The Consumer Price Index (CPI) is a measure of inflation obtained by comparing current prices with base prices. The inflation rate equals the percent of change in the CPI over that period. (a) Calculate the inflation rate from 2010 to 2020. (b) If a pair of sneakers cost $72 in 2010, use the inflation rate from part (a) to estimate the cost of the sneakers in 2020. a. The inflation rate from 2010 to 2020 is %. (Round to one decimal place as needed.)
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The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost-of-living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982–1984 for comparison (the CPI for this period is 100). The CPI for March 2014 was 236.29. This means that $100 in the period 1982–1984 had the same purchasing power as $236.29 in March 2014. In general, if the rate of inflation averages r% per annum over n years, then the CPI index after n years is $$ \mathrm{CPI}=\mathrm{CPI}_{0}\left(1+\frac{r}{100}\right)^{n} $$ where $C P I_{0}$ is the CPI index at the beginning of the n-year period. (a) The CPI was 215.3 for 2008 and 233.0 for 2013. Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate. (b) Using the inflation rate from part (a), in what year will the CPI reach 300?
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Problems 69-72 require the following discussion. The Consumer Price Index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost-of-living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982-1984 for comparison (the CPI for this period is 100). The CPI for January 2013 was $230.28 .$ This means that $\$ 100$ in the period $1982-1984$ had the same purchasing power as $\$ 230.28$ in January 2013. In general, if the rate of inflation averages $r$ percent per annum over $n$ years, then the $\mathrm{CPI}$ index after $n$ years iswhere $\mathrm{CPI}_{0}$ is the CPI index at the beginning of the $n$ -year period. U.S. Bureau of Labor Statistics (a) The CPI was 179.9 for 2002 and 229.6 for 2012 . Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate. (b) Using the inflation rate from part (a), in what year will the CPI reach $300 ?$
Problems 69–72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost-of-living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982–1984 for comparison (the CPI for this period is 100). The CPI for March 2014 was 236.29. This means that 100 in the period 1982–1984 had the same purchasing power as 236.29 in March 2014. In general, if the rate of inflation averages r% per annum over n years, then the CPI index after n years is $$\mathrm{CPI}=\mathrm{CPI}_{0}\left(1+\frac{r}{100}\right)^{n}$$ where $C P I_{0}$ is the CPI index at the beginning of the n-year period. Consumer Price Index (a) The CPI was 215.3 for 2008 and 233.0 for 2013. Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate. (b) Using the inflation rate from part (a), in what year will the CPI reach 300?
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