Gavin's grandfather, Mr. Jones, has just turned 90 years old and is applying for a lifetime annuity

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Gavin's grandfather, Mr. Jones, has just turned 90 years old and is applying for a lifetime annuity that will pay $\$ 10,000$ per year, starting 1 year from now, until he dies. He asks Gavin to analyze it for him. Gavin finds that according to statistical summaries, the chance (probability) that Mr. Jones will die at any particular age is as follows:

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Then Gavin (and you) answer the following questions:

(a) What is the life expectancy of Mr. Jones?

(b) What is the present value of an annuity at $8 %$ interest that has a lifetime equal to Mr. Jones's life expectancy? (For an annuity of a nonintegral number of years, use an averaging method.)

(c) What is the expected present value of the annuity?

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Investment Science

ISBN: 9780199740086

2nd Edition

Authors: David G. Luenberger

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