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Updated from 11:43 a.m. EDT

Treasury Secretary Timothy Geithner said Tuesday that the government's $700 billion bailout fund has at least $109.6 billion in resources left, and he anticipates that $25 billion will be paid back by borrowers.

Geithner's remarks appeared in a letter to Elizabeth Warren, the head of the Congressional Oversight Panel, ahead of his testimony in Washington, where he said that the "vast majority" of U.S. banks have more capital than they need and that some could be allowed to repay funds distributed under the Troubled Asset Relief Program.

Under his accounting projections, Geithner said that $355.4 billion in funds was used by the previous administration, with

American International Group

(AIG) - Get American International Group, Inc. Report

receiving $40 billion, while

Citigroup

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and

Bank of America

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got a combined $52.5 billion. Another $24.9 billion went to automakers such as

General Motors

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and

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Chrysler

.

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The previous administration also used $218 billion in the Capital Purchase Program and $20 billion in the original Term Auction Loan Facility, or TALF, according to Geithner's letter.

Among those banks receiving money under the Capital Purchase Program, Citigroup, Bank of America,

Wells Fargo

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and

JPMorgan Chase

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each received $25 billion.

Goldman Sachs

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and

Morgan Stanley

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each received $10 billion under that program.

By comparison, Geithner said the Obama administration has used $235 billion. A second investment to AIG was worth $30 billion, while $50 billion went to housing, $5 billion to auto suppliers, $35 billion to TALF for asset expansion, another $25 billion to TALF for legacy securities, $15 billion to help unlock small business lending markets and $75 billion net to the Public-Private Investment Program.

Geithner said that seven recipients of TARP funds through the Capital Purchase Program have already repaid the Treasury and that several others have announced the intention to do so in the near future. He added that the estimate of $25 billion in repayments over the next year is "conservative" and is a figure "lower than many private analysts expect."

During his remarks before the Congressional Oversight Panel Tuesday, Geithner said that some firms could be allowed to repay TARP funds, which sparked a rally in major U.S. bank stocks. Geithner said that a "vast majority" of banks have more capital than needed, though he did caution that any decision on repayments would be left to bank regulators.

He also stressed that his estimates assume 100% take-up of the $220 billion made available for housing and liquidity programs, "which require significant voluntary participation from financial participants. If any of those programs experience less than full take-up, additional funds will be available," he said.

Geithner's comments will be heavily scrutinized after a

government TARP watchdog

said the Treasury's Public-Private Investment Program was vulnerable to fraud, abuse, conflicts of interest and money laundering.

Neil Barofsky, the special inspector general for the TARP, also said the partnership could expose taxpayers to higher losses without corresponding increases in the potential for profit.

In his prepared testimony, Geithner defended the plan as being set at the minimum cost to taxpayers, arguing that it "strikes the right balance." Taxpayers, he said, will share the risk with investors, while allowing the private sector to use competition to set market prices for troubled assets.

"If the government alone purchased these legacy assets from banks, it would assume the entire share of the losses and risk overpaying," Geithner said before the panel. "Alternatively, if we simply hoped that banks would work off these assets over time, we would be prolonging the economic crisis, which in turn would cost more to the taxpayer over time."

Geithner also defended a drop in bank lending by many of the institutions receiving TARP funds, saying that it is impossible to judge how the financial markets would have operated without the actions by the government.

"After all, in normal recessions demand for credit falls. In recessions that are following a long period of substantial borrowing, demand for credit falls much more sharply," Geithner said in his prepared remarks. "This is such a moment. There is no past experience that provides a good guide as to what to expect to have occurred in our financial markets absent the intervention that took place."

During the Q&A session following Geithner's prepared remarks, Rep. Jeb Hensarling (R., Texas) voiced his concern about

reported plans

for the U.S. to convert the preferred stock positions in major financial institutions into common stock, making the government a major shareholder.

"That risk worries me too," Geithner said in response. "We want to make sure that there is the capital the system requires and that it is targeted to where it is needed."

Geithner added that the current stress tests being performed will help with clarity and transparency of banks' balance sheets, and that banks in need of additional capital can raise it. Geithner said there are a variety of different ways raise capital, whether in the market, through conversions or taking money from the government.