1A. Professors Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $83,000 at age 65, the firm will pay the retiring professor $675 a month until death. If the monthly interest rate is 0.50%, what monthly annuity payment can the firm offer to the retiring professor? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

1B. A couple will retire in 40 years; they plan to spend about $23,000 a year in retirement, which should last about 20 years. They believe that they can earn 9% interest on retirement savings. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year. How would the answer to the part before change if the couple also realize that in 15 years they will need to spend $53,000 on their childs college education?

1C. A store offers two payment plans. Under the installment plan, you pay 25% down and 25% of the purchase price in each of the next 3 years. If you pay the entire bill immediately, you can take a 10% discount from the purchase price. Assume the product sells for $100.Calculate the present value of the payments if you can borrow or lend funds at an interest rate of 5 percent. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Calculate the present value if the payments on the 4-year installment plan do not start for a full year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)