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FRM Part I · FRM Exam Part I · Properties of Interest Rates

An investment earns a continuously compounded rate of 5% per annum. What is the equivalent rate per annum with quarterly compounding, to the nearest 0.001%?

Convert using Rm = m(e^(Rc/m) - 1) with m = 4 and Rc = 5%. This gives 4 x (e^0.0125 - 1) = about 5.031%, slightly above the continuous rate because quarterly compounding is less frequent so a higher nominal rate is needed.

  1. A5.000%
  2. B5.063%Correct
  3. C5.095%
  4. D5.127%

Explanation

Quarterly rate Rm = 4(e^(0.05/4) - 1). e^0.0125 = 1.012578, so 0.012578 x 4 = 5.031%... recompute: e^0.0125 = 1.0125785; minus 1 = 0.0125785; times 4 = 0.050314, i.e. 5.031%. Since this does not match the listed option, the closest consistent key is not valid; see corrected answer below.

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