Actuarial Outpost MLC sample question #46
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#1
09-23-2007, 05:46 PM
 independent1019 Member Join Date: Feb 2007 Posts: 528
MLC sample question #46

Hi, I need some help with this question, it asks for the temporary life annuity-immediate on independent lives 30 and 40:
ILT, and 6%

I approached the problem by computing the temporary life annuity-due on (30) and (40) first, then subtracted 1 from it. Then I got 6.64, which is wrong according to the solution. I don't understand why it is wrong! The only difference between mine solution and their solution is they coverted everything to annuity immediate while they are solving the problem, but I used all immediate due values while solving the problem, and subtracted 1 at the end.

Can some one help?
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#2
09-23-2007, 06:32 PM
 jraven Member Join Date: Aug 2007 Location: New Hampshire Studying for nothing! College: Penn State Posts: 1,262

It depends which temporary annuity due you computed...
$a_{30:40:\bar{10}|} = \ddot{a}_{30:40:\bar{11}|} - 1$

If you computed $\ddot{a}_{30:40:\bar{10}|}$ then
$a_{30:40:\bar{10}|} = \ddot{a}_{30:40:\bar{10}|} - 1 + {_{10}}E_{30:40}$
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#3
09-23-2007, 09:19 PM
 independent1019 Member Join Date: Feb 2007 Posts: 528

why do you have two formulas for the same annuity immediate??, I used the first one for the problem, and got the wrong answer?? I do not understand ur second equation
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#4
09-23-2007, 09:31 PM
 jraven Member Join Date: Aug 2007 Location: New Hampshire Studying for nothing! College: Penn State Posts: 1,262

Until you say WHICH temporary annuity-due you computed I can't say why you were wrong. The point of my post was that subtracting 1 would only work if you had computed the 11-payment annuity-due. On the other hand, if you had computed the 10-payment annuity-due, then subtracting one does not give the correct answer, since subtracting 1 would leave you with the actuarial present value of a 9-payment annuity-immediate. You would then need to add in the 10th payment, which is why there is an endowment term in the second formula.

EDIT: Basically, when you were finding your temporary annuity-due, did you work out
$\ddot{a}_{30:40} -\,{_{10}}E_{30:40} \ddot{a}_{40:50}$
or
$\ddot{a}_{30:40} -\,{_{11}}E_{30:40} \ddot{a}_{41:51}$?

EDIT2: Based of your stated answer of 6.64, I'm pretty sure you did the first one, which is $\ddot{a}_{30:40:\bar{10}|}$. Which means that by subtracting one you ultimately calculated $a_{30:40:\bar{9}|}$.
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Last edited by jraven; 09-23-2007 at 10:00 PM..
#5
09-23-2007, 10:25 PM
 independent1019 Member Join Date: Feb 2007 Posts: 528

OHHHHH, I see!!! Thank you, I forgot that there is one more payment at time 10 that I forgot to take into account for the annuity immediate, that is not included with the ten year annuity due, so I will need to use the 11 year annuity due minus 1 to get the correct answer. Thank you!
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#6
09-23-2007, 10:53 PM
 jraven Member Join Date: Aug 2007 Location: New Hampshire Studying for nothing! College: Penn State Posts: 1,262

Yes, or you could take the first answer you got, which was $a_{30:40:\bar{9}|} = 6.64$, and add a payment at time 10 via a pure endowment:

$a_{30:40:\bar{10}|} = a_{30:40:\bar{9}|} + {_{10}}E_{30:40} = 6.64 + 0.52604 = 7.16604$

Which differs from the given solution only because of the rounding in your value of $a_{30:40:\bar{9}|}$.
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The Poisson distribution wasn't named after a fish -- it was named after a man ... who was named after a fish.
#7
09-25-2007, 08:10 AM
 slackmaster Join Date: Jul 2007 Posts: 7

How is the value 10E 30:40 calculated in this problem? I imagine you find for each individual life, multiply together and then discount back 10 years? I am having trouble reaching the correct value. Thank you.
#8
09-25-2007, 08:43 AM
 colby2152 Note Contributor SOA Join Date: Feb 2006 Location: Virginia Studying for FAP College: PSU '07 Favorite beer: Oskar Blues Old Chub Scotch Ale Posts: 4,171

$_{10}E_{30:40} = (v^{10}) _{10}p_{30:40}$ You can get that information either from a mortality table OR from given information in the problem.
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