WASHINGTON — Profit at the Federal Reserve banks soared to a record $82 billion last year, a windfall for taxpayers that also underscores the depth of the Fed’s continued involvement in the nation’s financial markets.

The 12 regional banks that make up the Federal Reserve system held $2.4 trillion in government debt, mortgage-backed securities and other investments at the end of 2010, according to a combined financial statement the Fed published Tuesday. The banks transfer almost all of their profits to the Treasury Department. The $79 billion received by the government this year is a 66 percent increase over last year’s payment of $47.5 billion.

The Fed transferred roughly $25 billion a year in the decade before the crisis.

“It’s interest that the Treasury didn’t have to pay the Chinese,” Federal Reserve Chairman Ben S. Bernanke told Congress in January.

The extraordinary results reflect the unique business model of a central bank. The Fed pays for its investments by creating new money, with the result that the return on those investments, after expenses, is pure profit.