15. a. Suppose a 65-year-old person wants to purchase an annuity from an insurance company that would pay $20,000 per year until the end of that persons life. The insurance company expects this person to live for 15 more years and would be willing to pay 6 percent on the annuity. How much should the insurance company ask this person to pay for the annuity?

b. A second 65-year-old person wants the same $20,000 annuity, but this person is much healthier and is expected to live for 20 years. If the same 6 percent interest rate applies, how much should this healthier person be charged for the annuity?