How do I convert from a semi-annual interest rate to montly?

Question

On a practice exam I am given a $.06$ compounded semi-annually and need it converted to monthly. I assumed it would be $.005$ because it has annual percentage of $.06/12$ but my answer is slightly off so I wanted to have this verified

Answer 1

The equation for semi-annually is $A=P(1+\frac{r}{2})^{2t} $ while for monthly it is $A=P(1+\frac{R}{12})^{12t}$ . Making these equations equal with r = 0.06 yields $$P(1+\frac{0.06}{2})^{2t}=P(1+\frac{R}{12})^{12t}$$ If we solve the above equation we get R = 0.05926…

Answer 2

If we have interest rate $i$ compounded in $n$ periods per year; the effective per annum interest is given by

$$(1+\frac{i}{n})^n$$

If we want to calculate some $i'$ associated with an $n'$ for the same per annum rate we must set the two to be equal:

$$(1+\frac{i}{n})^n=(1+\frac{i'}{n'})^{n'}$$

Given that in your case you know $n'$ that leaves 1 equation, 1 variable; easy to solve.