3) Mary has just turned 72 years old.

(a) (2 point) Based on the mortality tables on the last page of Note #8 and given that she is alive now, what is her life expectancy (rounded to the nearest month)? That is, given that she is now 72 years old, how many more years is she expected to live?

(b) (3 points) Suppose Mary has $500,000 that she will use to buy a life annuity. The annuity will pay her yearly income until she passes away. The payments are made at the end of each year. Assume that the last annuity payment will occur at the end of the year in which she dies. How much is the yearly annuity payment? [Assume that the interest rate is 3% p.a., monthly compounding. Be careful with this because the annuity income is made once a year.]