The Consumer Price Index for All Urban Consumers is a valuable tool for understanding how inflation affects the value of a dollar. Every month, the U.S. Bureau of Labor Statistics publishes a new CPI figure, which can be used to calculate the real value of a dollar at a point in time.

The index works as a multiple of the average prices from 1982 to 1984. The average price during this 36-month period was recorded as 100. Thus, if the current reading for the CPI-U index is 180, prices would have increased by 80% since the reference period (1982 to 1984).

Calculating the real value of current dollars
You can use the Consumer Price Index for two periods to see the real value of a dollar in terms of earlier-period dollars. For example, you might want to know how much $100 in today's dollars would buy if prices were the same as in January 1990.

Determining this is simply a matter of division and multiplication, once we have the CPI-U level for the relevant periods:

January 1990: CPI-U stood at 127.4.
November 2015: CPI-U stood at 237.4.

The formula below will help us calculate what November 2015 dollars are worth in terms of January 1990 dollars:

More recent dollars in terms of past dollars = Dollar Amount × Beginning-period CPI ÷ Ending-period CPI.

or

$100 × 127.4 ÷ 237.4 = $53.66

In other words, we know that $100 in Nov. 2015 would buy as many goods and services as $53.66 in Jan. 1990.

Calculating the real value of past dollars
We can also determine what a certain amount of dollars in an earlier year would be worth in a more-recent time period.

Suppose we want to know what $100 in January 1942 would be worth in terms of March 2005 dollars. We can go to the Bureau of Labor Statistics to find the CPI-U for the relevant periods.

January 1942: 15.7
March 2005: 193.3

The formula below calculates the real value of past dollars in more recent dollars:

Past dollars in terms of recent dollars = Dollar amount × Ending-period CPI ÷ Beginning-period CPI.

or

$100 × 193.7 ÷ 15.7 = $1,233.76

In other words, $100 in January 1942 would buy the same amount of "stuff" as $1,233.76 in March 2005.

Some important detail
Because the CPI-U is based on a "basket" of goods, it won't measure the change in price level for a particular good -- say, healthcare or rent. Rather, it shows us how the purchasing power of a dollar has changed over time based on a collection of goods and services purchased by the typical urban consumer in the United States.

However, for what it is intended to do -- capture the changes in average prices over time -- it's very useful for determining the value of a dollar in one year compared to another.

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