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

Rs 1,000 is paid at the start of each year for up to three years while an employee remains in service. The probability of being in service is 1 at the start of year 1, 0.90 at the start of year 2 and 0.72 at the start of year 3. With i = 10%, what is the expected present value?

The expected present value is Rs 2,413.22. Each payment is weighted by the probability of being in service at its payment date and discounted for the elapsed years. The terms are 1,000, 818.18 and 595.04.

  1. ARs 2,413.22Correct
  2. BRs 2,735.54
  3. CRs 2,479.34
  4. DRs 1,413.22
  5. Rs 2,359.13

Explanation

The value is 1000[1 + 0.9/1.1 + 0.72/1.21] = 1000(1 + 0.818182 + 0.595041) = 2,413.22. Option 2,735.54 ignores the decrements. Option 1,413.22 leaves out the first payment.

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