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

For a whole life assurance paying a sum assured of Rs 50,000 immediately on death, the actuarial present value at the given force of interest is Ā = 0.30. The same function evaluated at double the force of interest is ²Ā = 0.12. What is the variance of the present value of the benefit?

The variance equals the squared sum assured times the second moment minus the squared first moment. That is 2.5 billion × (0.12 − 0.09), which gives Rs 75,000,000. The second moment uses double the force of interest.

  1. ARs 450,000,000
  2. BRs 225,000,000
  3. CRs 75,000,000Correct
  4. DRs 300,000,000
  5. Rs 1,500

Explanation

Variance = S² (²Ā − Ā²) = 2.5×10^9 × (0.12 − 0.09) = 2.5×10^9 × 0.03 = Rs 75,000,000. Using 2.5×10^9 × 0.12 forgets to subtract the squared mean. Using 2.5×10^9 × 0.09 uses only the squared mean.

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