With interest rates relatively low, some homeowners are moving to refinance their mortgages. The logic seems obvious. If you can get a loan with a lower rate, you’ll pay less interest and reduce your monthly payments. What could be simpler?

Unfortunately, it’s all too easy to lose in the refinancing game even when it seems to save you money. In fact, refinancings have contributed to the recent mortgage crisis in the country. By trading in your old mortgage, you may well end up paying more interest, not less. The trouble is, each time you restart the clock on your debt, you return to the earliest years of a repayment schedule, when the lion’s share of every payment is applied to interest, not principal. Unless you’re refinancing to improve your cash flow, you’ll often be better off continuing to pay off your old mortgage, even at its higher rate.

To see how this works, consider the case of a homeowner who began making payments on a 30-year, $300,000 mortgage in January 1999. At an 8.25% rate, the homeowner would pay $2,254 a month for 30 years and a grand total of $511,368 in interest.

But suppose that on January 1, 2008, the homeowner refinanced, trading in his old mortgage for a new 30-year loan with a 7.25% rate. The principal of the refinanced mortgage would be $272,995, reflecting the $27,005 of the original $300,000 mortgage that had been paid off during the preceding eight years.

With the smaller principal and the new, lower rate, monthly payments on the refinanced mortgage would be only $1,862, instead of $2,254. However, the new mortgage wouldn’t be paid off until the end of 2037, eight years later than the retirement date on the original loan. And even though the new loan rate was a full percentage point lower than the old one, the homeowner would end up paying a total of $587,911 in interest to own the home outright–– $76,543 more than if he had simply continued to pay off the original loan.

Refinancing would be financially shrewd, however, if the homeowner chose to make the same payment on the new loan as he had on the original mortgage. Paying $2,254 a month at the lower rate would retire the mortgage by 2023, and the total interest paid would drop to $404,520—$106,874 less than would have been paid on the original mortgage.

The standard rule of thumb for deciding when to refinance a mortgage is that it makes sense any time you can find a loan rate that’s at least one percentage point lower than your current rate. But if you look at the bigger picture and do the math, you may find that it takes a two-percentage-point reduction to make the new loan pay off. Any less, and you’ll generally be better off keeping your old loan, unless you plan to make your usual mortgage payments at the new, lower rate.

Keep this in mind the next time you’re tempted by a bargain-rate mortgage. Reducing your nominal mortgage interest rate is only one chapter of a larger story.