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The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 2000 was 172.2. By 2012, it increased to 229.6. What was the geometric mean annual increase for the period?

Oct 27, 2015

#2
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Thanks guest that is an interesting way to tackle this question.

The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 2000 was 172.2. By 2012, it increased to 229.6. What was the geometric mean annual increase for the period?

I am going to try using the compound interest formula

\(FV=PV(1+r)^n\\ 229.6=172.2(1+r)^{12}\\ 1.333333333333333333333=(1+r)^{12}\\ \mbox{raise both sides to the power of 1/12}\\ 1.333333333333333333333^{1/12}=((1+r)^{12})^{1/12}\\ 1.333333333333333333333^{1/12}=1+r\\ r=1.333333333333333333333^{1/12}-1\\ r=0.024263181\\ r=2.426 \%\;\;\;\;approximately\)

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Oct 28, 2015

#1
+10

The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 2000 was 172.2. By 2012, it increased to 229.6. What was the geometric mean annual increase for the period?

Consumer Price Index went up:229.6/172.2=1.333..........etc. in 12 years. So, the average or "mean" annual increase is: 1.3333^1/12=1.0242=2.42% per year.

Oct 28, 2015
#2
+10

Thanks guest that is an interesting way to tackle this question.

The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 2000 was 172.2. By 2012, it increased to 229.6. What was the geometric mean annual increase for the period?

I am going to try using the compound interest formula

\(FV=PV(1+r)^n\\ 229.6=172.2(1+r)^{12}\\ 1.333333333333333333333=(1+r)^{12}\\ \mbox{raise both sides to the power of 1/12}\\ 1.333333333333333333333^{1/12}=((1+r)^{12})^{1/12}\\ 1.333333333333333333333^{1/12}=1+r\\ r=1.333333333333333333333^{1/12}-1\\ r=0.024263181\\ r=2.426 \%\;\;\;\;approximately\)

Melody Oct 28, 2015