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When is Refinancing Worthwhile?

My husband wants us to refinance our house now to save a little bit on the monthly payments of our mortgage. The rates are lower now than they were when we bought the house, but it hasn’t really been that long since we bought it, and the rates still seem to be going down. We will also have to pay a bunch of fees for mortgage refinancing, just like when we originally got the mortgage. Someone had to come out to reassess the value of the house, and there will have to be a lawyer at the signing of the papers. How much do you have to save per month to make it worthwhile to refinance?