Please help me answering this question?
(Uncertain annuity) Gavin’s grandfather, Mr. Jones, has just turned 90 years old and is applying for a lifetime annuity that will pay $10,0000 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:
age: 90 91 92 93 94 95 96 97 98 99 10 101
probability:.07 .08 .09 .10 .10 .10 .10 .10 .10 .07 .05 .04
The Gavin (and you) answers the following questions:
(a) What is 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 average method. )
(c) What is the expected present value of the annuity?