IAI Actuarial Core Principles · Business Economics · Impact of the macroeconomic environment on business
A lender requires a real return of 3% a year. Expected inflation is 6%. Using the exact Fisher relationship, what nominal interest rate should be charged, to two decimal places?
The nominal rate should be 9.18%. Under the exact Fisher relationship, one plus the nominal rate equals 1.03 multiplied by 1.06, giving 1.0918. The approximation of 9.00% omits the cross-product of real return and inflation.
- A3.00%
- B9.00%
- C9.18%Correct
- D8.74%
- 6.18%
Explanation
Fisher: (1+i) = (1+r)(1+π) = 1.03 × 1.06 = 1.0918, so i = 9.18%. The simple sum 9.00% ignores the cross term 0.03 × 0.06 = 0.18%. Subtracting rather than compounding gives a lower figure such as 8.74% (1.06/1.03 type errors).
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