3. (Unceriain annuity o) Gavin's grandfathe, M? Jones, has just uned 90 years old and is applying for a lifetime annuiiy that will pay $10,000 per year, stariing I year from now, until he dies He asks Gavin lo analyze ii toi him Gavin finds hat according to siatisiical sum maries, the cliance (probability) that Mi Jones will die at any particular age is as follows: age90 91 92 93 94 95 96 97 98 99 100 101 probability 07 08 09 10 10 10 10 10 10 07 05 04 Then Gavin (and you) answer the fullowing questiuns: (a) Wha is the life expectancy of Mt Jones? (b) what is uhe present value of an annuity at 8% interest that has a lifetime equal to Mr Jones's litc expectancy7 (For an annuity of a nonintegral number of years, use an averaging metliud ) (c) What is the expected present value of the annuity