CPR and SMM

CFA Level II
#1

Hi everyone,

I have a question regarding the conversion from CPR and SMM, which is covered halfway thru Book 5.

The original text states that to convert from SMM to CPR you use the formula below:

CPR = 1-(1-SMM)^12

this make sense to me, and I algebriacally tried to do the reverse, convert CPR to SMM, this is what I got:

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

However, according to p472 #8, the correct way of doing this is:

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


Am I missing something here? Granted, its been a while since 8th grade algebra, but I did this calc by hand a couple times and keep comeing up with the same answer, the book solution (problem 8 formula) doesn't make sense to me....

Thanks in advance for the help!
#2

It’s better (in my humble view) to write:

1 – CPR = (1 – SMM)^12

Then,

(1 – CPR)^(1/12) = 1 – SMM

1 – (1 – CPR)^(1/12) = SMM

#3

Ok I see it now, thanks!

#4

You’re welcome.