The continuously compounded interest formula is:



  • P = Principle
  • e = 2.718...
  • r = Annual interest rate
  • t = time in years

If instead of an annual interest rate, I got a monthly interest rate, how would that work. Would I have to change the time in years to time in months? Or lets say I got a interest rate per quarter, would t = time in quarters?


You have the right idea. Euler's number e links all continuously compounded growth/decay functions in that it represents the amount by which and initial amount will grow (decay) if one continuously compounds (decays) 100% per unit period.

In the equation you give, you would want r to be the per unit interest rate (meaning monthly interest if that is what you are given) and t to be the number of unit periods (meaning the total number of months if that is what you are given).

As an example: consider a case where you are given $100 principle, compounded continously at a monthly rate of 1% for three years. Your equation would be $100e^(36*0.01)

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.