If you got this offer in the mail promising to save you money on your mortgage, would you believe it?

Elliott Torres and his wife received a letter like this last May, while they were struggling with the payments for their home on the West Side of Chicago. Torres, a night-shift foreman at a printing plant, was doing everything he could to help make ends meet. He took on side jobs: handyman stuff, fixing windows, painting, patching drywall. Their routine was the hard hustle, all so that each month they could muster the $2,000 in mortgage payments to keep their red brick house, their dream home.

The letter that would change their lives sat, unread, for months, while the deadline ticked away. On July 12, Torres finally took a good look.

“I thought it was too good to be true,” he recalls. But it happened to be his 45th birthday, and he decided it would not hurt to drive down to the lending office with his wife Juanita to see what could be done.

The appeal of the traditional 30-year fixed-rate mortgage is predictability: The interest rate is locked in at the start, protecting homeowners from rising rates. But if interest rates ever go down in those 30 years, homeowners can lower their monthly payments by refinancing at a lower rate. At least, that’s the theory. (Ben Bernanke himself refinanced his mortgage.)

After the recession, the Federal Reserve took unprecedented action to boost the economy and the housing market, pushing interest rates to record lows. Which should have left many homeowners like the Torreses with a decision: to refinance, or not?

But a recent analysis of 1 million fixed-rate mortgages in the U.S. showed that millions of Americans choose wrong. Many Americans have neglected a historic opportunity to save money on their mortgages, which has consequences not only for their own finances, but also for the economic recovery. In fact, a recent study estimated that in December 2010, 20 percent of American households with fixed-rate mortgages could and should have refinanced—but didn’t. Of these people, the median homeowner could have saved over $45,000 in payments over the lifetime of the loan.

Economists Benjamin Keys, Devin Pope, and Jaren Pope looked at a snapshot of mortgages from December 2010, when the average interest rate was around 4.3 percent. They first determined how many people were paying a higher rate, which turned out to be the vast majority:

There are upfront costs to refinancing, of course, usually a couple thousands of dollars depending on the value of the loan. And for tax reasons, some families may prefer to pay the higher rate. But even taking those and a host of other factors into account, the researchers estimated that around 41 percent of these homeowners should have wanted to refinance in December 2010.

But can I qualify?

Just because homeowners want to refinance doesn’t mean that they can qualify. When evaluating a refinancing application, lenders look at payment history, the value of the home, credit scores, and other measures of financial health. So the researchers whittled the sample down to people with excellent credit histories who never missed a payment.

In the end, they estimated that 20 percent of the homeowners not only stood to gain from a refinance at the time, but they almost certainly would have qualified for one. Why hadn’t they done so already? Did they not know they could save money? Were they daunted by the process?

To help answer that question, the researchers partnered with Neighborhood Housing Services of Chicago, a lending non-profit. Using the non-profit’s database of mortgages, they identified people who would benefit from a refinance and had good enough credit to qualify for one. NHS sent the people letters offering to help. Here’s what they found:

  • Only about 17 percent went through with the refinancing. (The Torres household was one.)
  • The majority never replied, and when the researchers followed up, a quarter said they never even opened the letter.
  • Another quarter said they opened the letter and meant to follow up, but never got around to it.
  • The missed opportunity was huge. The median savings for households in 2013 who did not respond to the offer was $26,400 over the lifetime of the loan, or about $94 a month.

Refinancing, of course, can be a headache. Homeowners have to first know that it’s an option, then figure out if they’re making the right decision at the right time, and then go through the hassle all over again of proving that they qualify for a loan. The tempest of paperwork and acronyms and calculations can spook even savvy homeowners into inertia, leaving a significant chunk of money on the table.

Why we don’t refinance

The U.S government has been grappling recently with reluctant refinancers. In 2009, the Obama administration introduced the Home Affordable Refinancing Program, one of the signature post-crisis interventions for struggling homeowners. The theory was that the lower monthly mortgage bills from a refinance would put more money in people’s pockets, acting as a kind of stimulus.

But HARP has been seen as something of a failure. The program was very slow to take off, and revamped in 2011 to expand eligibility and entice lenders. As of this June, 3.1 million homeowners have ever refinanced through HARP, falling short of the program’s original goals of helping 4 to 5 million homeowners. Last year, an inspector general’s report noted, “Educating borrowers and encouraging their participation continues to be a major challenge.”

What, in general, discourages people from refinancing? The researchers note in their paper that the results “are consistent with both behavioral explanations such as procrastination and inattention, as well as lack of information as possible reasons why households fail to respond to offers that appear to be in their financial best interest.”

People, in other words, can be irrational and self-sabotaging. Or simply confused. A 2013 study from Fannie Mae asked eligible borrowers why they did not refinance under HARP: 22 percent said they they did not trust the lender who contacted them, and 18 percent said they didn’t know they qualified. No surprise, then, that the head of the Federal Housing Finance Agency has had to emphasize that HARP “is not a scam.”

Andrew Celis, who teaches financial literacy classes at NHS Chicago, said that fear plays a role, especially among low-income families who worry that rocking the boat will jeopardize their mortgage. “A lot of homeowners that we communicate with on this issue sort of have just held their eyes to the ground, and have said, ‘I’m going to do whatever I need to do to make my payments monthly,’” Celis said.

Warming up to a better deal

Elliott Torres had briefly looked into refinancing in the past, but he always seemed to hit roadblocks. Paperwork. Something about his credit history. Something about his savings. The offer from NHS promised to walk him through the whole process. Torres wondered what the catch was.

There was no catch. Two weeks later, they were all set. Back in 2000, when they had bought the house, interest rates were hovering around 8 percent. Their new interest rate? Four percent. Torres says the refinance saves the family around $400 a month. They can afford a second cellphone for Juanita now, instead of having to share one.

And they don’t have to worry about keeping their house anymore.

In their neighborhood of Humboldt Park, Torres said he can feel the stirrings of gentrification. Property taxes have gone up. It’s a historically Latino place, but the residents are getting less and less Latino. The recession wiped out a lot of his neighbors.

“Half the people are gone,” Torres said. “Their houses are foreclosed on and everything.”

He wondered if a refinance could have made a difference for them, too.

“I’m not sure,” he added. “I don’t know that much about realty, but…”