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Fisher Equation : Relationship between Nominal and Real Interest rates

Under Inflation

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Exploring the Essential Aspects of Fisher Equation

Fisher equation, named after its designer Irving Fisher, is a concept in Economics that defines the relationship between nominal interest rates and real interest rates under the influence of inflation. This blog explores the different elements of the equation with examples, along with the pros and cons associated with it.

What Is the Fisher Equation?

The Fisher equation is a concept of economics stating the relationship between nominal interest rates and real interest rates. The bond given between the two is derived under the effect of inflation. According to the Fisher equation, the nominal interest rate is equal to the sum of the real interest rate and inflation. The concept of the Fisher equation has great significance in the field of finance and economics. This is because it is used in calculating returns on investments (ROI) or estimating the nature of nominal and real interest rates.

Also, the Fisher equation elucidates a state of affairs where investors or lenders demand an additional reward. The demand for an additional reward is justified to compensate for the loss of purchasing power due to growing inflation. Moreover, the applications of the Fisher effect has been protracted considering its growing demand in the market. This method now successfully deals with the analysis of the money supply and international trading of currencies. So, the designer of such a beautiful concept in the field of finance and economics was an excellent American economist, Irving Fisher. Thus, the Fisher equation rapidly gained popularity in the market due to its unmatched work in the theory of interest.

How Do You Calculate the Fisher Effect?

Fisher Equation Formula

The exact formula to justify the relationship between the real interest rate and nominal interest rate can be given as follows:

(1 + nominal interest rate) = (1 + real interest rate) * (1 + inflation rate)


In mathematical terms, the Fisher equation is broadly expressed using the formula given below:

(1 + i) = (1 + r) * (1 + Pi)


i = the nominal interest rate

r = the real interest rate

Pi = the inflation rate


Therefore, the approximate relationship between the real interest rate and the nominal interest rate can be shown as follows:

i ≈ r + Pi


Fisher equation Examples

To understand the working of the Fisher equation, you can refer to the example shown as follows:

Suppose you own a firm having the real rate of return to 3.5% and expected inflation to 5.4%. According to the above formula, the approximate nominal rate of return can be calculated as 0.035 + 0.054 = 0.089, or 8.9%. Therefore, substituting the value of i and r in the formula for the Fisher equation, (1 + i) = (1 + r) * (1 + Pi), the value for the nominal rate of interest is 9.1%.


What Is the Inflation Rate?

The inflation rate is a measure of the price inflation comprehending the annual percentage change in the consumer price index (CPI). Thus, the inflation rate contributes to the development of an economy as it compares an increase in the general price level of goods. It is imperative to monitor the inflation rate as an independent inflation rate can damage an economy severely. Moreover, excessive growth in the liquidity can often lead to a higher rate of inflation which can further result in hyperinflation.


What Is the Nominal Rate of Interest?

The nominal rate of interest is the type of interest rate which is measured before considering the inflation in an economy. It is compared with the real interest rate before referring to inflation. Therefore, the term nominal can also see the advertised or pre-fixed interest rate on loan. This pre-fixed interest rate does not have permission to take into account any fees or compounding of interest. Moreover, the interest rate set by the Federal Reserve, also known as the federal funds rate, can also be identified as a nominal rate.

What Is the Relationship Between Nominal and Real Interest Rate?

 A nominal interest rate elucidates the financial return earned by an individual in return of the deposited money. In the Fisher equation, the value of the nominal interest rate and the actual interest rate is similar. It highlights the financial growth for a specific interval of time deciphering the total amount owed to a financial lender. On the contrary, a real interest rate refers to the amount reflecting the buying capacity of the money borrowed over a specific time. The two interest rates work in the direction to identify the financial growth for a pre-defined interval of time. Thus, the fundamental relationship among them can be determined by the nature of their work.


Pros and Cons of the Fisher Effect

Pros of the Fisher effect

  • Fisher effect distinguishes between the nominal interest rate and the real interest rate giving a clear picture for these interest rates.
  • It contributes to sustainable development of the economy as it detects a situation where investors or lenders demand an additional reward.

Cons of the Fisher effect

  • The elasticity of demand to interest rates: With the continuous rise in the price of the assets, the high-interest rates prove to be worthless in reducing demand. This gives rise in the central banks the need to increase the real interest rate to affect.
  • Liquidity Trap: It works on the concept of reducing nominal interest rates to influence the expenditure in favour of the business. Thus, to attract investment, the bank needs to increase the interest rates and eliminate all the possibilities of failure.

Textbooks On Fisher Equation

Book 1

Monetary Economics, 2nd Edition

Published by Routledge in 2008

By Jagdish Handa (Author)


Book 2

Consumer Price Index Manual: Theory and Practice (EPub)

Published by International Monetary Fund in 2004


Book 3

The Rate of Interest Paperback

Published by Martino Fine Books in 2009

By Irving Fisher (Author)


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