# Closer Look 4

## Tutorial: Calculating Inflation

This tutorial will show how to calculate an inflation rate from a price index.

## Inflation and Price Indexes

The key to calculating an inflation rate is to remember that the inflation rate is the percentage change in the price index from year to year.  The inflation rate must be calculated. It cannot be read from the price index directly except when comparing to the base year.

Let’s start with the following imaginary reported data on a price index:

 Year Price Index 1994 100 1995 110 1996 121 1997 133.1 1998 139.8

To repeat, an inflation rate is a percentage change in a price index from one year to another year.  So, a formula for calculating an inflation rate could be:

(PriceIndexLaterYear/PriceIndexEarlierYear – 1.0) * 100 = InflationRate

Using the above formula we can calculate the inflation rate from 1994 to 1995 as follows:

(110/100 – 1.0) * 100 = 0.1 * 100 = 10%

If we repeat this for 1995-1996, the following year, we get the same inflation rate of 10%.

(121/110 – 1.0) * 100 = (1.1 – 1.0) * 100 = 0.1 * 100 = 10%

Notice that although the inflation rate was 10% for both years, the price index itself rose by 10 in 1995 (100 to 110), but in 1996 the price index rose by 11 (110 to 121) which was still only a 10% increase.

This brings us to the most common mistake by students in calculating inflation rates. It is very tempting to simply look at the absolute increase in the price index as assume that is the inflation rate. But it isn’t. For example, in the above table, the price index rises from 121 in 1996 to 133.1 in 1997. That’s an absolute increase of 12.1. But the inflation rate is only 10%. That’s because 133.1 is 10% larger than 121.

Deflation rates are calculated the same way. In fact, a “deflation rate” is really only a negative inflation rate, indicating the price index went down. Be sure to keep track of any resulting negative sign and be sure you are using the right value for each year.  For example, let’s suppose that in the earlier year the price index was 88. Then prices declined (deflation) so that the price index in the following year was 85.  Using our formula we would have:

(85/88 -1.0) * 100 = (0.966 – 1.0) * 100 = -.034 * 100 = -3.4%