Using the Consumer Price Index table

The Consumer Price Index

This week, students got a green handout sheet with the consumer price index number for the years 1950 to 2015.  The simplest way to use it goes as follows.

How did prices change from 1960 to 1980? We use the two CPI values.

CPI(1960) = 29.6
CPI(1980) = 82.4

82.4/29.6 = 2.78378.....

29.6/82.4 = .35922...

What these numbers mean is that on average, a $10 item in 1960 sold for 10*2.78378... = $27.84 in 1980, while a $10 item in 1980 would have sold for 10*.35922... = $3.59.

We can use this to figure out the cost of living increase in any given year by dividing the CPI for that year by the CPI for the previous year.  For example, the rate in 1975 would be

CPI(1975)/CPI(1974) = 53.8/49.3 = 1.09127789... This is 1 + rate, so rounded to the nearest tenth of a percent we would have 9.1% and to the nearest hundredth of a percent it would be 9.13%.

Let's look at the number CPI(1980)/CPI(1960) = 2.783783... This gives us how much prices increased in the 20 year period from 1961 to 1980. To get the average increase over those 20 years, we take (2.783783)^(1/20) = 1.05252... This is 1 + rate, so the average rate = .05252... or 5.3% if rounded to the nearest tenth of a percent and 5.25% rounded to the nearest hundredth.