1. Annuities. Professor's Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $1,000,000 at age 65 , the firm will pay the retiring professor $10000 a month until death. a. If the professor's remaining life expectancy is 30 years, what is the monthly rate on this annuity? b. What is the effective annual rate? c. If the monthly interest rate is 0.5%, what monthly annuity payment can the firm offer to the retiring professor