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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events

For a life policy with sum assured ₹80,000, level premiums of ₹1,500 per annum paid continuously, δ = 0.04 and μ = 0.02 at the current age, the policy value at time 20 is ₹30,000. Using Thiele's equation and a single Euler step of size h = 0.1 working backwards, V(19.9) ≈ V(20) − h × dV/dt. What is the approximate policy value at time 19.9 (₹)?

The approximate policy value at time 19.9 is ₹29,830. Thiele gives dV/dt = 1,700, and stepping back by 0.1 subtracts 170 from 30,000. Dropping the mortality term or stepping the wrong way gives the other values.

  1. A29,730
  2. B29,830Correct
  3. C29,915
  4. D30,170
  5. 30,270

Explanation

dV/dt = 0.04×30,000 + 1,500 − 0.02×(80,000 − 30,000) = 1,200 + 1,500 − 1,000 = 1,700. Then V(19.9) ≈ 30,000 − 0.1×1,700 = 29,830. Omitting the death term gives dV/dt = 2,700 and 29,730. Stepping forward instead of backward gives 30,170.

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