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

a) Monthly Payment = Principal*R*(1+R)N/{[(1+R)N]-1}

where R= interest rate per month; R = 9%/12 =0.75%per month

N= Number of total months; N=180 months

Monthly Payment = $100,000*0.75%*(1+0.0075)180/{[(1+0.0075)180]-1}

= $750*(1.0075)180/[(1.0075)180-1]

= $750*3.83804327/2.83804327

= $1,014.27

b) For first payment interest portion = Principal amount*interest rate per month

=$100,000*0.75% = $750

Principal portion = Monthly payment - Interest portion

= $1,014.27 - $750 = $264.27

c) Principal outstanding for second month = Total loan - Principal portion of first payment

= $100,000 - $264.27(from part b) = $99,735.73

Seond interest payment = Loan outstanding * interest rate per month

= $99,735.27*0.75% = $748.02

Total repayment in second instalment = $99,735.73+$748.02 = $100,483.75

d) Monthly Payment = Principal*R*(1+R)N/{[(1+R)N]-1}

where R= interest rate per month; R = (9%-0.5%)/12 = 8.5%/12 =0.7083%per month

N= Number of total months; N=180 months

Monthly Payment = $100,000*0.7083%*(1+0.007083)180/{[(1+0.007083)180]-1}

= $708.30*(1.007083)180/[(1.007083)180-1]

= $708.30*3.56244109/2.56244109

= $984.72