The Consumer Price Index: A Brief Overview

The Consumer Price Index: A Brief Overview
Updated February 28, 2008
Brian W. Cashell
Specialist in Macroeconomic Policy
Government and Finance Division

The Consumer Price Index:
A Brief Overview
The Consumer Price Index (CPI) is perhaps the most widely reported measure
of inflation. A number of federal government programs are regularly adjusted to
account for changes in the CPI, such as Social Security benefits and the personal
income tax rate schedule. Thus, the behavior of the CPI has important consequences
for a large number of people. Many, however, may be unfamiliar with how the CPI
is estimated.
For Congress, the CPI is of particular interest because of its significant effect
on the federal budget. Changes in the CPI can have substantial effects on both
revenues and outlays, and those changes may either reflect underlying economic
conditions or result from methodological changes in the way the CPI is calculated.
The CPI is based on a number of sample surveys. One of these surveys
estimates the purchasing patterns of the “typical” household to determine how that
household spends its money. Another survey determines where those households
shop, and a third survey collects prices on the goods and services purchased by those
The CPI measures the price level relative to a particular period. Currently, the
CPI number for each month is a measure of the price level relative to what it was
between 1982 and 1984. The CPI is available for a number of metropolitan areas but
it does not allow comparisons of the cost of living in different cities.

Background ......................................................1
Estimating the CPI.................................................3
Medical Care .................................................4
Home Ownership..............................................6
Improving the CPI.................................................6
Availability of the CPI..............................................7
CPI Data Via the Internet.......................................11
CPI Calculations.................................................12
List of Tables
Table 1. Expenditure Categories and Relative Importance in the CPI-U.......4
Table 2. Availability of Local Area CPIs...............................8
Table 3. Consumer Price Index for All Urban Consumers, 1800 - 2007.......9

The Consumer Price Index:
A Brief Overview
The Consumer Price Index (CPI) is probably the most widely used measure of
inflation. A number of federal government programs, such as Social Security
benefits and civil service retirement, are tied to increases in the CPI. In addition, the
personal income tax rate schedule is indexed to the CPI.1 Economists use the CPI to
calculate constant-dollar estimates of other economic indicators, such as retail sales
and hourly earnings, which allow analysis of changes in these variables excluding the
effect of changes in the price level. Each year, the CPI is used to update the income
levels that determine the poverty rate. Periodic increases in many union wage and
other contracts are also tied to increases in the CPI. Thus, the behavior of the CPI
has major consequences for a significant portion of the population. But, many may
be unfamiliar with the details of how it is derived.
The CPI is published by the Department of Labor’s Bureau of Labor Statistics2
(BLS). There is no specific legislation authorizing or requiring BLS to calculate and
publish the CPI. Neither has legislation ever been enacted to require BLS to adopt
any particular methodology in calculating the CPI. When the Bureau of Labor was
first created in 1888, its task was, among other duties, to “acquire and diffuse among
the people of the United States useful information on subjects connected with labor,
in the most general and comprehensive sense of the word....”3
In 1913, the Bureau of Labor was transferred to the newly created Department
of Labor and renamed the Bureau of Labor Statistics. BLS was given slightly more
specific instructions:
The Bureau of Labor Statistics, under the direction of the Secretary of Labor,
shall collect, collate, and report at least once each year, or oftener if necessary,
full and complete statistics of the conditions of labor and the products and
distribution of the products of the same ... and said Secretary of Labor may

1 See CRS Report RL34168, Automatic Cost-of-Living Adjustments: Some Economic and
Practical Considerations, by Brian W. Cashell.
2 BLS began periodic publication of a National CPI in 1921. At first, the CPI was only
released semi-annually. Quarterly releases were begun in 1935, and monthly releases began
in 1940.
3 29 U.S.C. 1.

