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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives

A policy pays ₹1,00,000 at the end of the year of the second death of two independent lives (x) and (y). Take the one-year probabilities of death as q_x = 0.02 and q_y = 0.04, and v = 0.95 for one year. The policy term is one year. What is the expected present value of the benefit, i.e. the cost of an assurance on the last survivor status limited to one year?

The expected present value is ₹76. The benefit is paid only if both lives die within the year, which has probability 0.02×0.04 = 0.0008 under independence. Multiplying by ₹1,00,000 and the discount factor 0.95 gives ₹76.

  1. A₹76Correct
  2. B₹95
  3. C₹3,800
  4. D₹7
  5. ₹76,000

Explanation

Both lives must die within the year: probability = 0.02×0.04 = 0.0008. Present value = 100000×0.0008×0.95 = ₹76. The ₹95 would use v=1.19 incorrectly or other error; ₹3,800 uses only one life's... 0.04×0.95×100000 = 3,800, ignoring the other life.

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