Question: Sarah has found her dream house, worth $500,000, and is considering taking out a loan from a bank for this amount. She has received offers from three different banks, for which she will make minimum monthly payments to pay off the loan:
Bank A has offered her a 30-year loan and will charge her 4.5% interest (compounded monthly).
Bank B has offered her a 15-year loan and will charge her 9.9% interest (compounded monthly).
Bank C does not charge interest to customers. Instead, the bank will purchase Sarah's home up front, and charge her a monthly fee of $2800 for 30 years.
Assuming that Sarah is able to make minimum monthly payments in each scenario (and no more), which bank is offering her the best deal? That is, which deal will charge her the least amount of total interest? You must justify your answer by showing all work.