What Is the Fisher Equation on Interest Rates and Inflation?

The Fisher Equation defines the impact of the inflation on your fixed-income investments. There are 2 versions of the Fisher Equation: the easy-to-remember version and the exact version.

Easy-to-remember version of the Fisher Equation:

r = i - π

where: 
  i - the nominal interest rate
  r - the real interest rate
  π - the inflation rate

This version is easy to understand. "i" represents the profit you are making from the investment, but that profit will be depreciated by the inflation "π". So the real profit "r" should be "i - π".

For example, if you make a 1-year term deposit to a bank, it gives you a 5% interest rate (i, the nominal interest rate). And if the inflation rate (π) is 2% for the next year, then the real interest rate (r) on your deposited money is about r = i - π = 5% - 2% = 3%.

Exact version of the Fisher Equation:

(1 + i) = (1 + r) * (1 + π)

where: 
  i - the nominal interest rate
  r - the real interest rate
  π - the inflation rate

To understand this version, we need to consider the impact of inflation on the total values involved in the investment. Let's start from the following 3 relations:

Future face value based on the nominal interest rate:
  fv = cv * (1 + i)      (1)

Future real value based on the real interest rate:
  rv = cv * (1 + r)      (2)

Future face value based on the inflation rate:
  fv = rv * (1 + π)      (3)

where: 
  fv - the future face value of the investment
  rv - the future real value of the investment
  cv - the current value of the investment
  i - the nominal interest rate
  r - the real interest rate
  π - the inflation rate

Derive the Fisher Equation from the above relations:

Combine relation (1) and (3):
  cv * (1 + i) = rv * (1 + π) 

Replace "rv" with relation (2):
  cv * (1 + i) = cv * (1 + r) * (1 + π) 

Remove "cv" to get the Fisher Equation:
  (1 + i) = (1 + r) * (1 + π) 

If we apply the exact version of the Fisher Equation to the sample example, we have:

(1 + 5%) = (1 + r) * (1 + 2%) 

r = (1 + 5%) / (1 + 2%) - 1

r = (1 + 0.05) / (1 + 0.02) - 1

r = 0.029411764705882 = 2.94%

As you can see that the exact real interest rate is 2.94%, slightly lower than the approximation of 3%.

⇒ Relation of Inflation and Interest Rates

⇐ Impact of Interest Rates on Stock Market

⇑ Interest Rates and Stock Market

⇑⇑ Interest Rates