FRM Part I · FRM Exam Part I · Properties of Interest Rates
A 2-year zero-coupon bond with a face value of 100 trades at a price of 90.00. What is the 2-year zero rate expressed with continuous compounding?
The continuously compounded 2-year zero rate is 5.27%. Take the natural log of 100/90, which is 0.1054, and divide by the 2-year maturity. The 5.41% figure is the annual-compounding equivalent, and 10.54% ignores the time divisor.
- A5.27%Correct
- B5.41%
- C5.56%
- D10.54%
Explanation
With continuous compounding, 90 = 100e^(-2R), so R = ln(100/90)/2 = 0.105361/2 = 5.27%. The 5.41% figure is the annually compounded rate, (100/90)^(1/2) - 1. The 10.54% figure is a distractor that forgets to divide the log return by 2 years.
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