Fisher Equation Calculator
Calculate real and nominal interest rates
Fisher Equation Formulas
Understanding the Fisher Equation
The Fisher Equation, named after economist Irving Fisher, describes the relationship between nominal interest rates, real interest rates, and inflation. It shows that nominal rates include compensation for both time value of money and expected inflation.
Real interest rate represents the true increase in purchasing power—what you actually earn after accounting for inflation. If you earn 5% nominal but inflation is 3%, your real return is only about 2%.
The exact formula is (1+nominal) = (1+real)(1+inflation). The approximation (real ≈ nominal - inflation) works well for low rates but becomes inaccurate at high inflation levels.
Real vs Nominal Rates
Nominal Rate
Stated rate on contracts. What you see quoted by banks.
Real Rate
Purchasing power change. Adjusted for inflation.
Inflation Premium
Portion of nominal rate compensating for expected inflation.
Negative Real Rates
When inflation exceeds nominal rate. Purchasing power declines.
Historical Perspective
| Period | Nominal Rate | Inflation | Real Rate |
|---|---|---|---|
| 1970s Stagflation | 10-15% | 8-14% | 0-2% |
| 1980s Volcker | 15-20% | 6-10% | 8-12% |
| 1990s Normal | 5-8% | 2-4% | 3-5% |
| 2010s ZIRP | 0-2% | 1-2% | -1 to 0% |
| Post-2020 | 4-5% | 3-8% | -3 to 1% |
Applications of Fisher Equation
Investment Decisions
Compare real returns across assets. Stocks, bonds, and real estate should be evaluated on real returns.
Loan Analysis
Borrowers benefit from inflation reducing real debt burden. Lenders lose purchasing power.
Monetary Policy
Central banks set nominal rates targeting real rates. Real rates drive economic activity.
Cross-Country Comparison
Real rates enable comparison across countries with different inflation. Use for international investing.
Frequently Asked Questions
Why does the approximation break down at high inflation?
The approximation ignores the cross-term (real × inflation). At 50% inflation and 5% real rate, exact nominal = 57.5%, but approximation gives 55%. The 2.5% error is the ignored cross-term.
Which inflation measure should I use?
For consumer decisions, use CPI. For investment decisions, consider expected future inflation, not past. TIPS spreads reflect market-expected inflation.
Can real rates be negative?
Yes, and they often are after inflation spikes. Negative real rates mean cash and bonds lose purchasing power. This encourages investment in real assets.
How does this relate to TIPS?
Treasury Inflation-Protected Securities pay a real rate (currently quoted around 2%). The difference between regular Treasury yields and TIPS is the market's expected inflation.
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