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

A liability consists of payments of Rs 1,000 at the end of year 1 and Rs 1,000 at the end of year 2. Using an effective annual interest rate of 10%, what is the discounted mean term of the payments?

The discounted mean term is 1.48 years. Weight each payment time by its present value at 10%: (909.09×1 + 826.45×2) divided by the total present value of 1,735.54 gives about 1.476, which is less than the undiscounted average of 1.5.

  1. A1.50 years
  2. B1.34 years
  3. C1.48 yearsCorrect
  4. D1.65 years
  5. 1.10 years

Explanation

PV weights: 1000v = 909.09 and 1000v² = 826.45, total 1,735.54. DMT = (1×909.09 + 2×826.45)/1735.54 = 2561.98/1735.54 = 1.4762, i.e. 1.48. The 1.50 option ignores discounting (simple average), and 1.34 is the modified duration 1.4762/1.10.

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