“It started right after the Jan. 3 surprise Federal Reserve reduction in rates,” said Dan Harris, chief executive of Lowestloan.com, an online mortgage company in Valhalla, N.Y. “The next day, the phone was ringing off the hook.”

Although mortgage rates began falling late last year, the Fed’s cutting interest rates half a percentage point early in January got the public’s attention. That was followed by a second half-point cut on Jan. 31, and another in March.

There are a number of reasons people seek to refinance mortgages. Some want lower monthly payments, and others decide to swap an adjustable-rate loan for one with a fixed rate, said Doug Duncan, chief economist for the mortgage bankers group.

Many decide to take advantage of the appreciation in property values and take out loans against their increased home equity to help accomplish personal or financial goals.

But refinancing doesn’t make sense in all cases. The traditional rule of thumb was that there needed to be at least a two-point spread between the rate on the existing mortgage, say 9 percent, and the rate on the refinanced mortgage, say 7 percent, to make it worthwhile after a borrower paid the costs for the new loan.

Still, a would-be refinancer needs to make sure that he can recoup the costs associated with refinancing, generally the equivalent of 2 to 3 percent of the new loan’s total value.

These costs can include a new appraisal, title search, credit check, attorney fees and closing fees. Borrowers also may be charged points, which are the fee paid to the lender to hold down the interest rate on a loan. One point is equal to 1 percent of the loan’s value.

There are a number of online calculators to help you determine if refinancing makes sense. The mortgage bankers site, www.mbaa .org, has one, as do most lenders.