Homeowners choose not to refinance their mortgages for any number of reasons. But when they don’t, they lose out on tens of thousands of dollars in savings.

Exactly how much they lose depends on each borrower’s individual circumstances, but a first-of-its-kind study attempts to quantify what people forfeit by not turning in their old loan rates for lower ones.

Researchers found that the median household, having failed to refinance, gave away $45,000 in savings over the life of its mortgage. The study — by Benjamin Keys and Devin Pope from the University of Chicago, also found that the mistake of not refinancing is widespread.

The justifications people have for not refinancing are almost as varied as the borrowers themselves. One factor is that calculating the financial benefit — or loss — is relatively complex. Another is that the benefits are not always immediate, but rather accrue over time.

But other factors often are at play. Refinancing can be expensive, often requiring cash out-of-pocket to cover a number of upfront costs.

In other instances, the borrower’s balance is so low that refinancing is seen as not worth the trouble. In other cases, they no longer have the good credit necessary to win approval from lenders. And in yet other cases, they might owe more than their houses are currently worth, meaning they’d have to bring large amounts of cash to the table to gain lower rates.

Worse, perhaps, is that 4 out of 10 of those people were still living in their homes two years later, continuing to make the full and on-time monthly payments, even though rates had continued to decline.

Take a household with a 30-year, fixed-rate loan of $200,000 at 6.5% at origination. When rates declined to 4.5% between 2008 and 2010, the savings by refinancing over the life of the mortgage is more than $80,000, even after accounting for transaction costs.

When rates reached all-time lows in late 2012, they had dipped to 3.35%. So someone with a contract rate of 6.5% would save roughly $130,000 by refinancing.