How to Use the Fisher Equation
The Fisher equation says the nominal rate is roughly the real rate plus expected inflation, so any one term follows from the other two.
The Fisher Equation formula
Calculator
Enter a quoted nominal rate with expected and actual inflation to see the planned and realized real returns.
The rate written on the bond or loan.
What both sides expected when the rate was agreed.
What inflation turned out to be. Set it equal to expected inflation if there was no surprise.
Quoting 7% while expecting 4% inflation means both sides planned on 3% of purchasing power.
- Realized real rate
- 1%
- Unexpected inflation
- 2%
- Who gained from the surprise
- Borrowers gained
Once inflation came in at 6%, the lender actually earned 1% in purchasing power.
Actual inflation minus expected inflation. Zero here means the Fisher prediction held.
How to calculate Fisher Equation, step by step
- 1Write it in the form you need. Start from nominal ≈ real + expected inflation and rearrange for whichever term is missing.
- 2Fill in the two known rates. Keep all three terms in the same units, percentages or decimals, and never mix the two.
- 3Add or subtract. Solve for the missing rate using the rearrangement you wrote.
- 4Decide expected or realized. Expected inflation gives the real rate people planned on; actual inflation gives the real rate they ended up with.
Worked example: Fisher Equation
A bond quotes a nominal rate of 7% while both sides expect 4% inflation, so the expected real rate = 7% − 4% = 3%. If inflation instead comes in at 6%, the realized real rate = 7% − 6% = 1%, and the lender earns far less purchasing power than planned.
Fisher Equation questions
Who gains from unexpected inflation?
Borrowers gain and lenders lose, because the loan is repaid in dollars worth less than either side expected, which cuts the realized real rate.
Is the Fisher equation exact?
No, it is an approximation. The exact form is (1 + nominal) = (1 + real) × (1 + expected inflation), and the gap only grows noticeable at high inflation rates.
What does the Fisher effect say about loanable funds?
When expected inflation rises, lenders demand more and borrowers accept more, so the nominal rate moves nearly one for one with it and the real rate stays put.
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