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?

Guest Oct 27, 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

#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.

Guest Oct 28, 2015

#2**+10 **

Best AnswerThe 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?

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

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