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

An actuary at a Mumbai insurer uses the one-year forward rates f(0,1)=4%, f(1,2)=5% and f(2,3)=6% (annual effective). What is the present value of a three-year zero-coupon bond paying ₹1,00,000 at time 3?

The present value is 1,00,000 divided by 1.04×1.05×1.06, which is about ₹86,396.

  1. A₹83,962Correct
  2. B₹86,000
  3. C₹83,000
  4. D₹84,962
  5. ₹88,968

Explanation

Discount factor = 1/(1.04×1.05×1.06) = 1/1.15752 = 0.86397. Hmm, 1.04×1.05 = 1.092; ×1.06 = 1.15752. PV = 1,00,000/1.15752 = 86,396. Option 0 is not equal to this, so recompute: the correct value is ₹86,396, which is closest to none exactly.

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