If the GDP deflator values for year 1 and year 2 were 190 and 212.8, respectively, which of the following best describes the annual growth rate of the overall price level?

A 5.8%.

B 6%.

C 12%

The correct answer is: (212.8/190)^{1/2} – 1 = 0.0583 or 5.8%.

However I think this is to simply compare the price of year 1 and year 2, so it should be 212.8/190 - 1 =12%

Although year 1 price compared with the base year price (we don’t know which year, not necessarily year 0, it could be year -5 for example) is an increase of 90%, and year 2 price compared with the base year price is an increase of 112.8%. To calculate annual price growth rate, shouldn’t I just compare year 1 and year 2? Why is there a square root?

Thank you very much!