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#1




Understanding temporary life annuities
Hey everyone, this is my first post on this website. I'm sure you'll see more of me in the future, and hopefully I'll be able to return the help I get.
Anyway, I'm having a difficult time trying to conceptualize the formula for temporary annuities. The specific formula I'm referring to is slide #7 from this site: http://www.math.binghamton.edu/arcon...c/sect53.pdf I don't fully understand why there is a second term to this. I understand that the formula is important for mean and variance, and also that it can easily be shown that it's equal to the current payment formula. But where I get tripped up is that when I look at a timeline, it seems like all the possible payments are covered in the summation. So how does it intuitively make sense that there should be a term after the summation? Any help would be appreciated. Thanks. pdk17 
#2




I don't really agree with the formula, especially after seeing the example on slide 11. I would have calculated . Maybe it's the same as the way they're calculating it, it's just not the formula that I'm used to. I've done ASM and TIA and didn't see that formula in either place (not that I can remember at least). I don't know how to do the angle over the 3 in Latex
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ASA Last edited by BruteForce; 03212014 at 04:49 PM.. 
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Jim Daniel
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Jim Daniel Jim Daniel's Actuarial Seminars www.actuarialseminars.com jimdaniel@actuarialseminars.com 
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If (x) survives n1 years, then all of the payments are covered. Why is it that we need an extra term after that for those that survive n years? Why do they matter to us? Last edited by pdk17; 03212014 at 05:01 PM.. Reason: To respond to someone else as well 
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In the longer formula with the "extra" term you can transition between those two formulae just by replacing adoubledot with a, which makes it (arguably) more convenient as a general formula.
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#7




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The second formula on Slide #7 just comes from combining the final term in the summation with the term outside the summation. Jim Daniel
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