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Fisher Approximation: Nominal, Real & Inflation Rates

Use the additive Fisher approximation to relate a nominal rate, real rate and expected inflation for the same period.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

A real rate of 2 percent plus expected inflation of 3 percent gives an approximate nominal rate of 5 percent. The exact compounded relationship would give 5.06 percent.

Approximate nominal rate = real rate + expected inflation rate

Worked example

Enter these known values and leave the other values blank.

Approximate real interest rate
2 %
Expected inflation rate
3 %
Approximate nominal interest rate
5 %

Assumptions and limitations

  • This deliberately retains the source’s additive approximation. Exact simple-rate compounding uses (1 + nominal) = (1 + real) Ă— (1 + inflation), which also includes the product of real rate and inflation.
  • All rates must cover the same period and use compatible conventions. For expected purchasing-power returns use expected inflation; realized inflation answers a different retrospective question.
  • Negative rates and deflation are allowed above minus 100 percent. The approximation becomes less accurate as the magnitude of either real rate or inflation increases.
  • The relationship is a calculation convention. It does not forecast inflation, set a market interest rate or adjust for taxes, fees and investment risk.

Common questions

Why does 2 percent plus 3 percent return 5 rather than 5.06?

This calculator uses the additive approximation. The missing 0.06 percentage point is the product of 0.02 and 0.03 in the exact compounded relationship.

Can expected inflation be negative?

Yes. That represents expected deflation; use the same period as the interest rates.

References

Bookify keeps the additive Fisher approximation and restricts the modeled simple rates to values above minus 100 percent.

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