
Explanation:
Assuming 100PSA, CPR = 6% * = 2%
Thus, 175PSA = 1.75 × 2% = 3.50%
SMM = $1 - (1 - 0.035)^{1/12} = 0.002965$
Note that, a pool of mortgages is said to have 100%- PSA if its CPR starts at 0 and with monthly increments of 0.2 % until 6% is reached in month 30, after which the CPR remains constant at 6%. In other cases, the prepayment scenarios are specified as multiples of 100% PSA.
Note that, PSA =
where,
m = number of months since origination.
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Q.3049 AMZ Ventures has invested in a mortgage pool. It has a $24 million principal balance outstanding with the scheduled monthly principal payment. Assuming a public securities association (PSA) of 175%, what is the single monthly mortality rate (SMM) in month 10?
A
0.002363
B
0.002793
C
0.002965
D
0.002467