Fisher Equation
The Fisher equation relates nominal interest rates, real interest rates, and inflation.
Learn the formula with economic examples.
The Formula
Approximate form: i ≈ r + π
The Fisher equation, named after American economist Irving Fisher who formulated it in 1930, describes the relationship between nominal interest rates, real interest rates, and inflation. It shows that the nominal interest rate you see at the bank is actually composed of two parts: the real return on your money and compensation for inflation.
The approximate form (i ≈ r + π) works well when inflation is low (under about 10%). For higher inflation rates, the exact form should be used because the cross-product term (r × π) becomes significant.
Understanding this equation is crucial for investors, borrowers, and policymakers. A savings account paying 5% interest with 3% inflation gives a real return of only about 2%. If inflation exceeds the nominal rate, the real return is negative — your money loses purchasing power despite earning interest.
Variables
| Symbol | Meaning |
|---|---|
| i | Nominal interest rate (the stated or observed rate) |
| r | Real interest rate (adjusted for inflation) |
| π | Expected inflation rate |
Example 1
A bond pays a nominal interest rate of 6%. If expected inflation is 2.5%, what is the real interest rate?
Using the exact formula: (1 + r) = (1 + i) / (1 + π)
(1 + r) = 1.06 / 1.025 = 1.03415
r = 0.03415
Real interest rate ≈ 3.42% (the approximate method gives 3.5%)
Example 2
In a high-inflation economy, inflation is 25% and the real interest rate is 4%. What nominal rate must a bank offer?
Using the exact formula: (1 + i) = (1 + r) × (1 + π)
(1 + i) = 1.04 × 1.25 = 1.30
i = 0.30
The approximate method would give i ≈ 4% + 25% = 29%, which underestimates by 1%.
Nominal rate = 30% (exact formula matters at high inflation)
When to Use It
The Fisher equation is fundamental in finance and macroeconomics.
- Comparing investment returns after adjusting for inflation
- Setting interest rates in monetary policy
- Evaluating whether savings accounts preserve purchasing power
- Pricing inflation-indexed bonds (TIPS in the United States)