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What is the incentive for a bank to refinance a mortgage at a lower rate?
It can be a good thing for the bank to refinance your loan for you - since you will be keeping the loan at that particular institution.  This gives them more time to enjoy the free money you pay them in interest for the remaining life of the loan. Banks that offer "No closing costs" are betting that mortgage payers will move their mortgage to get the lower interest rates - and whomever holds the loan, gets the interest payments.