IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
A life table gives l_60 = 90,000, l_61 = 88,200 and l_62 = 86,310. What is the value of 1|q_60, the probability that a life aged 60 survives one year and then dies within the following year?
The deferred probability is (l_61 - l_62)/l_60, which is 1,890 divided by 90,000, giving 0.0210. The denominator must be the number alive at age 60, because the probability is conditional on being alive at 60 only.
- A0.0200
- B0.0210Correct
- C0.0214
- D0.0230
- 0.0420
Explanation
1|q_60 = (l_61 - l_62)/l_60 = (88,200 - 86,310)/90,000 = 1,890/90,000 = 0.0210. Option A is q_61 = 1,890/88,200 = 0.02143 only if rounded differently; using l_61 as the base is the wrong denominator. Option E is 2q_60 = 3,690/90,000 = 0.041, not the deferred probability.
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