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

Independent lives (x) and (y) have constant forces of mortality 0.02 and 0.03, and the force of interest is 0.05. An annuity of Rs 12,000 per year is payable continuously to (y) only after the death of (x), for as long as (y) survives. What is its EPV?

The EPV is Rs 30,000. The reversionary annuity factor is the single-life annuity to (y), 1/0.08 = 12.5, minus the joint-life annuity, 1/0.10 = 10, giving 2.5. Multiplying by Rs 12,000 gives Rs 30,000.

  1. ARs 51,428.57
  2. BRs 150,000.00
  3. CRs 120,000.00
  4. DRs 201,428.57
  5. Rs 30,000.00Correct

Explanation

A reversionary annuity is a_y - a_xy. Here a_y = 1/0.08 = 12.5 and a_xy = 1/0.10 = 10, so the factor is 2.5. Then 12,000 x 2.5 = Rs 30,000. Rs 51,428.57 reverses the roles, using a_x - a_xy. Rs 150,000 is the whole annuity to (y), a_y.

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