FRM Part I · FRM Exam Part I · Interest Rates
An analyst has a 2-year zero rate of 4.0% and a 3-year zero rate of 5.0%, both continuously compounded. What is the implied forward rate for the year from year 2 to year 3, continuously compounded?
The implied forward rate is 7.0%. With continuous compounding, the forward equals the 3-year zero rate times 3 minus the 2-year rate times 2, divided by one year: 15% minus 8%. This is above both zero rates because the curve slopes upward.
- A4.5%
- B5.0%
- C6.0%
- D7.0%Correct
Explanation
Forward = (5.0%×3 - 4.0%×2)/(3-2) = 15% - 8% = 7.0%. The 6.0% option wrongly uses 5%+1%, and 4.5% is a simple average of the two zero rates. Check: 2×4% + 7% = 15% = 3×5%.
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