How does the continuously compounded interest formula work in terms of months?

Question

The continuously compounded interest formula is:
Pe^rt
Where:

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?

Euler's Disgraced Stepchild · Accepted Answer

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)

How does the continuously compounded interest formula work in terms of months?

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