Actuarial Outpost Probability involving annuity immediate
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#1
11-30-2018, 03:40 PM
 vandykec SOA Join Date: Sep 2017 College: UW-Madison Posts: 5
Probability involving annuity immediate

Given:

3-year term annuity immediate with
present value of term annuity immediate is = 2.690404
standard deviation of term annuity immediate is = 0.535225

How would I find the probability of the present value of the annuity immediate being less than 2.0?
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#2
11-30-2018, 03:53 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,073

Is that everything you are given? Initially it seems like not enough info. You want to calculate 3_p_x (if i > 0).
#3
11-30-2018, 04:04 PM
 vandykec SOA Join Date: Sep 2017 College: UW-Madison Posts: 5

My apologies, 3_p_x = 0.927.
i = 3%
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#4
11-30-2018, 04:12 PM
 vandykec SOA Join Date: Sep 2017 College: UW-Madison Posts: 5

Would the answer be 1 - prob of survival to age 3 since annual payments are 1? So, in order for present value to be less than 2, survival to age 3 must not happen? So, the answer would be 0.072?
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#5
11-30-2018, 04:15 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,073

That sounds right.
#6
11-30-2018, 04:21 PM
 vandykec SOA Join Date: Sep 2017 College: UW-Madison Posts: 5

Thank you!
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 Tags annuity, present value, probability, standard deviation, variance