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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Term structure of interest rates

Annual effective spot rates are 4.00% for a 1-year zero-coupon bond and 5.00% for a 2-year zero-coupon bond. What is the one-year forward rate from time 1 to time 2, to two decimal places?

The forward rate is 6.01%. It equals the ratio of the 2-year accumulation factor 1.05 squared to the 1-year factor 1.04, minus one. Averaging the spot rates to get 4.50% ignores compounding and gives the wrong answer.

  1. A4.50%
  2. B5.01%
  3. C6.01%Correct
  4. D5.00%
  5. 6.25%

Explanation

(1+f) = (1.05)^2/1.04 = 1.1025/1.04 = 1.06010. So f = 6.01%. The simple average 4.50% ignores compounding, and 5.01% is wrongly obtained by adding rates.

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