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  #11  
Old 09-17-2018, 12:24 PM
windsowe windsowe is offline
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It's 6.3 from the LTAM 165:

Stuart, now age 65, purchased a 20-year deferred whole life annuity-due of 1 per year at age 45.
You are given:
(i) Equal annual premiums, determined using the equivalence principle, were paid
at the beginning of each year during the deferral period.
(ii) Mortality at ages 65 and older follows the Standard Ultimate Life Table.
(iii) i = 0.05
(iv) Y is the present value random variable at age 65 for Stuart’s annuity benefits.
Calculate the probability that Y is less than the actuarial accumulated value of Stuart’s
premiums.
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Old 09-17-2018, 12:27 PM
Academic Actuary Academic Actuary is online now
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Quote:
Originally Posted by windsowe View Post
I have a question about curtate future lifetime. In question 6.3 of the LTAM MC 165, why do we had 1 to the curtate future lifetime of the 65 year old? Why wouldn't the probablility involved simply a:K(t) of a 65 year old instead of a:K(t)+1 of a 65 year old? Thanks for your help!
Because its an annuity due.
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Old 09-17-2018, 12:30 PM
windsowe windsowe is offline
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Ah---that helps a lot!
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Old 09-17-2018, 12:34 PM
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Jim Daniel Jim Daniel is offline
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Quote:
Originally Posted by windsowe View Post
I have a question about curtate future lifetime. In question 6.3 of the LTAM MC 165, why do we had 1 to the curtate future lifetime of the 65 year old? Why wouldn't the probablility involved simply a:K(t) of a 65 year old instead of a:K(t)+1 of a 65 year old? Thanks for your help!
Count how many payments are made, depending on K. If K = 0, for example, so that T=0.xxx, then 1 payment was made. And 1 = 0 + 1. In general, K+1 payments are made.
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