Hi all: Can anyone explain how to get the circled part for the future service liability for Question 11.24? It is in Chapter 11, page 36-37. I have attached the solution to the question. Thank you very much!
The first line considers the FSL as follows: - the first term relates to the value of the 0.5 years of future service completed before retirement if the member retires in the year (x,x+1), ie on average at age x+0.5, - the second term relates to the value of the 1.5 years of future service completed before retirement if the member retires in the year (x+1,x+2), ie on average at age x+1.5, and so on, with this pattern continuing (with the half-years of service), until the maximum of 40 years service is reached. Given that the life is currently aged x, and has m past years service, the maximum of 40 years of service will be reached at age x+40-m. So the final set of terms relate to the value of the 40-m future years of service completed before retirement at any age after x+40-m. The number of years of service does not change for these terms, as 40-m is the maximum number of future years of service allowed. The first line simplifies to the second line algebraically as shown in the attached.
