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

A pension fund has a single liability of Rs 10,000 due in 10 years. The effective annual interest rate is 5%. It will immunise using two zero-coupon bonds maturing at 4 years and 14 years, satisfying the present value and discounted mean term conditions. What maturity payment (to two decimal places) must the 14-year bond provide?

The 14-year bond must pay Rs 7,293.04. The liability has a present value of Rs 6,139.13; matching the mean term of 10 years needs 60 percent of this in the 14-year bond, which is Rs 3,683.48, accumulated for 14 years at 5 percent.

  1. ARs 3,683.48
  2. BRs 4,862.03
  3. CRs 6,000.00
  4. DRs 7,293.04Correct
  5. Rs 7,366.96

Explanation

PV of liability = 10,000 / 1.05^10 = 6,139.13. Weight w in the 4-year bond: 4w + 14(1-w) = 10 gives w = 0.4, so 0.6 goes in the 14-year bond: 0.6 × 6,139.13 = 3,683.48. Accumulating at 5% for 14 years: 3,683.48 × 1.05^14 = 7,293.04. Option B uses the weights the wrong way round, and option A stops at the present value.

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