Real rates are defined as nominal rates that have been adjusted for which of the following?

Question

BlackTom AI · Accepted Answer

Real rates are nominal rates adjusted for inflation.

1. Relevant knowledge points and concepts
- Nominal interest rate (i) is the observed quoted rate, not accounting for price-level changes. 
- Real interest rate (r) measures the change in purchasing power and therefore removes the effect of inflation (π). 
- Fisher relation links them: (1 + i) = (1 + r)(1 + π), with the common approximation r ≈ i − π for small rates.

2. Step-by-step reasoning
- Start from the Fisher equation: (1 + i) = (1 + r)(1 + π).
- Solve for r to express the real rate in terms of nominal rate and inflation: r = (1 + i)/(1 + π) − 1.
- This shows the real rate is computed by adjusting the nominal rate for inflation; nothing in the formula subtracts default risk, accrued interest, or interest-rate volatility.

3. Calculation with intermediate steps (example)
- Suppose nominal i = 6% (0.06) and inflation π = 2% (0.02).
- Compute (1 + i)/(1 + π) − 1 = (1.06 / 1.02) − 1.
- 1.06 / 1.02 = 1.039215686; subtract 1 gives r = 0.039215686 ≈ 3.9216% (approx. 4%).
- Using the approximation r ≈ i − π gives 0.06 − 0.02 = 0.04 (4%), close to the exact value for small rates.

4. Why the correct answer is correct
- The definition of real rate explicitly removes inflation’s effect to reflect true purchasing-power return; the Fisher equation mathematically demonstrates this.

5. Why other options are incorrect
- Default risk: a credit-risk premium added to compensate for possible borrower default; not what “real” adjusts for. 
- Accrued interest: an accounting/bond pricing concept, not an inflation adjustment. 
- Interest rate risk: risk of market rate changes affecting price/value; real rates do not remove this risk. 
- “Both inflation and interest rate risk”: incorrect because the real rate only adjusts for inflation.

6. Conclusion
- The correct answer is Inflation, which matches the provided answer.

Real rates are defined as nominal rates that have been adjusted for which of the following?单项选择题

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