Many banks charge points on mortgage loans. Each point is the equivalent of a 1% charge on the amount borrowed and is paid before the loan is made as part of the closing costs of buying a home (closing costs include points, title fees, attorney's fees, assessor's fees, and so on).
(a) If $100,000 is borrowed for 25 years, for each of the following, find the payment size and the total paid over the life of the loan (including points).
(i) 7 ½ %, compounded monthly, with 0 points
(ii) 7 ¼ %, compounded monthly, with 1 point
(iii) 7%, compounded monthly, with 2 points
(b) Which loan in part (a) has the lowest total cost over the life of the loan?