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

A member earns an annual salary of Rs 5,00,000. Over the next year the probabilities of decrement while in service are: death 0.02 and withdrawal 0.10. On death the benefit is 5 times salary, and on withdrawal it is 2 times salary, each paid at the end of the year of exit. Using an interest rate of 8% per annum, what is the expected present value of these benefits?

The expected present value is Rs 1,38,888.89. Expected benefits at year end are 0.10 x 2 x 5,00,000 plus 0.02 x 5 x 5,00,000, totalling Rs 1,50,000. Discounting this by one year at 8% gives the answer.

  1. ARs 1,50,000.00
  2. BRs 1,38,888.89Correct
  3. CRs 2,50,000.00
  4. DRs 1,44,337.57
  5. Rs 1,62,000.00

Explanation

Expected benefit = 0.10 x 2 x 5,00,000 + 0.02 x 5 x 5,00,000 = 1,00,000 + 50,000 = 1,50,000 at year end. Discounting one year at 8% gives 1,50,000/1.08 = 1,38,888.89. Rs 2,50,000 results from swapping the multiples of salary between the two decrements.

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