The CPI-U (U.S. city average, all items) has the following annual averages: Year

Question

The CPI-U (U.S. city average, all items) has the following annual averages:

Year Index

2006 207.6

2007 210.2

2008 214.4

2009 215.5

2010 219.4

For each year from 2007 to 2010, determine the annual inflation rate in percent to two decimal places.

Year Inflation Rate

2007 %

2008 %

2009 %

2010 %

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.

Explanation / Answer

Year Inflation Rate

2007 = (CPI of 2007 - CPI of 2006)/CPI of 2006*100 = 2010.2 - 207.6/207.6 = 1.252408 %

2008 = (CPI of 2008 - CPI of 2006)/CPI of 2006*100 = 2014.4 - 207.6/207.6 3.27553 %

2009 = (CPI of 2009 - CPI of 2006)/CPI of 2006*100 = 2015.5 - 207.6/207.6   3.805395%

2010 = (CPI of 2010 - CPI of 2006)/CPI of 2006*100 = 219.4 - 207.6/207.6 5.684008 %

For Annual Inflation rate X from 2006 to 2010

207.6(1+x)^4 = 2019.4

(1+x)^4 = 219.4/207.6

X = 1.39%

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