IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts
A 2-year term assurance on a life aged x pays Rs 1,000 at the end of the year of death. Mortality is q_x = 0.1 and q_{x+1} = 0.2, and the effective annual interest rate is 10%. What is the expected present value of the benefit?
The expected present value is Rs 239.67. Death occurs in year one with probability 0.1 and in year two with probability 0.9 × 0.2 = 0.18. Discounting at 10% gives 1000 × (0.1/1.1 + 0.18/1.21).
- ARs 205.58
- BRs 239.67Correct
- CRs 256.20
- DRs 263.64
- Rs 280.00
Explanation
P(death in year 1) = 0.1. P(death in year 2) = 0.9 × 0.2 = 0.18. EPV = 1000 × (0.1/1.1 + 0.18/1.21) = 1000 × (0.090909 + 0.148760) = 239.67. Using 0.2 for year 2 without the survival factor gives 256.20, which is wrong.
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