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Let's say I have a utility rate of 0.15 which inflates by 0.5% per year. I then want to convert that annual rate to a monthly rate and determine what the rate would be for month $n$.

The way I'm doing it now (which just feels incorrect) is: $\mathrm{utilityRate}\Bigl( (1.0 + \text{rate of inflation})^{n/12}\Bigr)$

Is this correct, or am I completely off base?

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    @Hnery; I started the comment before cleaning up the LaTeX, and misinterpreted; then I didn't correct the comment before sending.2012-07-02

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If the rate of inflation is constant every month then $(1 + \text{annual rate of inflation})^{n/12}$ is indeed what happens to the price level starting at $1$. So your formula looks sensible.

So in your example with $0.5\%$ annual inflation, this becomes $1.005^{n/12}$. The utilities I know would only change rates once a year if inflation was so low.

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    @ChrisCashwell: it will be close, particularly if the inflation rate is low. The correct monthly rate is as you implied in your question: $(1.0 + \text{annual rate of inflation})^{1/12}-1$. To the extent that $(1+\text{monthly rate})^{12}\approx 1+12*\text{monthly rate}$ they will agree.The next term is $6(\text{monthly rate})^2$, so you can see if you think that is big enough to care about.2012-07-02