FRM Part I · FRM Exam Part I · Properties of Interest Rates
An investment earns a continuously compounded rate of 6% per year. What is the equivalent annual rate with semiannual compounding, to the nearest 0.01%?
The equivalent semiannually compounded rate is 6.09%. Exponentiating 6% gives 1.061837 for one year; taking the square root gives 1.030455 per half-year, so the nominal rate is 2 times 3.0455%, or 6.09%. The 6.18% figure is the annual effective rate instead.
- A6.09%Correct
- B6.00%
- C6.18%
- D5.91%
Explanation
Set (1 + R/2)^2 = e^0.06 = 1.061837. Then 1 + R/2 = sqrt(1.061837) = 1.030455, so R/2 = 3.0455% and R = 6.09%. The 6.18% option is the effective annual rate (e^0.06 - 1 = 6.18%), which is annual, not semiannual compounding.
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