If the nominal interest rate in an economy is 5% and the rate of inflation is 11%, the real interest rate is:

Question

If the nominal interest rate in an economy is 5% and the rate of inflation is 11%, the real interest rate is:

BlackTom AI · Accepted Answer

Apply the Fisher equation for the relationship between nominal, real interest rates and inflation: (1 + nominal) = (1 + real) × (1 + inflation). This exact formula yields the real rate r = (1 + nominal)/(1 + inflation) − 1.

1. Relevant knowledge points and concepts
- Nominal interest rate is the quoted rate (5% here).
- Inflation reduces purchasing power, so the real interest rate adjusts nominal by inflation.
- The exact adjustment uses the Fisher equation; a common approximation is real ≈ nominal − inflation, but that is only approximate and can be inaccurate when rates are not tiny.

2. Complete reasoning step by step
Use the exact Fisher formula: r = (1 + i)/(1 + π) − 1, where i = nominal rate (0.05) and π = inflation rate (0.11).

3. Calculations with intermediate steps
1 + i = 1 + 0.05 = 1.05
1 + π = 1 + 0.11 = 1.11
Divide: (1.05)/(1.11) = 105/111. Simplify if desired: 105/111 = 35/37 ≈ 0.9459459459
Subtract 1: 0.9459459459 − 1 = −0.0540540541
Convert to percent: −0.0540540541 × 100% ≈ −5.40540541% ≈ −5.4%

4. Why the correct answer is correct
This result accounts for compounding: the nominal return of 5% is measured in money terms while prices rise by 11%, so in real purchasing-power terms the investor loses about 5.405% annually. The exact Fisher formula gives −5.405% (rounded to −5.4%).

5. Why the other options are incorrect
- 11%: that is the inflation rate, not the real return.
- 6%: this would be the naive difference 5% − 11% = −6% (and with wrong sign if listed as positive 6%); it’s an approximation and also mis-signed if positive.
- 5.4%: positive 5.4% is the wrong sign; the real rate is negative because inflation exceeds nominal interest.

6. Conclusion
Using the Fisher equation gives a real interest rate of approximately −5.4%, which matches the provided correct answer: −5.4%.

If the nominal interest rate in an economy is 5% and the rate of inflation is 11%, the real interest rate is:单项选择题

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