A "life annuity" is an annuity that is paid only while the purchaser of the annuity (also called the annuitant) is alive. Life annuities are an investment tool typically used by retirees to provide a fixed series of payments in retirement. For Questions 1 and 2 below, assume the interest rate is 5% (APR) per year. 1. Suppose John is 65 years old and has just retired. John wishes to invest in a life annuity which pays $60,000 per year. a. If John lives to be 80 years old (the annuity makes 15 annual payments), what is the present value of the annuity? b. If John lives to be 90 years old (the annuity makes 25 annual payments), what is the Ipresent value of the annuity? c. If John lives to be 100 years old (the annuity makes 35 annual payments), what is the present value of the annuity? d. If John expects there is an equal (one-third) probability that he will live to be 80, 90, or 100 years old, calculate the expected present value of the annuity. The expected present value of an annuity is also called the "actuarial present value