(a) Assume that a pension plan offers to pay a lump sum of $200,000 on a person's 65 th birthday, or an annuity of $x for the remainder of the person's life. Interest rates are 10 percent, and a person's life expectancy has been determined statistically as being 80 years. What is the value of x (the amount of the annuity) that would make the two alternatives equivalent on an expected present value basis? (b) A person joins the pension plan at age 30. How much will she have to pay into the pension fund at the end of each year in order to accumulate a balance of $150,000 in the fund at age 65