Refinance Costs   When you refinance your mortgage, you usually pay off your original mortgage and sign a new loan. With a new loan, you again pay most of the same costs you paid to get your original mortgage. These can include settlement costs, discount points, and other fees. You also may be charged a penalty for paying off your original loan early, although some states prohibit this. The total expense for refinancing a mortgage depends on the interest rate, number of points, and other costs required to obtain a loan. To obtain the lowest rate offered, most mortgage companies will charge several points, and the total cost can run between three and six percent of the total amount you borrow. So, for example, on a $100,000 mortgage, the company might charge you between $3,000 and $6,000. However, some companies may offer zero points at a higher interest rate, which may significantly reduce your initial costs, although your payments may be somewhat higher.