There is insufficient information contained in your question to give an accurate answer. Some of the important pieces of information needed to answer this question are: ‘How much do you owe?’; ‘How long do you intend to live in the property or keep the loan’; ‘How much will refinancing cost you to lower your rate 1.25%?’; ‘How long do have to pay on your current loan?’; ‘Is the savings based on a fixed or an adjustable rate that might change in the future?’.
With the answer to these questions, and maybe even some others that I haven’t thought of, a mortgage professional can give you your options so you can make an informed decision on whether refinancing makes sense for your situation.
I’ll give a somewhat extreme example to show why there are no ‘rules of thumbs’ and illustrate why each individual should evaluate their needs on their own circumstances.
Someone owes $400,000 on a home they live in and intend to live there for the foreseeable future. They have 24 years left to pay on their loan. Closing costs are $8,000 or 2% of their loan amount to lower the rate 1.25%. They get their investment in refinancing back in less than two years. (2% / 1.25%/year = 1.6 years – this is not exact, but good enough for illustration purposes.) Sounds like a pretty good deal since they intend to stay in the home and not pay off the loan for at least a couple of years and probably a lot longer.
Same situation except that the closing costs are only $4,000 and the customer owes $50,000 and has only 5 years left to pay. $4,000 is 8% of the loan amount and the customer saves 1.25%/yr the first year and considerably less in the next four years. In this example the customer needs more than 8 years to recoup a savings of 1.25% in the rate even if their loan balance wasn’t rapidly declining. (It is due to amortization.) If their current loan would be paid off in 5 years and they have no reason to extend their term, they would actually lose money by lowering their rate. I want to reiterate that, due to amortization, dividing the closing costs, as a percentage of the loan amount, by the percentage difference in the rates does not give an accurate enough answer to use in evaluating your options in deciding whether a refinance will save you money or achieve your financial goals. Plus believe it or not there are times when saving money is not the only reason, or even the primary reason, to refinance a loan.
Contact a mortgage professional that can give you an answer to this question that applies to your unique situation.
One of the huge considerations here, as Harlan pointed out, are the closing costs involved. Many loan officers, including myself, use lender contributions to pay most or all closing costs. If you can lower your rate without incurring costs, the answer to your question is decidedly yes. Keep in mind that your loan size will directly impact the amount of costs your lender can pay. The higher the loan size, the higher the lender contribution to your closing costs is available.