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#1




SOA #85
To get EPV of benefit at time 2, SOA official solution integrates from 0 to infinity, see attachment, the integration result is 1000* e^0.08.
I am trying to integrate from 2 to infinity, with the formula below. I got 1000* e^.04 as the result. ∫ (benefit) * (tPx) * (discount factor) * mu ∫ (1000e^.04t) * (e^02t) * (e^.04t) * (.02) dt Apparently something is not correct in my formula, could you tell me how to fix it and your reasoning? Thanks! 
#2




In your formula, when you integrate from 2 to infinity, you are doing it from the perspective of time t = 0. You need to do it from the perspective of time t = 2 because when calculating benefit reserves, we are conditioning on the fact that the life has survived to that time, in this case, t = 2.
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#3




I'm very lost on this problem... Why doesn't this work?
∫ (1000e^.04(t+2)) * (e^02(t+2)) * (e^.04(t+2) * (.02) dt from 2 to infinity. Also in the official solution, what is going on with them breaking up mu(65+t) into mu(65)*t? Thanks. 
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