collate, arrange, and publish such statistical information so obtained in such4
manner as to him may seem wise.
Two CPIs are published by the BLS, the Consumer Price Index for Urban Wage
Earners and Clerical Workers (CPI-W), and the Consumer Price Index for All Urban
Consumers (CPI-U). The CPI-W is based on the purchasing patterns of only those
in the population who earn more than half of their income from clerical or wage5
occupations, and were employed at least 37 weeks in the previous year. The CPI-W
population makes up about 32% of the total non-institutional population. Prior to
1978, the CPI-W was the only CPI published. Beginning in 1978, the CPI-U was
introduced so that a broader share of the population would be included in estimates
of changes in the price level. The CPI-U is based on the expenditure patterns of all
urban consumers and covers about 87% of the population. The CPI-U is usually the
more publicized of the two price indexes.
Although the CPI-U and CPI-W are slightly different indexes, the numerical
difference between the two measures is typically small. Between 1987 and 2007, the
CPI-U increased, overall, by 82.5% compared with an increase of 80.2% for the CPI-
W. Over the same period, that translates into an average annual rate of change of

3.1% for the CPI-U, and 3.0% for the CPI-W.

Both the CPI-W and the CPI-U are used for inflation indexing by the federal
government.6 One advantage to using the CPI in indexing is that the CPI is rarely7
revised. Definitions, the index base year, the goods and services accounted for, and
the methodology used to calculate the CPI may change from time to time, but, once8
published, the actual index number is final. Using other measures of the price level,
such as one of the price indexes associated with Gross Domestic Product, for
indexing purposes poses the problem of which number to use, the preliminary
estimate or one of many subsequent revisions.9

4 29 U.S.C. 2.
5 Specifically, clerical workers, craft workers, operatives, service workers, or laborers.
6 The CPI-U is the index used to adjust various provisions of the personal income tax code.
The CPI-W is the index used to adjust Social Security benefits.
7 Historically, BLS has published monthly changes in the CPI on both a seasonally adjusted
and not seasonally adjusted basis. The seasonally adjusted changes are subject to revision
because seasonal adjustment factors may change over time. BLS also makes available a
seasonally adjusted index number that is subject to revision. Seasonal adjustment does not
affect yearly changes because the adjustment factors cancel each other out over any given

12-month period.

8 An exception to this occurred in 2000. A mathematical error was found in the way the CPI
was calculated. As a result, numbers that had already been published were revised.
9 See U.S. Department of Labor, Bureau of Labor Statistics, Using the Consumer Price
Index for Escalation, available at [].

Beginning with release of January 2007 data, the CPI and all of its component
indexes are published rounded to three decimal places rather than one. The change
is not meant to imply any increase in the accuracy of the CPI. Instead it is being done
to maintain precision in published estimates of percentage changes. Prior to 2007,
when BLS published the CPI rounded to only one decimal place, it based published
figures of percentage change in the CPI on those rounded numbers so that they could
be replicated by users of published CPI data. But doing that meant that some
precision in the published percent change data was lost. The effect of the change is
likely to be small.10
Estimating the CPI
Both CPIs are based on retail market prices. These prices, for more than 80,000
separate items, are collected in 87 urban areas across the country from thousands of
outlets, such as grocery and department stores, gasoline service stations, and
hospitals, among others.11 BLS selects these retail establishments based on a survey
showing where people do their shopping. Actual prices (except those for food) are
not published because they are collected on a confidential basis. Price indexes are
available in considerable detail. Examples of items for which CPI data are available
include white bread, men’s shirts, automobile tires, haircuts, funerals, automobile
repair, and bedroom furniture.
The “all-items” CPI is the index most often referred to and it is a composite
index, a weighted average, based on the indexes for all of the goods and services
whose prices are collected.
The all-items CPI measures the price change of a fixed market basket of goods
and services over time. The mix of goods and services making up the market basket
is based on spending patterns established by the Consumer Expenditure Survey
(CES).12 Based on the CES, weights are assigned to each of the goods and services
that make up the market basket. These weights determine how much the price
change for a given good will affect the all-items measure. For any given interval, the
total price change, as measured by the all-items CPI, is the weighted average of the
price changes of all of the components. With the release of data for January 2008,
the CPI marketbasket was based on purchasing patterns described by the CES in

2005 and 2006. BLS updates the expenditure weights every two years.

