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

Annual effective spot rates are y1 = 6.00%, y2 = 6.50% and y3 = 7.00%. Find the implied forward rate f(2,3), the one-year rate from time 2 to time 3, to two decimal places.

The implied forward rate from time 2 to 3 is 8.01%. It is found by dividing 1.07 cubed (1.225043) by 1.065 squared (1.134225) and subtracting one. Simply quoting the 3-year spot rate of 7% ignores the earlier years' rates.

  1. A7.00%
  2. B7.51%
  3. C8.01%Correct
  4. D7.00% plus 0.50%
  5. 6.75%

Explanation

(1.07)^3 = 1.225043. (1.065)^2 = 1.134225. Ratio = 1.08008, so f = 8.01%. Using y3 directly (7.00%) ignores the forward structure.

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