CFA Level I · CFA Level I Exam · The Time Value of Money in Finance
The nominal risk-free rate is 5.00% and expected inflation is 2.00%. Using the exact Fisher relation, the real risk-free rate is closest to:
Using the exact Fisher relation, the real rate is 1.05 divided by 1.02 minus one, which is about 2.94%. The simple subtraction of 3.00% is only an approximation and slightly overstates the real risk-free rate.
- A2.94%Correct
- B3.00%
- C3.06%
Explanation
(1 + nominal) = (1 + real)(1 + inflation). So real = 1.05/1.02 − 1 = 1.029412 − 1 = 2.94%. The approximation 5 − 2 = 3.00% overstates it. 3.06% results from dividing by 1.05 incorrectly, i.e., 3/0.98 style error.
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