FRM Part I · FRM Exam Part I · Interest Rates
A zero-coupon investment pays 8% per annum with semiannual compounding. What is the equivalent continuously compounded rate, to two decimals? (ln 1.04 = 0.039221)
The continuously compounded equivalent is 7.84%. Using Rc = 2 × ln(1.04) gives about 0.0784. A continuous rate is lower than the semiannual nominal rate because continuous compounding grows faster per unit of nominal rate.
- A7.84%Correct
- B7.92%
- C8.00%
- D8.16%
Explanation
Rc = m ln(1 + Rm/m) = 2 × ln(1.04) = 2 × 0.039221 = 0.078442, i.e. 7.84%. The 8.16% option wrongly reverses the conversion by using m(e^(R/m) - 1) style logic. Continuous rate must be below the periodically compounded nominal rate.
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