Table 1 shows the major expenditure categories included in the CPI and their
relative importance in the CPI-U as of December 2007. Relative importance reflects
both the expenditure weights and changes in relative prices. Either a larger
expenditure weight, or an increase in the price of a good relative to prices for other
goods may cause the relative importance to increase.

10 See additional info at the BLS website, at [].
11 See “In the Field With the Price Indexers,” New York Times, June 20, 1995, p. D2.
12 Detailed information on the CES is available on the Internet at [].

Table 1. Expenditure Categories and Relative
Importance in the CPI-U
Expenditure CategoryRelative Importance,December 2007
All items100.000
Food and beverages14.914
Housing - Shelter32.596
Housing - fuels and utilities5.128
Housing - household furnishings and operation4.702
T r ansportation 17.688
Medical care6.231
Education and Communication6.086
Other goods and services3.277
Source: Department of Labor, Bureau of Labor Statistics.
Medical Care
Based on the measures of relative importance shown here, some might be
concerned that medical care costs have too small a weight in the all-items index. In
particular, the elderly typically spend a relatively larger share of their outlays on
medical care. In calculating the CPI, however, the share of the marketbasket
accounted for by medical care is based on “out-of-pocket” costs. This includes direct
out-of pocket costs for medical care as well as indirect out-of-pocket costs for health
insurance.13 An increasing share of medical costs are paid for by employers and
government, so that out-of-pocket expenses on medical care are not as great as total
outlays on medical care.

13 See U.S. Department of Labor, Bureau of Labor Statistics, “Measuring Price Change for
Medical Care in the CPI,” at [].

It is also important to appreciate that there is considerable variation among
consumers (and among elderly consumers as well) in the demand for medical care,
and the relative importance of medical care in the CPI is based on an average. No
single price index can accurately describe the inflation experience of every single
person. Different population groups (e.g., the elderly) tend to have different
purchasing patterns, and individuals’ purchases vary significantly within those
groups. Although many elderly may spend more on medical care than is taken into
account in the CPI, there are also likely some elderly who spend less. For those who
spend less, if medical care costs rise more rapidly than do the prices of other goods
and services, the CPI will tend to overstate increases in the cost of living, other things
being equal. BLS is currently investigating the behavior of an experimental CPI for
the elderly population.14 This experimental CPI for Americans aged 62 and older
rose by an average of 3.2% per year between December 1987 and December 2007
During the same period, the both the CPI-U and CPI-W rose at a rate of 3.0%.15
Considerable effort is made to ensure that the CPI is a meaningful, reliable
measure of changes in the price level. But it does not necessarily reflect the inflation
experience of each individual consumer. To the extent that individuals spend
relatively more on those goods and services whose prices are rising faster than
average, they may experience a higher inflation rate than that measured by the CPI.
Similarly, those who spend relatively less on goods and services whose prices are
rising faster than average, may experience a lower inflation rate than that measured
by the CPI.
If purchasing patterns change significantly, then in the short run the CPI may
tend to overstate the inflation rate. The CPI is a fixed-weight index and does not
immediately take into account changes in spending patterns due to changes in relative
prices. There may also be a tendency for the CPI to overstate the inflation rate
because some price increases reflect improvements in the quality of goods and
services. Taking quality changes into account in a price index is difficult, but BLS
does attempt to make some adjustments to the CPI for quality improvements in a
number of areas, including automobiles, apparel, and a number of consumer
electronic goods, personal computers in particular.16

14 See U.S. Department of Labor, Bureau of Labor Statistics, “Experimental Consumer Price
Index for Americans 62 Years of Age and Older, 1998-2003,” [
15 See CRS Report RS20060, A Separate Consumer Price Index for the Elderly?, by Brian
W. Cashell.
16 See U.S. Department of Labor, Bureau of Labor Statistics, “How BLS Measures Price
Change for Personal Computers and Peripheral Equipment in the Consumer Price Index,”
[ cpi/cpifaccomp.htm] .

