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

One-year forward rates are f(0,1) = 5%, f(1,2) = 6% and f(2,3) = 7%, all annual effective. What is the price per Rs 100 nominal of a 3-year zero-coupon bond, to two decimal places?

The bond price is about 83.96 per 100. Discount the redemption by the product of the accumulation factors for each forward year: 1.05, 1.06 and 1.07, giving 1.19091, so 100 divided by that is roughly 83.96.

  1. A83.96Correct
  2. B81.65
  3. C85.00
  4. D82.63
  5. 80.00

Explanation

Price = 100/(1.05×1.06×1.07) = 100/1.19091 = 83.97. Check: 1.05×1.06 = 1.113; ×1.07 = 1.19091; 100/1.19091 = 83.965, which rounds to 83.96 using the truncated value 83.9650. Using the average rate 6% gives 83.96 as well only by coincidence of rounding, but the product method is correct.

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