FRM Part I · FRM Exam Part I · Properties of Interest Rates
An investment pays 5% per annum with annual compounding. What is the equivalent continuously compounded rate, to the nearest 0.01%?
The equivalent continuously compounded rate is 4.88%. It is found by taking the natural log of 1.05, which equals 0.04879. The continuous rate is below the annual rate because continuous compounding produces more growth per unit of nominal rate.
- A4.88%Correct
- B5.00%
- C5.13%
- D4.75%
Explanation
Rc = ln(1.05) = 0.04879, or 4.88%. Continuous compounding yields more growth for a given nominal rate, so the continuous rate must be lower than 5%. 5.13% is wrong because it converts in the wrong direction (e^0.05 - 1).
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