Only a quarter to a third of credit-card users pay off their bills in full every month. Most Americans carry a balance, and as new research shows, a surprising number of them pay close to the minimum each month — even when it’s clear that they could easily settle their debt faster and save a ton of money in interest payments.

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Too many Americans, it seems, have a broken understanding of what the minimum payment on their credit card means and what purpose it serves.

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In fact, as the research illustrates, minimum payments are a cunning tool, calibrated to extract as much profit from people as possible.

Over the past few decades, most credit card companies have tweaked their formulas lower and lower. It used to be that you had to pay at least 5 percent of your credit-card balance each month; these days, the typical rate for a minimum payment is about 2 percent.

The logic behind this trend, as an industry consultant once explained to PBS, was to make people comfortable with carrying more debt and for longer periods of time. Lower minimums meant higher balances. Card issuers would prefer if customers drew out the repayment process as long as possible, because that maximizes the amount of interest.

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The government has tried to help people better understand these brutal calculations. In 2003, regulators banned the practice of setting the rates so low that if people followed the minimum payment, it would be impossible to get out of debt. A 2009 law forced card issuers to print boxes on people’s statements showing them how long it would take to become debt free depending on how much they paid.

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Yet, it seems that many Americans keep committing the same financial errors — and the problem may be hard-wired into our brains.

Some people clearly don't understand what's going on

Recently, in one of the largest studies of its kind, economists Benjamin Keys and Jialan Wang reviewed data from millions of credit card accounts between 2008-2013. They analyzed what happened to customers when credit card companies made small, routine adjustments to their minimum payment policies.

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Sometimes, minimum payments would go up a smidge — on average, by about $15 per account. These sudden increases didn’t seem to cause much financial stress. The economists couldn’t find evidence of more missed payments, which suggests that most Americans can afford to pay down their credit card debt a little faster.

But Keys and Wang noticed that at least 10 to 20 percent of people behaved quite strangely. They would always try to stay just ahead of the minimum. If their minimum payment went up, they would pay the new minimum plus a little extra. If it went down, they would decrease their payments a little, but not all the way.

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This behavior makes no sense. Credit card debt is the priciest kind of debt for most Americans, and financial advisers say you should try to get rid of it as quickly as possible. You shouldn’t even be paying attention to fluctuations in the minimum payment, because you should already be paying as much as you can.

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But it seems that a large chunk of Americans are unduly influenced by changes in the minimum payment. From their behavior, it is clear that they have the wherewithal to pay down their debt faster. Yet they cling to the minimum payment — a number that was not designed with their best interest in mind.

The evil genius of the credit card statement

There are two, intertwined explanations for what is happening. Some of this can be blamed on financial illiteracy. Not enough people know that the minimum payment should not be used as rule of thumb. “Consumers don’t have a lot of guidance for what to pay,” said Keys, an economics professor at the Wharton School. “The minimum payment may sometimes be misinterpreted as advice from the card issuer.”

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But this financial mistake also reveals a deeper psychological truth. Cognitive scientists have shown that we are easily led astray by the information that is right in front of us. The minimum payment is one of the most obvious numbers on a credit card statement. Even if we think we understand what it means, it still influences how we think about our debt.

This weird effect is called “anchoring bias.” Lab experiments find that the mere presence of a minimum payment on a credit card bill reduces how much people think they can pay. When the minimum payment was hidden, people in the study increased their estimated payments by 70 percent.

Keys and Wang have used their trove of data to show that in the real world, anchoring bias significantly impedes how some people pay back their credit card debt. This is the secret psychological genius of the minimum payment — it can subtly encourage you to stay in debt for longer.

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One of the goals of the Card Act in 2009 was to combat this problem. Credit card companies now have to tell you, for instance, how much you should be paying to retire your debt in three years. The effort has been modestly successful in encouraging people to accelerate their credit card payments.

Keys and Wang estimate that in 2013 alone, the new guidance — which appears on a box on your credit card statement — saved Americans around $62 million in interest.