FRM Part I · FRM Exam Part I · Properties of Interest Rates
Continuously compounded zero rates are 4.0% for 1 year and 4.5% for 2 years. What is the continuously compounded forward rate for the period from year 1 to year 2?
The forward rate is 5.0%. With continuous compounding, the forward equals the 2-year zero rate times 2 minus the 1-year zero rate times 1, divided by one year: 9.0% minus 4.0% equals 5.0%. A simple average of the zero rates would be incorrect.
- A4.25%
- B5.00%Correct
- C4.50%
- D5.50%
Explanation
Forward rate = (R2*T2 - R1*T1)/(T2-T1) = (4.5%*2 - 4.0%*1)/1 = 9.0% - 4.0% = 5.0%. The 4.25% option is a simple average of the two zero rates, which ignores the different time weights.
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