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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 200,000 at the end of the year if the life dies within the year. The probability of death is q = 0.01 and the annual effective interest rate is 5%. What is the variance of the present value random variable of the benefit?

The variance is E[Z²] minus (E[Z])². E[Z²] is 362,811,791.38 and the squared mean is 3,628,117.91. The result is Rs 359,183,673.47. Equivalently, it is S²v²pq, which has the same value.

  1. ARs 362,811,791.38
  2. BRs 377,142,857.14
  3. CRs 396,000,000.00
  4. DRs 377,324,263.04
  5. Rs 359,183,673.47Correct

Explanation

Z = 200,000/1.05 with probability 0.01, otherwise 0. E[Z] = 1,904.76 and E[Z²] = 4×10^10 × 0.01 / 1.1025 = 362,811,791.38. Variance = 362,811,791.38 − 3,628,117.91 = 359,183,673.47. The option Rs 362,811,791.38 omits the subtraction of the squared mean.

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