Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $200,000 at age of 65, the firm will pay professor $1,500/month until death. If the professor's remaining life expectancy is 20 years, what is the monthly rate on this annuity? What is the effective annual rate? For the same initial payment of $200,000 at age of 65 and live for another 20 years, if the monthly rate is 0.5%, how much monthly payment the professor could receive?

2. You want to buy a house. You can make an initial payment of $200,000 and can afford monthly payment of $1,800. If the APR of the mortgage loan is 4.8% and you finance the purchase over 30 years (360 months), what is the maximum price you can pay for the house?