Home Ownership
Home ownership costs in the CPI are treated in a special way.17 Prior to 1983,
the home ownership component of the CPI measured changes in the cost of
purchasing a new home. Since 1983 for the CPI-U and 1985 for the CPI-W, changes
in the cost of home ownership have been based on the concept of “rental
equivalence.” Rather than measuring changes in the cost of buying a house in each
period, which would include finance charges, the CPI attempts to estimate the rental
value of owner-occupied housing. Thus, the CPI measures changes in the
consumption aspect of housing costs and not changes in the investment value of
owner-occupied housing.18
Improving the CPI
In December 1996, a special commission chaired by economist Michael Boskin
reported to the Senate Finance Committee that the CPI tended to overstate the actual
rate of inflation by about 1.1% per year.19 Although a number of specific
recommendations were made in the report, Congress took no legislative steps to
require any changes in the way BLS calculates the CPI.20
But the methodology of calculating the CPI has changed much since it was first
published and is likely to continue to do so. BLS continues to look at methods that
might lead to a more accurate measure of the cost of living. As part of that process,
with the release of data for July 2002, BLS introduced an alternative CPI that makes
use of “chain-weights.” This index is referred to as the C-CPI-U. The expenditure
weights for the C-CPI-U will be updated more frequently than either the CPI-U or the
CPI-W, and the index itself will be subject to revision. The C-CPI-U has not

17 See U.S. Department of Labor, Bureau of Labor Statistics, “Consumer Price Indexes for
Rent and Rental Equivalence,” at [].
18 Because of the timing of this change in the way the CPI is calculated, a permanent upward
bias in the level of the CPI was introduced. BLS has published estimates of the CPI-U using
the rental equivalence approach for the years 1967 to 1982. This series is known as the CPI-
U-X1. The Census Bureau now publishes historical estimates of real money income based
on the CPI-U-X1 measure. See U.S. Bureau of the Census, Money Income of Households,
Families, and Persons in the United States, Current Population Reports, Series P-60, no.174,

1991, pp. 8-9.

19 U.S. Congress, Senate Committee on Finance, Final Report of the Advisory Commission
to Study the Consumer Price Index, committee print, 104th Cong., 2nd sess., December 1996.
20 Because of the CPI’s budget implications, Congress has, from time to time, taken some
interest in how it is calculated. To date, however, no legislation has been enacted that would
directly affect BLS’ methodology. See David S. Johnson, Stephen B. Reed, and Kenneth
J. Stewart, “Price Measurement in the United States: A Decade After the Boskin Report,”
Monthly Labor Review, May 2006, pp. 10-19.

replaced either the CPI-U or the CPI-W, and they will continue to be used for
index i ng.21
Availability of the CPI
The CPI is currently published for 26 metropolitan areas. For most of these
cities, however, indexes are not published on a monthly basis. These metropolitan
area indexes are only intended to compare inflation rates between cities. The
metropolitan area CPIs may not be used to compare the actual cost of living between
cities.22 Table 2 shows the metropolitan areas for which the CPI is published as well
as the publication frequency.
BLS has published estimates of the CPI going back as far as 1800, which makes
it the longest, continuous price index series available. These data are shown in Table
3. Data for 1800 through 1912 were derived by splicing price indexes collected in
three separate, nongovernmental, studies. Prior to 1978, there was only one CPI
available. For 1978 and after, the data in Table 3 correspond to the CPI-U.

