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

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

• Do you wish for the outcome to be the same? Probably it's good to post the entire question. Commented Feb 1, 2021 at 20:58

2 Answers

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.

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…