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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

A risk analyst has a continuously compounded rate of 5% per year. What is the equivalent nominal annual rate with semiannual compounding?

The equivalent semiannual nominal rate is about 5.06%. Each half-year must grow by e^0.025 - 1, or about 2.53%, to match continuous compounding at 5%, and doubling that gives 5.06%. A discretely compounded nominal rate must exceed the continuous rate.

  1. A4.94%
  2. B5.00%
  3. C5.06%Correct
  4. D5.13%

Explanation

The semiannual nominal rate = 2 x (e^(0.05/2) - 1) = 2 x (1.025315 - 1) = 5.06%. The 5.13% figure is the effective annual rate (e^0.05 - 1), not a semiannual nominal rate. The 4.94% figure comes from converting in the wrong direction, 2 x ln(1.025).

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