Question

PLEASE HELP ME WITH THIS

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
1	6%
3	7%
8	9%

Answer 1

Loan amount	100,000
Time period(30*12)	360
Rate(9%/12)	0.0075
Preset Value Factor	(1-(1+r)^-t)/r
PVF at r = 0.0075, t - 360	124.28
Monthly Payment(Loan Amoun/PVF)	$804.62
or
PMT function in excel	$804.62

2)Total interest payable

Total no. of monthly payments = 30*12 = 360

Total amount paid = $804.62*360 = 289,664.14

Total interest payable = 289,664.14 - 100,000 = $189,664.14

3) Interest in the first payment = 100,000*0.075 = $750

1-(1+r) Current Market Price = C * - FaceValue (1+r)

where c = coupon payments, r = rate per payment, t = time period

in the question c = 750 in all scenario

scenario 1)

Total times payments, t = 1*12 = 12

Yiield = 6%/12 = 0.005

Current Market Price = 750 * - 1- (1 +0.005) -12 0.005 100000 (1 +0.005)12

= 8,714.20 + 94,190.53 = $102,904.73

Scenario 2)

Total time payments = 3*12 - 36

Yiled = 7%/12 = 0.005833

=24,289.85 + 81,1107.89 = $105,397.74

Current Market Price = 750 * - 1- (1 + 0.005833) -36 0.005833 - + 100000 (1 + 0.005833 36

Scenario 3)

Tota time payments = 8*12 = 96

Yield = 9%/12 = 0.0075

Current Market Price = 750 * - 1- (1 + 0.0075) - 96 0.0075 - + 100000 (1 +0.007596

=51,193 + 48,806.17 = $100,000

If you have any doubt, ask me in the comment section.

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