The credibility of the system that underpins lending around the globe came under renewed assault Tuesday — and the consequences could find their way into Americans’ pocketbooks.

Libor, the London interbank offered rate, is a standard interest rate for loans between banks. It serves as a benchmark for more than $10 trillion in lending to businesses and consumers worldwide. In the United States, it is linked to the interest rates on student loans, credit cards and even some mortgages.

But London-based Barclays, one of world’s largest banks, admitted last week that it schemed to rig the benchmark rate during the financial crisis. On Tuesday, the bank’s chief executive, Bob Diamond, its chairman, Marcus Agius, and its chief operating officer, Jerry del Missier, resigned. The bank also released documents implying that England’s central bank was involved in the plan. Diamond is scheduled to appear Wednesday before Parliament.

That the controversy has infiltrated the highest levels of British finance suggests that the cracks in Libor may run deeper than previously thought. The U.S. Justice Department is investigating other banks but would not disclose how many or their names. A spokesman had no comment Tuesday, and other federal regulators also were silent.

The reports have shaken the financial industry, which has long regarded the benchmark interest rate as the cornerstone of one of banking’s most basic functions: lending money.

“These benchmarks were regarded by the public for a long time as an accurate and fair representation of what’s going on in the marketplace, and now we see they’re not that at all,” said Aru Subramanian, an attorney with Susman Godfrey who is leading a class-action suit by investors. “It’s a slap in the face to the public during a time when in the midst of bad economic times and everyone’s suffering.”

What changes, if any, will be made to the way Libor is calculated remain unclear. In research released this week, a Credit Suisse analyst predicted that the rate would move modestly higher under several likely scenarios. Some banks reportedly have begun considering abandoning the benchmark rate all together.

In the United States, Libor is popular primarily for products with variable interest rates. Most consumer loans are tied to Treasury bills or the prime interest rate, which is what domestic banks charge each other to borrow money.

Odysseas Papadimitriou, chief executive of the credit card comparison site, said lenders typically pick one index for their entire portfolio, rather than switch between several.

“It just makes it a maintenance nightmare,” he said.

Research by the Federal Reserve Bank of Cleveland found that in a sample of Ohio mortgages, nearly all of the adjustable-rate loans were linked to Libor. Sallie Mae, the nation’s largest private student lender, said all of the loans it originates use the index. senior financial analyst Greg McBride said Libor also is commonly tied to interest rates on credit cards, small-business loans and some corporate bond offerings.

“I don’t see it as very likely that it would be completely phased out,” he said. “It may become even less prevalent than it already is for consumer loans in the U.S.”

Libor is set by a panel of the world’s biggest banks, including JPMorgan Chase and Citigroup. Surveys are taken every business day to determine the average rate at which the institutions would lend to each other.

Banks then use that as a benchmark for the interest rates on all kinds of loans. That means a rise in the benchmark could result in a universal increase in the cost of credit for loans tied to Libor.

Although it typically moves in tandem with the Federal Reserve’s target interest rate, Libor spiked in the midst of the 2008 financial crisis. For homeowners with adjustable-rate mortgages that reset during that time, the increase resulted in an average jump in monthly payments of $100 for every $100,000 in principal, according to the Cleveland Fed’s study.

But Libor then fell much quicker than many financial analysts had expected, given the shaky health of the world’s biggest banks. It has since been in step with the Fed’s rate.