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Answer: $1,249,172
**Correct answer: C. $1,249,172** ### Step 1: Compute monthly interest The mortgage pool balance is **$900 million** and the WAC is **6.60%**. Monthly interest rate: \[ \frac{6.60\%}{12} = 0.55\% \] Monthly interest: \[ 900{,}000{,}000 \times 0.0055 = 4.95\text{ million} \] ### Step 2: Compute scheduled principal Total mortgage payment is **$5.748 million**. Scheduled principal: \[ 5.748 - 4.95 = 0.798\text{ million} \] So scheduled principal is about **$797,929**. ### Step 3: Compute expected prepayment at 300% PSA For **month 1**, standard PSA CPR is **0.2% annualized**. At **300% PSA**: \[ CPR = 3 \times 0.2\% = 0.6\% \] Convert CPR to SMM: \[ SMM = 1 - (1 - CPR)^{1/12} \] This gives a small monthly prepayment rate, and applying it to the remaining balance after scheduled principal produces an expected prepayment of about **$451,243**. ### Step 4: Total principal reduction \[ 797{,}929 + 451{,}243 = 1{,}249{,}172 \] Thus the reduction in principal balance is **$1,249,172**.
Author: Manit Arora
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Q-106.2. A mortgage pool has a principal balance of $900 million and the weighted average coupon (WAC) of the mortgages in the pool is 6.60%. In the first month, the coupon paid by the mortgage pool (principal plus interest) is $5.748 million. The prepayment assumption is 300% PSA. In the first month, what is the REDUCTION in the principal balance; that is, what is the sum of the schedule principal and the expected prepayment of principal?
A
$898,751
B
$797,929
C
$1,249,172
D
$1,505,360
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