On its own, that cost could be absorbed by the agency. But, as the economy declined, the M.T.A. had lost hundreds of millions because tax receipts — which finance part of its budget — were falling. And its ability to renew its variable-rate bonds at low interest rates was hurt by the trouble at Depfa and other banks. The transportation authority now faces a $900 million shortfall, according to officials. It is “fairly breathtaking,” Mr. Dellaverson told the M.T.A.’s finance committee. “This is not a tolerable long-term position for us to be in.”

In a recent interview, Mr. Dellaverson defended New York’s use of variable bonds.

“Variable-rate debt has helped M.T.A. save millions of dollars, and we’ve been conservative in issuing it,” he said. “But there are risks, which we work hard to mitigate. Usually it works. But what’s happening today is a total lack of marketplace rationality.”

In a statement, the transportation authority said that it was exploring options to reduce the cost of the Depfa-backed bonds, that its variable-rate bonds had delivered savings even during the current turmoil and that the agency had remained within its budget on debt payments this year.

However, the transportation authority has already announced it will raise subway and train fares next year because of various fiscal problems, and may be forced to shrink the work force and reduce some bus routes. Some analysts say fares will probably rise again in 2010.

The Depfa fallout doesn’t end there. Rating agencies have downgraded the bonds of more than 75 municipal agencies backed by Depfa, including in California, Connecticut, Illinois and South Dakota. Officials in Florida, Massachusetts and Montana have cut budgets because of C.D.O.’s or similar risky bets.

And Hypo, the German company that bought Depfa, last week asked the German government for financial help for the third time. Depfa has frozen much of its business, according to Wall Street bankers, and though it continues to honor its commitments, some wonder for how long.

The Wisconsin school districts have filed suit against the Royal Bank of Canada and Stifel Nicolaus alleging misrepresentations. Board members hope they will prevail and schools and retirement plans will emerge unscathed. The companies dispute the lawsuit’s claims. Mr. Noack is not named as a defendant and is cooperating with the school boards.