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. According to a statistical summary, the chance (probability) that Mr Jones will die at any particular age is as follows.

1. (a)What is the life expectancy of Mr. Jones?
2. (b)What is the expected present value of the annuity at 8% interest per annum?

age 90 91 92 93 94 95 96 97 98 99 100 101

probability 0.07 0.08 0.09 0.10 0.10 0.10 0.10 0.10 0.10 0.07 0.05 0.04