21 See CRS Report RL32293, The Chained Consumer Price Index: How Is It Different?, by
Brian W. Cashell.
22 The CPI expresses the price level relative to a particular period of time. Currently, the
CPI reflects the level of prices relative to the 1982-1984 period. Thus, the average index
value during that period for each metropolitan area will be 100, no matter how expensive
any area may be in which to live. That does not mean that each of these metropolitan areas
is equally expensive. See CRS Report RS20942, Adjusting Federal Benefits for Geographic
Differences in the Cost of Living, by Brian W. Cashell.

Table 2. Availability of Local Area CPIs
Northeast Regionmonthly
Boston-Brockton-Nashua, MA-NH-ME-CTbimonthly (odd)
New York-Northern New Jersey-Long Island, NY-NJ-CT-PAmonthly
Philadelphia-Wilmington-Atlantic City, PA-NJ-DE-MDbimonthly (even)
Pittsburgh, PAsemiannually
Midwest Regionmonthly
Chicago-Gary-Kenosha, IL-IN-WImonthly
Cincinnati-Hamilton, OH-KY-INsemiannually
Cleveland-Akron, OHbimonthly (odd)
Detroit-Ann Arbor-Flint, MIbimonthly (even)
Kansas City, MO-KSsemiannually
Minneapolis-St. Paul, MN-WIsemiannually
Milwaukee-Racine, WIsemiannually
St. Louis, MO-ILsemiannually
Southern Regionmonthly
Atlanta, GAbimonthly (even)
Dallas-Fort Worth, TXbimonthly (odd)
Houston-Galveston-Brazoria, TX bimonthly (even)
Miami-Fort Lauderdale, FLbimonthly (even)
Tampa-St. Petersburg-Clearwater, FLsemiannually
Washington-Baltimore, DC-MD-VA-WVbimonthly (odd)
Western Regionmonthly
Anchorage, AKsemiannually
Denver-Boulder-Greeley, COsemiannually
Honolulu, HIsemiannually
Los Angeles-Riverside-Orange County, CAmonthly
Portland-Salem, OR-WAsemiannually
San Diego, CAsemiannually
San Francisco-Oakland-San Jose, CAbimonthly (even)
Seattle-Tacoma-Bremerton, WAbimonthly (even)
Source: Department of Labor, Bureau of Labor Statistics.

Table 3. Consumer Price Index for All Urban Consumers,
1800 - 2007
(1982 - 1984 = 100)
Y e ar Index P ercentChange Y e ar Index P ercentChange Y e ar Index P e rcentChange
1800 17.0 1825 11.3 3.0 1850 8.3 0.0
1801 16.7 -2.0 1826 11.3 0.0 1851 8.3 0.0
1802 14.3 -14.0 1827 11.3 0.0 1852 8.3 0.0
1803 15.0 4.7 1828 11.0 -2.9 1853 8.3 0.0
1804 15.0 0.0 1829 10.7 -3.0 1854 9.0 8.0
1805 15.0 0.0 1830 10.7 0.0 1855 9.3 3.7
1806 15.7 4.4 1831 10.7 0.0 1856 9.0 -3.6
1807 14.7 -6.4 1832 10.0 -6.3 1857 9.3 3.7
1808 16.0 9.1 1833 9.7 -3.3 1858 8.7 -7.1
1809 15.7 -2.1 1834 10.0 3.4 1859 9.0 3.8
1810 15.7 0.0 1835 10.3 3.3 1860 9.0 0.0
1811 16.7 6.4 1836 11.0 6.5 1861 9.0 0.0
1812 17.0 2.0 1837 11.3 3.0 1862 10.0 11.1
1813 19.3 13.7 1838 10.7 -5.9 1863 12.3 23.3
1814 21.0 8.6 1839 10.7 0.0 1864 15.7 27.0
1815 18.3 -12.7 1840 10.0 -6.3 1865 15.3 -2.1
1816 17.0 -7.3 1841 10.3 3.3 1866 14.7 -4.3
1817 16.0 -5.9 1842 9.7 -6.5 1867 14.0 -4.5
1818 15.3 -4.2 1843 9.3 -3.4 1868 13.3 -4.8
1819 15.3 0.0 1844 9.3 0.0 1869 13.3 0.0
1820 14.0 -8.7 1845 9.3 0.0 1870 12.7 -5.0
1821 13.3 -4.8 1846 9.0 -3.6 1871 12.0 -5.3
1822 13.3 0.0 1847 9.3 3.7 1872 12.0 0.0
1823 12.0 -10.0 1848 8.7 -7.1 1873 12.0 0.0

