“An age retirement benefit of n/80ths of average salary where n is the total service at date of retirement” “Let the member aged x at the valuation date have exactly m years past service” This implies that the future years of service is k = n-m. Past Service Liability This has a factor of (m/80) x salary. Future Service Liability I would expect a factor of [(k/80) x salary] for working an additional k years. What has happened to this in the notes (pg 25) where the sum has only a factor of [(1/80) x salary]? The table (pg 24) with the pension pa column also ignores the k year factor eg. for retirement at age x+2.5, I would expect a factor of (2.5/80). Example If we look at a specific outcome; a life aged 55 with 20 years of past service who retires at 60. Valuation at age 55 - the past service benefit would be proportional to [(20/80) x salary]. Should the future service benefit not be proportional to (5/80) x salary? To me, this appears a reasonable expectation because if we move 5 years into the future, then the new valuation is at age 60 with 25 years of past service which is proportional to [(25/80) x salary]. Please help!
what they have on page 25 is the Commutation function Mx+t, it represents the sum over all possible future years of retirement for the year of service (x+t, x+t+1) ONLY. The 1/80 represents portion of benefit from a specific one year , say (x+t, x+t+1). m is fixed, n varies and so does k. This is because unlike your example we do not know when the member will retire. A little pracitise will reveal the tricks behind this chapter, no need to worry much.
I finally figured it out. I put some numbers into the table at the bottom of page 24. Example: Let x=47, NPA=50 (Factor of [S/(80*S_46)] has been left out of the table below) -------------------------------- Benefits accrued for future yr of service relating to: Ret Yr ----- Avg Ret Age ---- 47 to 48 ------ 48 to 49 ------- 49 to 50 47 to 48 ------ 47.5 --------- 0.5*Z_47.5 ---- 0 -------------- 0 48 to 49 ------ 48.5 --------- Z_48.5 --------- 0.5*Z_48.5 --- 0 49 to 50 ------ 49.5 --------- Z_49.5 --------- Z_49.5 -------- 0.5*z_49.5 50 ------------ 50.0 ---------- Z_50.0 --------- Z_50.0 -------- z_50 Summing across gives the factor I was looking for i.e k/80: 0.5*z_47.5 1.5*z_48.5 2.5*z_49.5 3.0*z_50.0 where as the notes have summed down each column to get the EPV on page 25.
