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I'm trying to figure out the average inflation between 1926 and 2015 so I can subtract it from the cumulative annual growth rate of average annual bond return during that period (5.4% according to Vanguard). I tried a few different online calculators and got over 1000%—I think it should be around 3%, apparently I'm doing something wrong. Sadly my math knowledge is at maybe a 7th grade level.

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Using index data from here: All Urban Consumers – (CPI-U) 1913-2017

Year       Annual
           Average
1926        17.7
2015       237.017

and the formula from here: Average inflation

Average inflation = (((2015 price index / 1926 price index)^(1/(2015 - 1926))) - 1) x 100

∴ Average inflation = (((237.017 / 17.7)^(1/89)) - 1) x 100 = 2.95815 %
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    This is correct but a little explanation might help. If average inflation is r then prices growing by a ratio of (1+r) each year will reach the right growth after 2015-1926 = 89 years. So we're trying to find the value of r such that 17.7 * (1 + r)^89 = 237.017 which re-arranges to the above. (The x 100 on the end is just to convert to a percentage value, i.e. 2.95+ rather than 0.0295+)
    – TheMathemagician
    Mar 31, 2017 at 10:04

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