Converting a Nominal Annual Rate to a Monthly Effective Rate

Summary

The document explains how to convert a nominal annual interest rate of four percent, compounded monthly, into an effective monthly rate. The questioner first compounds the monthly periodic rate through a year to obtain an annual effective rate, then reverses that annual growth into a monthly rate. The accepted reply confirms that reasoning and gives the direct interpretation: divide the nominal annual rate by twelve to obtain the monthly rate for this compounding convention.

The result is about one third of one percent per month. The explanation applies to a nominal annual rate explicitly compounded monthly; it does not address other compounding conventions, fees, or differences between nominal and effective quoting. It is a basic rate-conversion example rather than a trading strategy.

Key ideas

• A nominal annual rate compounded monthly implies equal monthly periodic rates.
• The monthly effective rate can be obtained directly by dividing the stated nominal rate by twelve.
• Compounding the monthly rate for a year and reversing the annual growth gives the same monthly result.

Tags

# Conversion of annual interest rate compounded monthly to monthly effective interest rate


# Conversion of 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.

## Answer by Cettt (score 1, accepted)

https://quant.stackexchange.com/a/37956

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!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.