An FI originates a pool of real estate loans worth $$20$ million with maturities of $10$ years and paying interest rates of $9$ percent per year.

a$.$ What is the average payment received by the FI$,$ including both principal and interest, if no prepayment is expected over the life of the loan?

n $=10$ I $=8\mathrm{.}5$ PV $=20,000,000$ CPT PMT $=3,048,154\mathrm{.}10$

b$.$ If the loans are converted into pass$-$through certificates and the FI charges a servicing of $50$ basis points, including insurance, what is the payment amount expected by the holders of the pass$-$through securities if no prepayment is expected?

n $=10$ I $=8\mathrm{.}5$ PV $=20,000,000$ CPT PMT $=3,048,154\mathrm{.}10$

c$.$ Assume that the payments are separated into interest only $($IO$)$ and principal only $($PO$)$ payments, that prepayments of $5$ percent occur at the end of years $3$ and $4,$ and that the payment of the remaining principal occurs at the end of year $5.$ What are the expected annual payments for each instrument? Assume discount rates of $9$ percent.