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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)? | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

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.

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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)?