Single Monthly Mortality Rate monthly, friends, derived, regarding, confusion

dontknow1987

Hi friends,

I was having confusion regarding how the CPR (conditional prepayment rate) vs SMM was derived.

Kindly let me know where I am going wrong..

CPR = (1+SMM)^(12) - 1 --> Assumption is SMM is monthly and the compounded value should give CPR which is yearly rate.

So SMM = (1+CPR)^(1/12) - 1

But the formulae given in the book is 1 - (1 - CPR)^1/12.

Kindly help me clear my confusion please.

thank you friends!