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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation

An Indian insurer must pay Rs 1,00,000 in exactly 6 years. It will hold only two zero-coupon bonds, maturing in 3 years and 8 years, chosen so that the present value of assets equals that of the liability and the discounted mean terms are equal, at an effective annual interest rate of 5%. What present value should be invested in the 8-year bond?

The 8-year bond should have a present value of Rs 44,772.92. The liability's present value is Rs 74,621.54, and matching the mean term of 6 years between terms of 3 and 8 requires a weight of 0.6 on the 8-year bond.

  1. ARs 29,848.62
  2. BRs 44,772.92Correct
  3. CRs 27,983.08
  4. DRs 66,150.00
  5. Rs 60,000.00

Explanation

PV of liability = 100000 × 1.05^-6 = 74,621.54. With weights w3 and w8 by present value: w3+w8=1 and 3w3+8w8=6, so w8=3/5=0.6. PV in the 8-year bond = 0.6 × 74,621.54 = 44,772.92. Using 0.4 gives 29,848.62 (weights swapped), and 0.375 (3/8) gives 27,983.08.

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