Please solve all the above questions and show your work. Thank you!

Problem 5-27 Annuities and Interest Rates (LO3) Professor's Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $88,000 at age 65, the firm will pay the retiring professor $800 a month until death. a. If the professor's remaining life expectancy is 20 years, what is the monthly interest rate on this annuity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Monthly rate on annuity b. What is the effective annual interest rate? (Use the monthly rate computed in part (a) rounded to 2 decimal places when expressed as a percent. Enter your answer as a percent rounded to 2 decimal places.) Effective annual rate % c. If the monthly interest rate is 1.00%, what monthly annuity payment can the firm offer to the retiring professor? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Monthly annuity payment