I am studying the caculation of future service benefit that pays an annuity amount based on certain salary scale.
ActEx note sums up r,v,z into a commutation function C, where
r = number of people retiring at age x
v = discount factor
z = average salary scale in accordance with the definition of final average salary
M is the sum of C for every future age from t=0 to t=normal pension age (NPA).
This part is understandable to me.
However, I do not understand why M is also summed to a function R from t=0 to t= NPA-x-1. The note says that M is the future service benefit arising from the year of age (x+t, x+t+1). I have this feeling that summing M's would mean double counting since it seems to me that M already sums over all future ages, there's no need to sum M again.
Could someone please explain to me why we sum M's to get the future service benefit? Thank you in advance.