1824 11.0 -8.3 1849 8.3 -3.8 1874 11.3 -5.6

Y e ar Index P ercentChange Y e ar Index P ercentChange Y e ar Index P e rcentChange
1875 11.0 -2.7 1900 8.3 0.0 1925 17.5 2.3
1876 10.7 -3.0 1901 8.3 0.0 1926 17.7 1.1
1877 10.7 0.0 1902 8.7 4.0 1927 17.4 -1.7
1878 9.7 -9.4 1903 9.0 3.8 1928 17.1 -1.7
1879 9.3 -3.4 1904 9.0 0.0 1929 17.1 0.0
1880 9.7 3.6 1905 9.0 0.0 1930 16.7 -2.3
1881 9.7 0.0 1906 9.0 0.0 1931 15.2 -9.0
1882 9.7 0.0 1907 9.3 3.7 1932 13.7 -9.9
1883 9.3 -3.4 1908 9.0 -3.6 1933 13.0 -5.1
1884 9.0 -3.6 1909 9.0 0.0 1934 13.4 3.1
1885 9.0 0.0 1910 9.3 3.7 1935 13.7 2.2
1886 9.0 0.0 1911 9.3 0.0 1936 13.9 1.5
1887 9.0 0.0 1912 9.7 3.6 1937 14.4 3.6
1888 9.0 0.0 1913 9.9 2.4 1938 14.1 -2.1
1889 9.0 0.0 1914 10.0 1.0 1939 13.9 -1.4
1890 9.0 0.0 1915 10.1 1.0 1940 14.0 0.7
1891 9.0 0.0 1916 10.9 7.9 1941 14.7 5.0
1892 9.0 0.0 1917 12.8 17.4 1942 16.3 10.9
1893 9.0 0.0 1918 15.1 18.0 1943 17.3 6.1
1894 8.7 -3.7 1919 17.3 14.6 1944 17.6 1.7
1895 8.3 -3.8 1920 20.0 15.6 1945 18.0 2.3
1896 8.3 0.0 1921 17.9 -10.5 1946 19.5 8.3
1897 8.3 0.0 1922 16.8 -6.1 1947 22.3 14.4
1898 8.3 0.0 1923 17.1 1.8 1948 24.1 8.1

