Exercise 5.20 Consider the following portfolio of annuities-due currently being paid from the assets of a pension fund. Age Number of annuitants 60 40 70 30 80 10 Each annuity has an annual payment of $10000. The lives are assumed to be independent. Assume mortality follows the Standard Ultimate Life Table, with interest at 5% per year. Calculate (a) the expected present value of the total outgo on annuities, (b) the standard deviation of the present value of the total outgo on annu- ities, and (c) the 95th percentile of the distribution of the present value of the total outgo on annuities, using a Normal approximation.
Exercise 5.20 Consider the following portfolio of annuities-due currently being paid from the assets of a pension fund. Age Number of annuitants 60 40 70 30 80 10 Each annuity has an annual payment of $10000. The lives are assumed to be independent. Assume mortality follows the Standard Ultimate Life Table, with interest at 5% per year. Calculate (a) the expected present value of the total outgo on annuities, (b) the standard deviation of the present value of the total outgo on annu- ities, and (c) the 95th percentile of the distribution of the present value of the total outgo on annuities, using a Normal approximation.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.4: Mathematics Of Finance
Problem 2E
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![PLEASE HELPI WITH ALL OF THEMI
Exercise 5.20 Consider the following portfolio of annuities-due currently
being paid from the assets of a pension fund.
Age
Number of annuitants
60
40
70
30
80
10
Each annuity has an annual payment of $10000. The lives are assumed to
be independent. Assume mortality follows the Standard Ultimate Life Table,
with interest at 5% per year. Calculate
(a) the expected present value of the total outgo on annuities,
(b) the standard deviation of the present value of the total outgo on annu-
ities, and
(c) the 95th percentile of the distribution of the present value of the total outgo
on annuities, using a Normal approximation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf13798f-fec8-4974-961f-6e1452ed32d8%2F43e13a16-d2d2-4702-a25a-11e952517e85%2Fbsfkozh_processed.png&w=3840&q=75)
Transcribed Image Text:PLEASE HELPI WITH ALL OF THEMI
Exercise 5.20 Consider the following portfolio of annuities-due currently
being paid from the assets of a pension fund.
Age
Number of annuitants
60
40
70
30
80
10
Each annuity has an annual payment of $10000. The lives are assumed to
be independent. Assume mortality follows the Standard Ultimate Life Table,
with interest at 5% per year. Calculate
(a) the expected present value of the total outgo on annuities,
(b) the standard deviation of the present value of the total outgo on annu-
ities, and
(c) the 95th percentile of the distribution of the present value of the total outgo
on annuities, using a Normal approximation.
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