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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Means and variances of assurance and annuity payments

A one-year term assurance pays Rs 100,000 at the end of the year if the life dies within the year. The mortality rate is q = 0.02 and v = 0.95. What is the variance of the present value of the benefit?

The variance is Rs 176,890,000. The second moment is 100,000² × 0.95² × 0.02 = 180,500,000. The squared mean is 1,900² = 3,610,000. Subtracting the squared mean from the second moment gives the variance of the discounted benefit.

  1. ARs 180,500,000
  2. BRs 176,890,000Correct
  3. CRs 196,000,000
  4. DRs 186,200,000
  5. Rs 13,300

Explanation

E[Z] = 100,000 × 0.95 × 0.02 = 1,900. E[Z²] = 10^10 × 0.9025 × 0.02 = 180,500,000. Var = 180,500,000 − 1,900² = 180,500,000 − 3,610,000 = 176,890,000. Rs 180,500,000 is wrong because it omits subtracting the squared mean.

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