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LongTerm Actuarial Math Old Exam MLC Forum 

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#1




Term Insurance Question
https://imgur.com/a/wtvpRHh
So that's a link to a question I'm stuck on. I tried using first principles instead of using the shortcut, since the shortcut isn't that intuitive for me. I can understand and calculate the pure endowment part, but for the term insurance this is what I did: tP45=1(t/58) and to find the force of mortality between 45 and 65, I took 20P45=.65517=e^(20ux). Then solved for ux as .02114. Then I integrated between 0 and 20 for (1(t/58))*.02114*(e^.06t), or tP45*ux*v^t. I ended up with an answer of .28037 for the 20 term insurance, while the solution has .200806. Can someone provide clarity on what I did wrong or why my approach may not work? Thank you in advance!
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Former Disney World Cast Member, currently no idea what I'm doing "I think you should refrain from quoting yourself. It sounds pompous."  SweepingRocks 
#2




You're acting as though mu is a constant, but it's not a constant when you have a uniform distribution on (0, 58) for the future lifetime T_{45}. If you want to use basic principles, note that the density function for T_{45} is the constant 1/58.
Quote:
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Jim Daniel Jim Daniel's Actuarial Seminars www.actuarialseminars.com jimdaniel@actuarialseminars.com 
#3




The shortcut:
tp45 = l(45+t)/l(45); mu(45+t) =dl(45+t)/l(45+t) Multiply and cancel l(45+t) which leaves dl(45+t)/l(45) = (1)/(10345) = 1/(10345)
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#4




Dumb question that I should know the answer to: does that mu equation apply all the time or just when deaths are uniform?
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Former Disney World Cast Member, currently no idea what I'm doing "I think you should refrain from quoting yourself. It sounds pompous."  SweepingRocks 
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