While it makes financial sense to pay off credit cards with the highest interest rate first, a University of Michigan study finds that consumers tend to pay off credit cards with the lowest balances.

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Many consumers resolve to pay off their credit cards, and their intentions are in the right place.

But according to a University of Michigan study, how they go about it is likely to be wrong.

Mathematically, consumers are best off eliminating the debt on the card with the highest interest rate first.

But researchers found that many of us tend to pay off the card with the smallest balance first, even if it carries the lowest interest rate.

By not tackling the most expensive debt first, we end up paying more in the long run.

So why do we do it?

“There is an emotional benefit to closing out an account,” said Scott Rick, assistant professor of marketing and co-author of the study.

Sure, it feels good to eliminate a card debt. And some financial advisers advise consumers to wipe out the smallest debt first.

But these days, when so many of us struggle to pay bills, we have to be smart about how we use every dollar.

And in this case, that means paying off the highest-rate credit card first.

Of course, paying off the smallest balance first isn’t a mistake if that card has the highest rate.

“We show that people do it even when it is a mistake,” Rick said.

He calls this tendency “debt account aversion.” In other words, if we have several debts, we fixate on reducing their number — not the total amount of indebtedness.

Rick noticed this idiosyncrasy when, as a doctoral student, he received a $600 government rebate.

He had two credit cards with balances, and he used most of the money to pay off a low-rate card with a low balance, instead of the bigger debt with a higher rate.

Only later did he think about why he made the wrong financial choice.

“There’s a lot of research on how they use credit cards to accumulate” debt, Rick said. “We know very little on how people manage their debt.”

Rick says consumers often aren’t aware of their cards’ interest rates or the compounding effect.

The CARD Act of 2009 required card issuers to show consumers on statements how long it would take to pay off the balance by making minimum payments.

And the Consumer Financial Protection Bureau now is looking at ways to simplify card agreements so consumers better understand the terms.

But Rick said credit-card statements should display the interest rate as prominently as the amount owed. Now, he said, the interest rate is buried on the second page.

“The rate should be in as big a font as the balance,” he said.

Some financial advisers recommend paying off the smallest balance first, regardless of the interest rate.

This gives consumers a sense of achievement, they say, and provides the momentum to tackle the card with the next-lowest balance, and so on, until all the debt is gone.

Some advisers suggest going with any approach that motivates people to pay off plastic.

“People naturally want to spend,” said Derrick Kinney, a financial adviser in Arlington, Texas.

“They don’t naturally want to pay off debt.”

Kinney suggests consumers tally their card balances and set a goal to pay off a set amount in the next 90 days.

“Whether you make payments on the smallest card or largest card, it really doesn’t matter,” he said.

“The key is to set a goal for 90 days. Pay it off aggressively.”