FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans
A life table shows 95,000 survivors at age 50 and 90,250 survivors at age 60 out of an original cohort. An insurer sells a 10-year pure endowment of 200,000 to a 50-year-old, paying only if the person is alive at 60. Ignoring discounting, what is the expected payout per policy?
The expected undiscounted payout is 190,000. The 10-year survival probability is 90,250 divided by 95,000, which equals 0.95, and multiplying by the 200,000 benefit gives 190,000. Using the original cohort as the base would wrongly understate the probability.
- A190,000Correct
- B10,000
- C180,500
- D95,000
Explanation
The survival probability from 50 to 60 is 90,250/95,000 = 0.95. The expected payout is 0.95 x 200,000 = 190,000. Option C uses 90,250/100,000 = 0.9025, a wrong base. Option B is the expected shortfall, 5% of 200,000.
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