7

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?

  • 2
    Divide by 12? Is there some subtext to this question that I am missing? – JohnFx Aug 5 '11 at 21:22
  • @JohnFX - He's asking about inflation, but it's like a credit card - the monthly interest rate corresponding to a 12% APR would not simply be (12%/12=1%). Due to compounding, the monthly rate (i.e. MPR, or CMGR) that would turn $100 on Day 0 into $112 in exactly one year would be slightly lower. And I'm assuming he's comfortable simplifying to case where "months" are actually equal-length periods, e.g. 30 days and redefining annual as 360 days, or each month equaling exactly 1/12th of a year. – Jon S Aug 5 '11 at 22:00
  • One consideration might be that I've rarely ever heard a monthly inflation rate given. The rates are usually expressed annualized. – Chuck van der Linden Aug 5 '11 at 23:30
  • Inflation is nothing like a credit card. Monthly inflation rates aren't given because there are seasonal and other market variations that make a monthly figure misleading. How you scale annual inflation to monthly really depends on what you're trying to do, and the accuracy required. – duffbeer703 Aug 6 '11 at 1:57
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    Maybe you're reading too much into the word "inflation" here. Perhaps it is to be taken simply as "growth rate", as opposed to "price increase of a basket of consumer goods". – Chris W. Rea Aug 6 '11 at 13:05
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%.

  • and if the annual inflation is below say 5%, you can simply divide by 12 for any practical purpose – ihadanny Nov 2 '12 at 23:02
2

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.

1

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.

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