FRM Part I · FRM Exam Part I · Interest Rates
An investment earns a continuously compounded rate of 5% per annum. What is the equivalent annually compounded rate, to two decimals? (e^0.05 = 1.051271)
The equivalent annually compounded rate is 5.13%. Converting a continuous rate uses e raised to the rate minus one, and e^0.05 is about 1.0513, so the annual rate must be above the 5% continuous rate.
- A4.88%
- B5.00%
- C5.13%Correct
- D5.25%
Explanation
Annual rate = e^0.05 - 1 = 0.051271, i.e. 5.13%. The 4.88% figure is wrongly computed as 1 - e^-0.05, which is a discount-style error. Continuous compounding always gives a lower rate than a higher-frequency-equivalent annual rate, so annual must exceed 5%.
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