How do I convert an annual inflation rate into a monthly rate? - More data version

Question

I know there was already some similar question, so far I didn't find satisfying answer. I try to calculate EU zone month-to-month inflation based on figures from EuroStat. They provide monthly inflation year-on-year. I'll try to get calculation on my own, but I'm no math genius.

Answer 1

To convert from yearly inflation to monthly inflation, take the twelvth root of the yearly number (expressed as a multiplier).

Example: Yearly inflation of 5% means the multiplier is 1.05. Twelvth root of that is about 1.004, so equivalent monthly inflation is about 0.4%. Of course in reality some months may be higher and others lower, but that's what it would be if they were all the same.

(This is sorta obvious if you think about the fact that 12 months of the monthly inflation has to multiply out to the yearly inflation. So monthly multiply to 12th power would be yearly. The above just runs the equation the other way.)

Note that the same approach works for converting between monthly and yearly interest. And can be extended; if you want daily, replace 12 with 365 (modulo leap years, but that's probably close enough).

Answer 2

For each month:

1. Add 1 to each annualized inflation rate,
2. Take the 12th root (in Excel, where the 2023-01 annualized inflation rate is 10%: A1 -> 10%, B1 =1+A1, C1 = POWER(B1, 1/12)). One row for each month. B2 would be 9.9%.

Then multiply all of the monthly rates. In Excel: =PRODUCT(C1:C1x), where "x" is the number of months.