Bear Stearns Cos., the No. investment bank, said Thursday a bigger-than-expected writedown in its mortgage portfolio caused the first quarterly loss in the company's 84-year history.5 U.S. Having said that, the total expense of a refinance mortgage depends on all those factors - interest rate, number of points, and other costs. Lenders will charge several points in order to offer you the lowest rates. With these, the total cost can run between three and six percent of the total amount you borrow. So, for instance, you borrowed $100,000 on a refinance mortgage loan.