Answer-first summary for fast verification
Answer: $1,136,151
With a constant SMM of 1% per month, the balance that prepays over 12 months is: \[ 10{,}000{,}000 \times \left(1 - (1-0.01)^{12}\right) \] \[ = 10{,}000{,}000 \times (1 - 0.99^{12}) \] \[ \approx 10{,}000{,}000 \times 0.1136151 = 1{,}136{,}151 \] So the nearest answer is **$1,136,151**.
Author: Manit Arora
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Question-509.2. If a pool of mortgages starts the year with a principal balance of $10.0 million and the single monthly mortality rate, SMM(n), is constant at 1.0%, which is nearest to the principal that prepays over the next twelve months (not including scheduled principal)?
A
$1,136,151
B
$1,200,000
C
$8,800,000
D
$8,863,849
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