# What is the Fisher Equation?

P.M. Willers
P.M. Willers

The Fisher Equation is used in economic theory to explain the relationship between interest rates and inflation. The theories behind it were introduced by American economist Irving Fisher. Fisher was one of the first economists to identify a difference between a real and a nominal interest rate, and his work in this area culminated in this equation.

Expressed mathematically, the Fisher Equation is

real rate of interest + inflation rate = nominal rate of interest.

In other words, the equation clarifies that the real interest rate for a loan is equivalent to the posted, or nominal, interest rate minus the rate of inflation. The Greek letter π is normally used to signify the

inflation rate

and should not be confused with the constant that π represents in geometry. The Fisher Equation is used in economic theory to explain the relationship between interest rates and inflation, so it is of particular importance to the real estate industry.

If inflation is taken into account, then it is not the real interest rate that changes, but the nominal interest rate that adjusts or alters with inflation. The inflation rate used when evaluating the equation is generally the expected inflation rate throughout the life of the loan. This being said, the Fisher Equation was hypothesized with the idea that the rate of inflation was constant. Taking into account the rate of inflation places the interest rate of a loan within a realm affected by current business, technology, and other world events that affect the real word economy. The Federal Reserve constantly monitors for inflationary risks to the U.S. economy, but may overlook increases in prices in oil or certain foods that tend to fluctuate often.

This equation can be implemented either ex-ante, meaning before, or ex-post, meaning after, an analysis of a loan. If the equation is used to evaluate the loan ex-post, for example, it could help to determine the purchasing power of the loan and calculate whether or not the loan was worthwhile. It is also used to help lenders determine what an interest rate should be. By using this equation, lenders can take into consideration any anticipated loss of purchasing power, either on the principal balance or on the interest, and set interest rates favorably.

The Fisher Equation is commonly used while estimating the worth of investments and evaluating the yield of bonds and investments after the fact. It should not be confused with Fisher’s Equation, otherwise known as the Fisher-Kolmogorov Equation. Fisher’s Equation is a differential equation dealing with heat and mass transfer within the field of natural sciences, rather than the field of economics.  