SOA Exam FAM Sample Question 6.13

Study guide: Exam FAM

For a fully discrete whole life insurance of 10,000 on (45), you are given:

(i) Commissions are 80% of the first year premium and 10% of subsequent premiums. There are no other expenses

(ii) Mortality follows the Standard Ultimate Life Table

(iii) $i = 0.05$

(iv) $_{0}L$ denotes the loss at issue random variable

(v) If $T_{45} = 10.5$ , then ${}_{0}L = 4953$

Calculate $\mathrm{E}\left[{}_{0}L\right]$ .

[A modified version of Question 19 on the Fall 2013 exam]

Concepts tested