Question

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security. The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum. a. What is the monthly payment on the mortgage pass-through? b. For the first monthly payment, what are the interest and principal portions of the payment? c. If the entire mortgage pool is repaid after the second month, what is the second month's interest and principal payments? D. What is the monthly payment received by investors of the mortgage pass-through if the FI deducts a 50 basis points servicing fee?

Answer 1

Solution

a).

Total present value (PV) = 50*100,000 = 5,000,000

Interest rate p.a. = 9% so I/Y = 9%/12 = 0.75%

N = 180

Solve for PMT using PV = 5,000,000; I/Y = 0.75%; N = 180. PMT = 50,713.33 (monthly payment)

b).

First month interest payment = PV*I/Y = 5,000,000*0.75% = 37,500

First month principal payment = PMT - interest payment = 50,713.33 - 37,500 = 13,213.33

c).

Principal amount remaining after 1st month = 5,000,000 - 13,213.33 = 4,986,786.67

2nd month interest payment will be 4,986,786.67*0.75% = 37,400.90

2nd month principal payment will be PMT - interest payment = 50,713.33 - 37,400.90 = 13,312.43

d).

Bond rate with 50 basis point servicing fee = 9% - 0.5% = 8.5%

Then I/Y = 8.5%/12 = 0.71%

PV = 5,000,000; N = 180; I/Y = 0.71%, solve for PMT. PMT = 49,236.98 (monthly payment which investors will receive.)