If the nominal interest rate is 7% p.a and the real rate of interest is 4% p.a, the expected inflation rate will be approximately

Question

BlackTom AI · Accepted Answer

Apply the Fisher equation that links nominal interest rate (i), real interest rate (r) and expected inflation (π): (1 + i) = (1 + r)(1 + π).

1) Relevant knowledge points and concepts
- Fisher equation: (1 + i) = (1 + r)(1 + π).  
- For small percentages the approximation i ≈ r + π is often used, but the exact relation above should be used when we want precision.

2) Complete reasoning process step by step
- Given i = 7% = 0.07 and r = 4% = 0.04. Solve the Fisher equation for π:
  (1 + i) = (1 + r)(1 + π) → 1 + π = (1 + i)/(1 + r) → π = (1 + i)/(1 + r) − 1.

3) Calculations with intermediate steps
- Compute (1 + i) = 1.07 and (1 + r) = 1.04.
- Divide: 1.07 / 1.04 = 107/104 = 1.0288461538...
- Subtract 1: π = 1.0288461538 − 1 = 0.0288461538 = 2.88461538%.

4) Why the correct answer is correct
- The exact expected inflation is ≈ 2.8846%, which when rounded to one decimal or the nearest whole percent is approximately 3%. The simple approximation i ≈ r + π gives 7% − 4% = 3%, which matches the exact value to a close degree because rates are small.

5) Why the other options are incorrect
- a. 1%: far below the exact value; would imply (1+r) much closer to (1+i), not supported by the numbers.  
- b. 4%: this is the real rate r, not the expected inflation π. Confuses r with π.  
- c. 11%: this is the sum i + r, an incorrect operation; neither the Fisher equation nor the approximation yields 11%.

6) Conclusion confirming the final answer
- Using the Fisher equation we find expected inflation ≈ 2.8846%, which rounds to 3%. Therefore the correct choice is d. 3%.

If the nominal interest rate is 7% p.a and the real rate of interest is 4% p.a, the expected inflation rate will be approximately单项选择题

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