Question

First Mortgage Investors purchases a $100,000 Face value MBS carrying a coupon of 9 percent and a maturity of 30 years.

1. What is the monthly payment on the MBS?

2. What is total interest paid over 30 years?

3. How much interest is paid in the first payment?

4. What will the MBS sell for in each of the following yield-survival scenarios? Years Survived Yield

to the left = years survived; to the right = yield

1; 6%

3; 7%

8; 9%

Answer 1

Answer :

(1). Monthly Payment =[P* R*(1 + R)^N] / [(1+R)^N-1]

Where P = face value (100000)

R = coupon rate per month (9% / 12)

N = number of months (30 * 12)

Monthly payment = [100000 * (9%/12) * ( 1 + (9%/12))^(30 * 12)] / [(1+(9/12))^ (30 * 12) - 1]

Monthly payment = [100000 * 0.0075 *(1.0075^360)] / [(1.0075 ^360) - 1]

= (750 * 14.73058) / 13.73058

= 804.62

(2).Total payment made over 30 years = Montly payments *12 months * 30 years

= 804.62 * 12 * 30

= 289664

Amount of interest over 30 years = Total payment made over 30 years - Face value

= 289664 - 100000

= 189664

(3). Interest paid in first payment = 100000 * 9% * (1/12) = 750

(4). Year survived = 1

Years to maturity = 29

Price of MBS = PV of coupon + PV of face value

= 9000 * PVAF (6%,29 years) + 100000 * PVF (6%,29 years)

= 9000 * 11.9867 + 100000 * 0.1609

= 123970

Year survived = 8

Years to maturity = 22

Price of MBS = PV of coupon + PV of face value

= 9000 * PVAF (9%, 22 years) + 100000 + PVF (9%,22 years)

= 9000 * 9.4424 + 100000 * 0.1502

= 100000