Loans:What is the effective monthly interest rate

What is the effective monthly interest rate on a $30000, ten year loan at 7% per year compounded monthly, when you make your payments semi-annually?

ANSWER:
0.58%

$(1+\frac{.07}{12})^1-1= \frac{.07}{12}=.0058$

Please note that the question has a red herring. It does not matter that your payments are semi-annually. It asks for the effective monthly rate. The question also highlights that the effective interest rate calculation has a simplification when the desired effective period is the same as the compounding period.

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