It used to be easy to guess how many Americans would have problems paying their credit card bills. Banks just looked at unemployment: Fewer jobs meant more trouble ahead.

The unemployment rate has long mirrored banks’ loss rates on card balances. But Eddie Ward, 32 and jobless, may be one reason that rule of thumb no longer holds. For many lenders, losses are now starting to outpace layoffs.

Experts predict that millions of Americans will not be able to pay off their debts, leaving a gaping hole at ailing banks still trying to recover from the housing bust.

The bank stress test results, released Thursday, suggested that the nation’s 19 biggest banks could expect nearly $82.4 billion in credit card losses by the end of 2010 under what federal regulators called an adverse economic situation.

But if unemployment breaches 10 percent, as many economists predict, the rate of uncollectible balances at some banks could far exceed that level. At American Express and Capital One Financial, around 20 percent of the credit card balances are expected to go bad over this year and next, according to stress test results. At Bank of America, Citigroup and JPMorgan Chase, about 23 percent of card loans are expected to sour.

What is more, the peak unemployment level that regulators used to drive their loss estimates is roughly what current rates are on track to reach. That suggests that if the unemployment rate gets much worse, credit card losses could be worse than what regulators projected.

Banks wrote off an average of 5.5 percent of their credit card balances in 2008, while the average unemployment rate was 5.8 percent. By the end of the year, the rate of credit-card write-offs was 6.3 percent.

For the banks, the economics of the credit card business are increasingly troubling. As the recession has dragged on, cardholders have sharply reduced spending. New customers with strong credit histories are increasingly hard to find.

Within the card industry, all eyes are now focused on the sharp increase in unemployment. At Citigroup, executives noted that the company’s 10.2 percent credit card charge-off rate for the first quarter had broken its “historic correlation with unemployment” and showed no sign of letting up.

Card executives say there will little improvement until the economy stabilizes and consumers are more optimistic.

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