# Conversion of annual interest rate compounded monthly to monthly effective interest rate [closed]

I am given that the annual interest rate is $r=4\%$ and that it is compounded monthly. I have to find the monthly effective interest rate.

If I wanted the annual effective interest rate, I would use the formula $r_e=(1+\frac{.04}{12})^{12}-1=.0407$ to find the yearly effective interest rate.

Then to go from yearly effective interest rate to monthly effective interest rate I would use: $r_e=(1+.0407)^\frac{1}{12}-1=.0033$.

Is this method correct? $.33\%$ does not seem high enough. Is there a more direct conversion? Thank you for your help.

• I am voting to close this question for being too basic as per quant.stackexchange.com/help/on-topic. This topic is covered in the early chapters of most introductory textbooks such as Hull's "Options, Futures and Other Derivatives" or Sundaresan's "Fixed Income Markets and Their Derivatives". – LocalVolatility Jan 28 '18 at 1:38

your result and your reasoning is correct. Just notice that there is a shorter way to the answer: $4/12 = 0.33$. Indeed, if the annual monthly compounded interest rate is $4\%$ than this means you get $4/12\%$ of interest every month!