FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
An investment earns an effective annual rate of 5%. What is the equivalent continuously compounded annual rate?
The equivalent continuously compounded rate is 4.88%, found as the natural log of 1.05. Continuous compounding grows money faster than annual compounding at the same nominal rate, so the continuous rate that matches a 5% effective annual yield must be lower than 5%.
- A4.76%
- B4.88%Correct
- C5.00%
- D5.13%
Explanation
The continuously compounded rate r satisfies e^r = 1.05, so r = ln(1.05) = 4.879%, about 4.88%. The 5.13% answer is e^0.05 - 1, which converts in the wrong direction. The 4.76% answer is 0.05/1.05, a wrong base.
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