1. A borrower took out a 30-year fixed-rate mortgage of $2,500,000 at a 6.2 percent annual rate. After five years, he wishes to pay off the remaining balance. Interest rates have by then fallen to 5.7 percent. How much interest did he pay over 5 years of the mortgage (to the nearest dollar)?
2. A homeowner can obtain on property valued at $250,000, a 30-year fixed-rate mortgage, LTV=90%, at a rate of 6.0 percent with zero points or at a rate of 5.5 percent with 2.25 points. If she will keep the mortgage for 30 years, what is the net present value of paying the points (to the nearest dollar)?
3. A homeowner can obtain a $350,000, 30-year fixed-rate mortgage at a rate of 6.0 percent with zero points or at a rate of 5.5 percent with 2.5 points. How long must the owner stay in the house to make it worthwhile to pay the points if the payment savings are invested monthly?