FRM Part I · FRM Exam Part I · Properties of Interest Rates
An investment pays an annually compounded rate of 8% per annum. What is the equivalent continuously compounded rate, to the nearest basis point?
The equivalent continuously compounded rate is about 7.70%. It is found as the natural log of 1.08, which equals 0.0770. Because continuous compounding grows money faster per unit of nominal rate, the continuous rate must be lower than the 8% annual rate.
- A7.70%Correct
- B8.00%
- C8.33%
- D7.41%
Explanation
Rc = ln(1.08) = 0.076961, or about 7.70%. Continuous compounding yields more growth per nominal rate, so the equivalent continuous rate must be below 8%. The 8.33% option wrongly inverts the conversion (ln of 1.0833-type error, i.e., using e^0.08 - 1).
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