9. The CPI-U (U.S. city average, all items) has the following annual averages:
YEAR INDEX
2006 201.600
2007 207.342
2008 215.303
2009 214.537
2010 218.056
a. For each year from 2007 to 2010, determine the annual inflation rate in percent to three decimal places.
b. Since inflation, like interest, is compounded from period to period (e.g., year to year), estimate the overall annual inflation rate per year from 2006 to 2010. Suggestion: Do not simply average the rates of Part a.
a) inflation formula = [ ( later CPI - starting CPI ) / starting CPI. ] *100.
2007 = [(207.342 - 201.600) / 201.600]*100
= (5.724 / 201.600)*100
= 2.839
2008 = [(215.303- 207.324) / 207.324]*100
= (7.979 / 207.324)*100
= 3.848
2009 = [(214.537- 215.303) / 215.303]*100
= ( - 0.766 / 215.303)*100
= - 0.355 (deflation) or negative inflation
2010 = [(218.056- 214.537) / 214.537]*100
= (3.519/ 214.537)*100
= 1.614
b) inflation from 2006 to 2010
= [ ( 2010's CPI - 2006's CPI ) / 2006's CPI. ] *100.
[(218.056- 201.600) / 201.600]*100
= (0.08162/ 201.600)*100
= 8.162
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