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Which of the following is an inflation-adjusted return on a loan or bond (i.e., the real interest rate) according to the Fisher relationship?
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11. Unemployment and Inflation
Nominal Interest, Real Interest, and the Fisher Equation
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What is the Fisher equation?
A
i ≈ r + π^e (more exactly (1 + i) = (1 + r)(1 + π^e))
B
i = r × (1 + π^e) (more exactly i = r(1 + π^e))
C
i ≈ r − π^e (more exactly (1 + i) = (1 + r)(1 − π^e))
D
i ≈ π^e (nominal interest rate equals expected inflation)
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Understand that the Fisher equation relates the nominal interest rate, the real interest rate, and the expected inflation rate.
Recall the approximate form of the Fisher equation: \(i \approx r + \pi^e\), where \(i\) is the nominal interest rate, \(r\) is the real interest rate, and \(\pi^e\) is the expected inflation rate.
Recognize the exact form of the Fisher equation, which accounts for compounding: \((1 + i) = (1 + r)(1 + \pi^e)\).
Note that the approximate form is derived by assuming the product \(r \times \pi^e\) is very small and can be ignored, simplifying the exact formula.
Use this understanding to identify that the correct Fisher equation expresses the nominal interest rate as approximately the sum of the real interest rate and expected inflation.
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