If inflation is 3% and the market interest rate charged for a loan (the nominal interest rate) is 7.2%, what is the 'real' interest rate?

Question

BlackTom AI · Accepted Answer

The real interest rate is given by the Fisher equation, which links the nominal interest rate, inflation, and the real rate: (1 + real) = (1 + nominal) / (1 + inflation).

1) Relevant knowledge points and concepts
- Nominal interest rate (i) is the observed market rate (here 7.2% or 0.072).
- Inflation rate (π) reduces purchasing power (here 3% or 0.03).
- Fisher equation (exact form) computes the real interest rate r: 1 + r = (1 + i) / (1 + π). A common approximation is r ≈ i − π, which is close when rates are small.

2) Step-by-step reasoning
- Use the exact Fisher equation to avoid small approximation error.
- Substitute i = 0.072 and π = 0.03.

3) Calculations (all intermediate steps)
- 1 + i = 1 + 0.072 = 1.072
- 1 + π = 1 + 0.03 = 1.03
- (1 + r) = 1.072 / 1.03 = 1.041747572...
- r = 1.041747572... − 1 = 0.041747572... = 4.1747572%

Rounded to one decimal place (as given in the choices) this is 4.2%.

4) Why the correct answer is correct
- The calculation shows the nominal gain after adjusting for inflation yields about a 4.1748% increase in real purchasing power; rounding gives 4.2%, matching option c. The approximation i − π = 7.2% − 3% = 4.2% is nearly identical here because rates are small.

5) Why the other options are incorrect
- a. 10.2% would be nominal + inflation (7.2% + 3%), which double-counts inflation and is not how real rates are derived.
- b. 2.4% is too low and does not follow the Fisher equation or the simple subtraction rule.
- d. −4.2% has the wrong sign; real rates are positive here because nominal exceeds inflation.

6) Conclusion
The correct real interest rate, using the Fisher equation and rounding to match the choices, is 4.2% (option c), which matches the provided answer.

If inflation is 3% and the market interest rate charged for a loan (the nominal interest rate) is 7.2%, what is the 'real' interest rate?单项选择题

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