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

A pension scheme has liabilities of Rs 1,000 due at the end of year 2 and Rs 1,000 due at the end of year 4. At an effective annual interest rate of 10%, what is the discounted mean term of the liabilities, to two decimal places?

The discounted mean term is 2.90 years. Weighting each payment time by its present value gives (2×0.826446 + 4×0.683013) divided by 1.509459, which is 2.90. It is below the simple average of 3 because the earlier payment has a larger present value.

  1. A3.00 years
  2. B2.90 yearsCorrect
  3. C3.10 years
  4. D2.50 years
  5. 2.73 years

Explanation

v²=0.826446 and v⁴=0.683013, so the PV is 1.509459 per unit. The numerator is 2(0.826446)+4(0.683013)=4.384947. DMT = 4.384947/1.509459 = 2.90. The simple average of 3.00 ignores discounting, and 3.10 results from swapping the weights.

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