IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Means and variances of assurance and annuity payments
A 10-year pure endowment pays Rs 100,000 to a life now aged x if the life survives 10 years. The 10-year survival probability is 0.90 and the annual effective interest rate is 6%. What is the expected present value of the benefit?
The expected present value is the sum assured times the survival probability times the 10-year discount factor. That is 100,000 × 0.90 × 0.558395, which gives Rs 50,255.53. Omitting survival or discounting gives the incorrect alternatives.
- ARs 55,839.48
- BRs 50,255.53Correct
- CRs 56,250.00
- DRs 90,000.00
- Rs 5,583.95
Explanation
E[Z] = 100,000 × 0.90 × 1.06^-10. Since 1.06^10 = 1.790848, v^10 = 0.558395. So E[Z] = 90,000 × 0.558395 = Rs 50,255.53. Rs 55,839.48 ignores the survival probability, and Rs 90,000 ignores discounting.
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