# CPR and PSA - Which Formula?

I’ve seen two different formulas used both for pools of loans seasoned less than 30 months:

1. CPR = %PSA * #months / 30 * 6% (mock exam, Q15, AM)

2. CPR = %PSA * 0.2% * #months (sample exam)

I know that 6% is the mortality rate after 30 months, so can someone explain the intuition specifically behind the first formula? Did I misunderstand the context within which it’s used? Thanks much.

6%/30 = .2%, so they’re equal. The short cut in the sample exam isn’t incorrect, unless the months were over 30. If you look at the book, the graph shows that your repayment rate goes up until 30 months and then the repayment rate would be steady. After 30 months the repayment is fat at 6%

With 100% PSA, CPR adds on 0.2% each month until it reaches 6% at month 30. (1/30)*6% = .2%, so we can find the CPR at any month before month 30 by taking the number of months as a proportion of 30 and applying it to 6%.

Don’t have the mock on hand, but if I recall correctly we had to find the CPR at month 20. So 20/30*6% = 4%. However this is for 100 PSA. The CPR implied by the rate in the formula was 5.1%, so the PSA has to be higher than 100.