FRM Part I · FRM Exam Part I · Properties of Interest Rates
A loan is quoted at 12% per annum with monthly compounding. A treasurer wants the equivalent continuously compounded rate. Which is closest?
The equivalent continuously compounded rate is about 11.94%. Use the conversion Rc = m × ln(1 + Rm/m) with m = 12 and Rm = 12%, giving 12 times ln(1.01), which is 0.1194. It is slightly below the quoted monthly-compounded nominal rate.
- A11.94%Correct
- B12.00%
- C12.68%
- D11.88%
Explanation
Rc = 12 × ln(1 + 0.12/12) = 12 × ln(1.01) = 12 × 0.00995033 = 0.119404, or 11.94%. The 12.68% option is the effective annual rate, a different measure. The 12.00% option ignores compounding frequency. 11.88% results from using ln(1.0099) type rounding error and is not the result.
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