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

At a given rate of interest, a_x = 12.00, a_y = 14.00 and a_xy = 10.50 (all annuities-due, annual). A reversionary annuity of Rs 10,000 per annum is payable annually in advance to (y) after the death of (x), for the remaining lifetime of (y). Find its present value.

The present value is Rs 35,000. It equals 10,000 times (a_y minus a_xy), that is 10,000 times (14.00 minus 10.50), since the annuity is paid to (y) only when (x) has died.

  1. ARs 35,000Correct
  2. BRs 15,000
  3. CRs 25,000
  4. DRs 20,000
  5. Rs 45,000

Explanation

The present value is 10,000 x (a_y - a_xy) = 10,000 x (14.00 - 10.50) = 10,000 x 3.50 = Rs 35,000. Using a_x instead of a_y gives 10,000 x 1.50 = Rs 15,000, which is wrong because the annuity is paid to (y), not (x).

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