In the example of Eddie and his friend, the loan was linked to the price of a single item, i.e., a pair of pants. Usually, however, it is customary to link loans to the average rise in the price of a given basket of goods, which is known as “the basket”. “The basket” includes a list of goods and services that an average urban family buys in the course of a month.א The U.S Bureau of Labor Statistics of the Department of Labor prepares the list of items included in the basket according to a comprehensive survey that it conducts.

The monthly change in the price of the basket is published in the form of an index, which is called the “Consumer Price Index” (CPI). The Consumer Price Index for each month measures how much prices have risen in a given month and it is published on the 13th of the following month.

For example, the October index is published on November 13. The basket of goods comprising the index is examined from time to time, and updated to better reflect the average consumption of an average American urban family.

The data is presented in the form of an index in which the first index each year reflects 100 points (or 100%). The following indexes are larger or smaller than the first one depending on whether there was a cumulative increase or decrease as compared to the first index.

When the most recent index is published, it is customary to note the percentage rise or fall in the index as compared to the preceding index. Additional information about the CPI, its composition, and adjustments can be found at the U.S Bureau of Labor Statistics.

Table 1.2 Changes in the CPI

Month Index Rise in Index This part is not published
January 100 Total spending for purchasing “the basket” in January was $2,500, meaning that $2,500 = 100 $2,500 = 100
February 102 2% $2,549
March 104 2% $2,599
May 108 3.8% $2,699
June 110 1.9% $2,749

Use the following formula in order to calculate the increase in the prices of goods between February and May:

108 (May index)/102 (February index) X 100% -100 = 5.88%

In professional terminology, it is said that the index rose 5.88% during this period.

Index Linkage

When a lender links their money to the rise in the index, they are in effect guaranteeing that they will be able to buy the same quantity of “baskets” with the money repaid as could have been bought with the money when it was loaned.

For example, assume that Eddie has been granted a $10,000 interest-free loan in January for four months. In January, he could have bought four “baskets” for $10,000, while the price of the basket in January was $2,500. Eddie wants to receive at the end of May enough money to buy four “baskets” at the new price of $2,699 per “basket”.

108 (May index)/100 (January index) X $10,000 = $10,800

Date A Date B
$10,000 $800

The Value of any Sum Adjusted to the Index

The value adjusted to the index is a term used to denote a sum of money in dollars needed on date B in order to buy the same quantity of “baskets” that could have been bought on day A for a given sum of money.

In the previous example, $10,800 (on date B) represents the value adjusted to the index of $10,000 on date A.

Another example

Assume that a person had $5,000 on date A. The index rose 30% by date B. The value of $5,000 adjusted to the index is $6,500. This sum of $6,500 on date B preserves the person’s purchasing power.