4. You want to buy a house valued at $1.2 million. For a house this valuable, the lenders demand a down payment of 25% and insist that the monthly payment on the 25 year mortgage loan is no more than 30% of your monthly gross income. The quoted rate on a 25 year fixed rate mortgage loan is 2.94% per year. Assume that you can make the down payment.

(a): What is the least amount of your yearly gross income for you to qualify for the loan?

(b): Suppose you qualify for the loan, buy the house on September 1, 2020, and make the first monthly payment on October 1, 2020. What percentage of the house do you own at the end of year 2025 assuming that there has been no change in the value of the house?