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February 11th, 2019, 07:25 AM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 635 Thanks: 85  The MTA Needs to Learn About Inflation
Newsday cited the Metropolitan Transportation Authority (MTA) for the inflation rate of 19 years and the annual average inflation. Using the annual average to the 19th power produces the 19 year total, which may sound good, but it isn't. With inflation, order matters. If consecutive years have 5 percent inflation, the two year total is 10.25 percent. If one year has 10 percent inflation and the next year has 0 zero, the two year total is 10 percent. This proves that the average of the two years (the mean of 10 and 0 = the mean of 5 and 5) is not sufficient to know the inflation after two years. Conversely, the inflation after 19 years is not sufficient to know the average of the 19 years. Working backwards from the 19 year rate to the average individual year will produce a rate close to the average of the 19 years, but not exactly the same.

February 11th, 2019, 01:40 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,298 Thanks: 1971 
If the price gets multiplied by $1+r$ over $n$ years, one can choose to define the average annual inflation over those years as $((1+r)^{1/n}  1)$ × 100%. If the price doubles over 20 years, that evaluates to $(2^{1/20} 1)$ × 100% = 3.5265% approximately. This seems to be a more useful method than the method you were alluding to. 

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