# Absolute Prepayment Speed vs Single Month Mortality

Friends, Do any of you know how the relationship shown below is derived. I read the formula somewhere but cant understand how they derived it. SMM = ABS / (1 - ABS(MONTHS PAID - 1)) If any of you know the reason, kindly help please. thank you, Gopal.

ABS = monthly prepayment rate (% of the original loan amount)------I SMM = monthly prepayment rate (% of the outstanding balance)-----II SMM = ABS / (1 - ABS(MONTHS PAID - 1))------III MPR is a repayment measure and is calculated by dividing the sum of the interest and principal payments received in a month by the outstanding balance. So MPR= ABS/ (%of the Original loan Amt.) Putting this in the II nd eqn. SMM= (ABS/ (%of the Original loan Amt.)) *(% of the outstanding balance) So here (% of the outstanding balance)/ (%of the Original loan Amt.) should be equal to 1 / (1 - ABS(MONTHS PAID - 1)) from I , II and III Using Componendo ((% of the outstanding balance)-(%of the Original loan Amt.))= ABS(MONTHS PAID - 1) However, I dont have an intuitive explaination of How this works… Can anyone help? Thanks…