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

For independent lives (x) and (y), a_x = 12.00, a_y = 10.00 and a_xy = 8.00 (annual, in advance). A pension of Rs 60,000 a year is paid annually in advance while at least one of the two lives survives. What is the expected present value?

The expected present value is Rs 8,40,000. The last-survivor annuity factor is 12 + 10 − 8 = 14, and multiplying by the annual pension of Rs 60,000 gives 8,40,000.

  1. ARs 8,40,000
  2. BRs 9,60,000Correct
  3. CRs 7,20,000
  4. DRs 12,00,000
  5. Rs 10,80,000

Explanation

Last-survivor annuity = 12 + 10 − 8 = 14. EPV = 60,000 × 14 = Rs 8,40,000. Check: 14 × 60,000 = 840,000. Option 'Rs 9,60,000' would correspond to 16 (adding the joint annuity instead of subtracting it).

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