Chapter 9, Problem 41RE

Employee training. In order to become a fellow of the Society of Actuaries, a person must pass a series of ten examinations. Passage of the first two preliminary exams is a prerequisite for employment as a trainee in the actuarial department of a large insurance company. Each year, $15\%$ of the trainees complete the next three exams and become associates of the Society of Actuaries, $5\%$ leave the company, never to return, and the remainder continue as trainees. Furthermore, each year, $17\%$ of the associates complete the remaining five exams and become fellows of the Society of Actuaries, $3\%$ leave the company, never to return, and the remainder continue as associates.

(A) In the long run, what percentage of the trainees will become fellows?

(B) In the long run, what percentage of the associates will leave the company?

(C) What is the average number of years that a trainee remains in this program before either becoming a fellow or being discharged?