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

One-year and two-year annual effective spot rates are 4.00% and 5.00%. What is the one-year forward rate from time 1 to time 2, to two decimal places?

The forward rate is 6.01%. It is the ratio of the two-year accumulation factor, 1.1025, to the one-year factor, 1.04, which gives 1.0601. Simply averaging the spot rates would understate it.

  1. A6.01%Correct
  2. B5.00%
  3. C4.50%
  4. D6.50%
  5. 5.50%

Explanation

(1+f) = 1.05^2/1.04 = 1.1025/1.04 = 1.06010, so f = 6.01%. The 4.50% option averages the spot rates and ignores compounding.

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