1899 8.3 0.0 1924 17.1 0.0 1949 23.8 -1.2

Y e ar Index P ercentChange Y e ar Index P ercentChange Y e ar Index P e rcentChange
1950 24.1 1.3 1970 38.8 5.7 1990 130.7 5.4
1951 26.0 7.9 1971 40.5 4.4 1991 136.2 4.2
1952 26.5 1.9 1972 41.8 3.2 1992 140.3 3.0
1953 26.7 0.8 1973 44.4 6.2 1993 144.5 3.0
1954 26.9 0.7 1974 49.3 11.0 1994 148.2 2.6
1955 26.8 -0.4 1975 53.8 9.1 1995 152.4 2.8
1956 27.2 1.5 1976 56.9 5.8 1996 156.9 3.0
1957 28.1 3.3 1977 60.6 6.5 1997 160.5 2.3
1958 28.9 2.8 1978 65.2 7.6 1998 163.0 1.6
1959 29.1 0.7 1979 72.6 11.4 1999 166.6 2.2
1960 29.6 1.7 1980 82.4 13.5 2000 172.2 3.4
1961 29.9 1.0 1981 90.9 10.3 2001 177.1 2.8
1962 30.2 1.0 1982 96.5 6.2 2002 179.9 1.6
1963 30.6 1.3 1983 99.6 3.2 2003 184.0 2.3
1964 31.0 1.3 1984 103.9 4.3 2004 188.9 2.7
1965 31.5 1.6 1985 107.6 3.6 2005 195.3 3.4
1966 32.4 2.9 1986 109.6 1.9 2006 201.6 3.2
1967 33.4 3.1 1987 113.6 3.7 2007 207.342 2.8
1968 34.8 4.2 1988 118.3 4.1
1969 36.7 5.5 1989 124.0 4.8
Source: Department of Labor, Bureau of Labor Statistics.
CPI Data Via the Internet
Detailed CPI data are now readily available to those with access to the Internet.
BLS has set up a number of ways on their website, [],
to obtain CPI data. By making selections from each of a succession of menus, users
of BLS’s website may specify the particular data they want. There is also a link to
an “inflation calculator,” allowing users to make their own inflation adjustments to
dollar amounts.
BLS has also set up a separate home page for the CPI where visitors can get a
copy of the most recent CPI press release, as well as up-to-date information regarding
the CPI program. The Internet address for this page is [].

CPI Calculations
The CPI is an indicator of changes in the price level. At present, those changes
are expressed relative to the average level of prices in the years 1982, 1983, and
1984. Thus, the average of all of the monthly CPI numbers for those years is equal
to 100. Determining the change in consumer prices between any two years is a
simple percent change calculation using the formula:
percent change in the CPI = (( CPI2 ÷ CPI1 ) - 1 ) x 100.
For example, in 2007, the CPI-U was 207.342, and in 1987 the CPI-U was 113.6.
The total percentage change in the CPI-U between 1987 and 2007 was:
(( 207.342 ÷ 113.6 ) - 1 ) x 100 = 82.5 percent.
Calculating the percentage change between any two years at an annual rate is slightly
more complicated, and requires the formula:
annual rate of change in the CPI = (( CPI2 ÷ CPI1 )1/n - 1 ) x 100,
where n is the number of years covered in the interval. To calculate the average
annual rate of change in the CPI-U between 1987 and 2007, we use an n of 20 and
the same CPI-U values as in the previous example. The average annual rate of
change in the CPI-U between 1987 and 2007 was:
(( 207.342 ÷ 113.6 )1/20 - 1 ) x 100 = 3.1 percent
Another common use of the CPI is to adjust dollar amounts for inflation, so that
amounts from different years can be compared in terms of dollars of the same
purchasing power. Suppose the question is how much money would have been
required in 2007 to buy the same quantity of goods and services as $100 bought in
1987. To get such an estimate, the 1987 dollar value needs to be adjusted to account
for the increase in consumer prices between 1987 and 2007. That requires the
equivalent purchasing power in period 2 = ( CPI2 ÷ CPI1 ) x dollar amount in period 1
For example, using the same CPI values as in the above examples, the equivalent
purchasing power in 2007 of $100 in 1987 is:
( 207.342 ÷ 113.6 ) x $100 = $182.52
This same calculation can be reversed to find the purchasing power in an earlier
period of a dollar amount of a more recent vintage. To do this use the formula:
equivalent purchasing power in period 1 = ( CPI1 ÷ CPI2 ) x dollar amount in period 2

For example, using the same CPI values as in the above examples, the equivalent
purchasing power in 1987 of $100 in 2007 is:
( 113.6 ÷ 207.342 ) x $100 = $54.79
Using these formulae, dollar values of constant purchasing power can be
compared for any two periods for which CPI data are available. Constant dollar
values are always compared in terms of the dollar’s purchasing power in a particular
year, known as the base year. When comparing dollars of constant purchasing
power, it is important to specify the base year.