# Annual interest rate compounded monthly to monthly effective interest rate

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.

We require $(1+i_m)^{12} =1.04$ i.e. $12$ compound payments will give $4$ % so \begin{eqnarray*} i_m= \sqrt[12]{1.04}-1=0.00327 \cdots \end{eqnarray*} So the mothly interest is $0.327$ %.