FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans
A life table gives survivors l60 = 80,000, l61 = 79,200 and l62 = 78,000. What is the probability that a person aged 60 survives to 61 and then dies before reaching 62?
The probability is 1.50 percent. Of 80,000 people alive at 60, 1,200 die between 61 and 62, since 79,200 minus 78,000 is 1,200, and 1,200 divided by 80,000 is 1.5 percent. Dividing by l61 would give a conditional probability instead.
- A1.50%Correct
- B1.00%
- C1.52%
- D98.50%
Explanation
The probability of dying in the second year from age 60 equals (l61 - l62)/l60 = 1,200/80,000 = 1.50%. Using l61 as the base gives 1.515%, which is the conditional probability given survival to 61, not the one asked. 98.50% is its complement, and 1.00% is the first-year death rate.
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