Mike decided it was time to purchase a home. He has $180,000 in annual income so he estimates that he can afford to have $5,300 per month go towards the principal and interest components of the mortgage payment. He has also saved $220,000 that can be applied towards a down payment on the house.

a. When he started looking at houses, the 30-year simple interest rate for purchase mortgages was 2.75%. He identified a $1.4 million house that seemed to have all of the amenities he was looking for. If he had purchased it for that price, what would have been the monthly mortgage payment (just principal and interest)?

b. Given the recent inflation and geopolitical uncertainty, interest rates have risen markedly and are now sitting at 7% for 30-year purchase mortgages. If Mike still needed to pay $1.4 million to purchase the home, what would be the mortgage payment? Does that fit within the budget?

c. At this new level of mortgage rates, and presuming that his budget can only withstand a $5,300 per month mortgage payment, what is the maximum he can afford to spend on the house?

d. This higher interest rate environment is causing problems for all home buyers. An innovative mortgage company realizes that because people generally get raises, they can afford to have their mortgage payment rise over time. They are offering a new mortgage product where the amount of the monthly payment (principal plus interest) rises 0.1% each month. If the interest rate on the mortgage is still 7% annually and Mike can afford to pay $5300 per month and the monthly 0.1% increase in payment, now how much can Mike afford to pay for the house?