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For the sake of argument, let's say that the annual rate is 12%. What is the corresponding monthly rate and how do I compute that? I'm assuming it's not as simple as 1%, and there is some compound component to this?

Dan
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3 Answers3

12

Take the equation

1 + r_{annual} = (1 + r_{monthly})^12

Notice, the right hand side is just compounding the rate 12 times.

We can rearrange the equation to solve for the monthly rate:

r_{monthly} = (1 + r_{annual})^(1/12) - 1

Substituting in r_{annual} = .12, we have r_{monthly} = 0.00949.

So, for an annual rate of 12%, that corresponds to a monthly rate of about 0.949%.

Derek Ploor
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As Derek suggests, you take the 12th root of the annual number. 1.12^(1/12) is what you want to input to a spreadsheet or calculator.

JoeTaxpayer
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I don't think that treating inflation like compounded interest is any more precise than dividing by twelve. Both approaches are approximations that may be appropriate for some purposes.

Think about 2008... the financial crisis in the Fall drove the annualized inflation rate to 0.1% -- the compounded monthly rate derived from that would have NO correlation to the actual inflation rate from January-August 2008.

If you truly want to understand the effects of inflation between arbitrary months, you want to look up the appropriate Consumer Price Index (CPI) figures from the Bureau of Labor Statistics and compute the inflation rate.

You can get the data you need from the BLS website. I believe they publish how the inflation rate is computed as well.

duffbeer703
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