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FRM Part I · FRM Exam Part I · Interest Rates

Continuously compounded zero rates are 3.0% for 1 year and 3.5% for 2 years. What is the implied continuously compounded forward rate for the period from year 1 to year 2?

The implied forward rate is 4.00%. With continuous compounding, the forward rate equals (3.5% x 2 - 3.0% x 1) divided by one year. Investing at 3% for a year and 4% for the next year gives the same total return as 3.5% for two years.

  1. A3.25%
  2. B3.50%
  3. C4.00%Correct
  4. D4.50%

Explanation

Forward rate = (3.5% x 2 - 3.0% x 1) / (2 - 1) = 4.0%. Check: e^(0.03) x e^(0.04) = e^(0.07) = e^(0.035 x 2). The 3.25% option is a simple average of the two zero rates, which ignores the different time weights.

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