Suppose you found a house that you want to buy, but you still have to determine what mortgage to use. Bank of Middle Texas has offered a 30-year fixed mortgage that requires you to pay 8 percent interest compounded monthly. If you take this offer, you will have to pay ‘‘3 points,’’ which means you will have to make a payment equal to 3 percent of the amount borrowed at the time you sign the mortgage agreement. Bank of South Alaska has offered a 30-year fixed mortgage with no points but at an interest rate equal to 8.4 percent compounded monthly. For either mortgage, the first payment would not be made until one month after the mortgage agreement is signed. The purchase price of the house is $250,000, and you plan to make a down payment equal to $40,000. 

a. If you make a down payment equal to $40,000 and borrow the rest of the purchase price of the house from Bank of Middle Texas, how much will you have to pay for the ‘‘3 points’’ when you sign the mortgage agreement? 

b. Assume that the points charged by Bank of Middle Texas can simply be added to themortgaged amount so that the total amount borrowed from the bank includes the points that must be paid at the time the mortgage is signed plus the net purchase price of the house (purchase price less the down payment). For example, the points that apply to a $100,000 mortgage would be $2,000, so the mortgage amount would be $102,000. Which bank offers the lower monthly payments?
c. What would the points on the Bank of Middle Texas mortgage have to equal for you to be indifferent between the two mortgages?