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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting and valuing cashflows contingent on multiple decrement events

A policy pays Rs 200,000 immediately on death within 10 years. The only other decrement is withdrawal, which pays nothing. Forces are constant: death 0.02, withdrawal 0.05, and force of interest 0.04. What is the expected present value at issue?

The expected present value is Rs 24,259.23. It equals the benefit times the death force divided by the sum of the death, withdrawal and interest forces, 0.11, multiplied by 1 - e^{-1.1} = 0.6671. Withdrawal both reduces survival and ends the policy.

  1. ARs 24,259.23Correct
  2. BRs 30,079.22
  3. CRs 84,907.31
  4. DRs 28,766.58
  5. Rs 38,121.66

Explanation

The value is 200000 x 0.02 x (1 - e^{-10(0.02+0.05+0.04)})/(0.11) = 200000 x 0.02 x 0.667129/0.11 = 24,259.23. Option 30,079.22 omits the withdrawal force from the exponent, so it overstates the probability of staying in force. Option 28,766.58 omits the discounting.

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