IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting and valuing cashflows contingent on multiple decrement events
In a double decrement table for a pension scheme, l_60 = 1000 members are in service at age 60. During the following year 12 members leave by death and 38 leave by withdrawal. What is the probability that a member aged 60 leaves service by withdrawal within the year (the dependent rate for withdrawal)?
The probability is 0.0380. The dependent rate of decrement by withdrawal equals withdrawals during the year divided by the number in service at the start of the year, which is 38 divided by 1000.
- A0.0120
- B0.0380Correct
- C0.0385
- D0.0400
- 0.0500
Explanation
The dependent (multiple decrement) rate for cause j is the number leaving by j divided by the number in force at the start of the year. Here that is 38/1000 = 0.0380. Dividing by 988 (0.0385) wrongly removes those who died from the base, but they were exposed at the start of the year.
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