the yield curve is flat.

A$.$ Assume no loans are prepaid in month$1.$ What is the total cash flow from the pool?

B$.$ If the market interest rate is $8\mathrm{.}5\%$ and expected to stay the same for the next $30$ years, what

is the value of the mortgage pool?

C$.$ If the market interest rate falls to $7\mathrm{.}5\%$ right after the MBS is issued and is expected to stay at

$7\mathrm{.}5\%$ for the next $30$ years, what is the value of the pool, assuming no prepayment?

D$.($continued with part C$)$ If $20\%$ of the borrowers prepay their loans in month $1$ and the rest

will keep the loan until maturity, what is the value of the pool?