Fisher Equation Calculator
Calculate the relationship between nominal interest rates, real interest rates, and inflation using the Fisher equation. This fundamental equation in monetary economics shows how inflation expectations are built into nominal interest rates.
Calculation Mode
Input Values
Fisher Equation Results
Nominal Interest Rate:
0.00%
Real Interest Rate:
0.00%
Inflation Rate:
0.00%
Equation Verification
Left Side (1 + i):
1.0000
Right Side (1 + r)(1 + p):
1.0000
Equation Balance:
Balanced
Economic Implications
Inflation Premium:
Real Return:
0.00%
Policy Signal:
N/A
Understanding the Fisher Equation
The Fisher equation, developed by economist Irving Fisher, establishes the relationship between nominal interest rates, real interest rates, and expected inflation. It shows that nominal interest rates compensate lenders for both the real return they expect and the inflation they anticipate.
The Fisher Equation
Exact Fisher Equation
- (1 + i) = (1 + r) × (1 + p)
- i = nominal interest rate
- r = real interest rate
- p = expected inflation rate
- All rates expressed as decimals
Approximate Fisher Equation
- i ˜ r + p
- Simple subtraction
- Accurate for low inflation rates
- Commonly used approximation
Solving for Different Variables
Rearranging the Fisher Equation
Solving for Real Rate
- r = [(1 + i) / (1 + p)] - 1
- r = i - p (approximate)
- Real return on investment
- Purchasing power gain
Solving for Nominal Rate
- i = (1 + r) × (1 + p) - 1
- i = r + p (approximate)
- Market interest rate
- Includes inflation compensation
Solving for Inflation
- p = [(1 + i) / (1 + r)] - 1
- p = i - r (approximate)
- Expected inflation rate
- Built into nominal rates
Real vs Nominal Returns
| Investment | Nominal Return | Inflation Rate | Real Return | Purchasing Power |
|---|---|---|---|---|
| Savings Account | 2.5% | 3.0% | -0.5% | Loss |
| Government Bond | 4.0% | 2.5% | 1.5% | Gain |
| Corporate Bond | 6.0% | 3.0% | 2.9% | Gain |
| Stock Portfolio | 8.0% | 3.0% | 4.9% | Strong Gain |
Applications in Economics
Monetary Policy
- Central bank interest rate decisions
- Inflation targeting
- Real interest rate management
- Economic stabilization
Investment Analysis
- Real return calculations
- Risk-adjusted returns
- Portfolio performance evaluation
- Asset allocation decisions
Bond Markets
- Bond yield analysis
- Real yield calculations
- Inflation expectations
- Treasury Inflation-Protected Securities
International Finance
- Currency carry trades
- Interest rate parity
- Exchange rate expectations
- Capital flow analysis
The Fisher Effect
Short-term Fisher Effect
- Nominal rates adjust to inflation changes
- Works well in efficient markets
- Strong empirical evidence
- Central bank policy transmission
Long-term Fisher Effect
- Nominal rates reflect long-term inflation expectations
- Stronger relationship over longer periods
- Market expectations drive rates
- Policy credibility matters
Limitations and Caveats
Market Imperfections
- Liquidity preferences
- Risk premiums
- Transaction costs
- Market segmentation
Expectations Formation
- Adaptive vs rational expectations
- Information asymmetries
- Behavioral biases
- Policy uncertainty
Key Takeaways for Fisher Equation Calculator
- The Fisher equation shows that nominal interest rates = real rates + inflation
- The exact equation is (1 + i) = (1 + r) × (1 + p), where approximation i ˜ r + p works for low rates
- The calculator can solve for any variable when the other two are known
- Real interest rates measure the true purchasing power return on investments
- Nominal rates include compensation for expected inflation
- The Fisher effect explains how interest rates adjust to inflation expectations
- Central banks use the Fisher equation to set monetary policy
- Use the calculator to understand the relationship between interest rates and inflation