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Refinancing makes financial sense when the interest rate savings outweigh the closing costs before you plan to sell or pay off the home. A common rule of thumb: refinance if you can lower your rate by at least 0.5–1% and you plan to stay long enough to reach the break-even point.
The break-even point is how many months it takes for your monthly savings to cover the closing costs. If you break even in 24 months and plan to stay 10 more years, refinancing is a great deal. If you are moving in 18 months, it probably is not worth it.