IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events
Two independent lives (x) and (y) have constant forces of mortality 0.04 and 0.06 respectively. The force of interest is 5% per year. What is the EPV of a continuous annuity of Rs 1,000 per year payable while both lives are alive?
The EPV is Rs 6,666.67. The annuity stops at the first death, so the joint-life force 0.04 + 0.06 = 0.10 is added to the force of interest 0.05, giving a factor 1/0.15 = 6.6667 and so Rs 6,666.67 for Rs 1,000 a year.
- ARs 11,111.11
- BRs 13,535.35
- CRs 9,090.91
- DRs 20,000.00
- Rs 6,666.67Correct
Explanation
The joint-life force is 0.04 + 0.06 = 0.10, so the annuity factor is 1/(0.10 + 0.05) = 6.6667. Multiplying by 1,000 gives Rs 6,666.67. Rs 11,111.11 uses only life (x), 1/0.09. Rs 13,535.35 is the last-survivor annuity.
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