FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
A rate is quoted as 5% per annum with semiannual compounding. What is the equivalent continuously compounded rate per annum?
The equivalent continuously compounded rate is 4.939%. Convert by taking twice the natural log of 1.025, since the semiannual rate is 2.5% per period. This is lower than 5% because continuous compounding is the most frequent compounding.
- A4.879%
- B4.939%Correct
- C5.000%
- D5.063%
Explanation
Rc = 2 x ln(1 + 0.05/2) = 2 x ln(1.025) = 2 x 0.024693 = 4.939%. The 4.879% option is ln(1.05), which wrongly treats 5% as an annual effective rate. The 5.063% option is the effective annual rate of the semiannual quote, not the continuous rate. The 5.000% option assumes no conversion is needed.
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