US credit card debt has topped $1 trillion — here's the most effective way you can pay it off, according to Harvard researchers

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By and large, Americans are drowning in credit card debt.

New data released by the Federal Reserve Thursday shows Americans' collective credit card debt has eclipsed $1 trillion, reaching its highest level since January 2009 and up 6.2% from a year ago.

Matt Schulz, senior analyst with CreditCards.com, expects the figures will only continue to rise.

"Americans' credit card debt will almost certainly reach its highest levels ever later this year and keep growing from there," he said. "Add in a few expected rate increases from the Fed over the next two years, and that makes it even more important than usual to focus on paying down your credit card debt."

So, what's the most effective way of taking control and eliminating your debt? Harvard researchers may have found the answer — and it isn't necessarily what you'd think.

Strictly looking at the numbers, it's smartest to pay down the accounts that carry the highest interest rates first. That way, you're staving off as much interest as possible and don't end up owing even more.

But what makes sense mathematically on paper doesn't always work best in real life. Paying down debt is as much about motivation as it is about money, and most people fall into a different camp of debt repayment: Prioritizing accounts with smaller balances, rather than those with higher interest rates, according to research from the University of Michigan.

While it typically goes against the advice of financial advisors, who will cringe as they see the lost dollars in interest piling up, new research from the Harvard Business Review supports this strategy for paying off credit cards.

After analyzing data from nearly 6,000 HelloWallet clients, a financial services provider that caters to Fortune 250 companies, Harvard researchers Remi Trudel, Keri Kettle, Simon Blanchard, and Gerald Häubl determined that consumers who focused on repaying one of several accounts, as opposed to chipping away and multiple accounts at once, paid off more of their debt over 36 months than their counterparts who took the opposite route.

The researchers then simulated these two strategies in a series of three experiments and found similar results. In the first experiment, participants were given a 'debt' divided equally into five accounts and told they could earn money by playing a game to pay it back. The participants who were assigned to pay off the accounts one at a time worked harder than those assigned to pay back their debts equally, finishing 15% more quickly.

Ultimately, the researchers concluded that the factor that made the biggest impact on how hard participants worked wasn't the amount they were paying back or how much was left in the account afterward, it was the percentage of the balance they ended up getting rid of.

That means if you have two credit card accounts, one with $4,000 in debt and another with $6,000 in debt, repaying $2,000 of the $4,000 account would feel much more productive than spreading $1,000 payments over both of the accounts. Even though it's the same amount paid, with the first one, you're already halfway there to closing it out — a mental victory.

"Focusing on paying down the account with the smallest balance tends to have the most powerful effect on people's sense of progress — and therefore their motivation to continue paying down their debts," Trudel writes on HBR.

Dave Ramsey, bestselling author of "The Total Money Makeover," also supports this strategy, which he calls the snowball plan.

"Mathematically, it makes sense to pay on the debt with the highest interest rate first. After all, doesn't that save you the most money?" Ramsey writes on his website. "Maybe, but it's more important to pay your debts in a way that keeps you motivated to keep going until you've wiped them all out. If you begin with the biggest one, you might think you're not making fast enough progress, lose steam, and not finish the job."

At the end of the day, steadily paying off any debt is better than doing nothing, so do what works for you.

Original reporting by Emmie Martin.

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