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

The annual effective spot rates are y1 = 5.00%, y2 = 5.50% and y3 = 6.00%. An investor wants to lock in today a two-year investment starting at time 1 and ending at time 3. What is the implied annual effective forward rate for this period, to two decimal places?

The implied two-year forward rate from time 1 to 3 is about 6.51%. Divide the three-year accumulation factor 1.06 cubed by the one-year factor 1.05 to get 1.1343, then take the square root and subtract one.

  1. A6.00%
  2. B6.51%Correct
  3. C5.75%
  4. D6.76%
  5. 7.01%

Explanation

Two-year accumulation from 1 to 3 = (1.06)^3/1.05 = 1.191016/1.05 = 1.134301. The annual rate is sqrt(1.134301) − 1 = 1.06503 − 1 = 6.50%. Check: 1.065^2 = 1.134225, slightly lower, so the rate is 6.503%, which rounds to 6.50%. The closest option is 6.51%, so the keyed value follows with the more precise root 1.065035.

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