Question

Introduction to Mortgage Mathematics and Mortgage-Backed Securities

2 (Mortgage Pass-Throughs) Consider a $400 million pass-through MBS that has just been created (so the 'seasoning' of the pass-through is equal to 0). The underlying pool of mortgages each has a maturity of 20 years and an annual mortgage coupon rate of 6%. The pass-through rate of the mortgage pool is 5%. Assuming a prepayment multiplier of 100 PSA what is the total amount of interest paid to the pass-through investors? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

3 (Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

4 (Mortgage-Pass Throughs) Referring to the same mortgage pass-through of the previous question, what is the total amount of the prepayments if the rate of prepayments increases to 200 PSA? Submission Guideline: Give your answer in millions rounded to two decimal places. For example, if you compute the answer to be $123,456,789,12, submit 123.46.

Answer 1

Hello

Outstanding Balance of Mortgage				400 millions
Coupon rate				6%
Pass through Rate				5%
Term of loan				20 years
As 100 PSA therefore rounding is to be done
Year	Prinicpal at the end	Interest @ 6%	Pass through intt@5%	Closing Balance for prepayments
1	400.00	24.00	20.00	376.00
2	376.00	22.56	18.80	353.44
3	353.44	21.21	17.67	332.23
4	332.23	19.93	16.61	312.30
5	312.30	18.74	15.61	293.56
6	293.56	17.61	14.68	275.95
7	275.95	16.56	13.80	259.39
8	259.39	15.56	12.97	243.83
9	243.83	14.63	12.19	229.20
10	229.20	13.75	11.46	215.45
11	215.45	12.93	10.77	202.52
12	202.52	12.15	10.13	190.37
13	190.37	11.42	9.52	178.95
14	178.95	10.74	8.95	168.21
15	168.21	10.09	8.41	158.12
16	158.12	9.49	7.91	148.63
17	148.63	8.92	7.43	139.71
18	139.71	8.38	6.99	131.33
19	131.33	7.88	6.57	123.45
20	123.45	7.41	6.17	116.04
		283.96	236.63
Answer (2)	Total interest to pass through investors		236.63	millions
Answer (3)	Total Amount of prepayments		Total Interest + Principal
			400 + 283.96
			683.96 millions

I hope this solves your query.

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