American International Group Inc. paid its $21 billion outstanding balance to the New York branch of the Federal Reserve on Friday and converted preferred stock owned by the Treasury Department into more than 1.6 billion shares of common stock that can be sold on the open market.

The common stock gives the government a 92 percent ownership stake. The Treasury Department is expected to start selling its shares in March.

Converting the government’s $47.5 billion investment in preferred shares into 1.6 billion common shares means the government paid about $30 for each share. AIG stock closed at $54 on Friday on the New York Stock Exchange. If it holds that value over the next two years, as the government unloads its shares, taxpayers would clear about $40 billion profit.

“We will work to make sure that the U.S. taxpayer will get back all of its money with a healthy profit,” AIG CEO Robert Benmosche told The Associated Press in an interview.

Treasury Secretary Timothy Geithner said in a statement that the government “remains optimistic that taxpayers will get back every dollar of their investment in AIG.”

The government came to the rescue of AIG in September 2008, at the depths of the financial meltdown. It did business with hundreds of firms around the world, and officials feared its collapse would wreck the financial system.

AIG became a symbol for excessive risk on Wall Street and a touchstone of public anger. It was criticized by some members of Congress for spending $440,000 on spa treatments for executives only days after it was bailed out.

The bailout, which included loans and federal guarantees, was the largest of a series of rescues announced during the stomach-churning weeks of the financial crisis in the fall of 2008.

Much of the $700 billion fund set up by the government to help wobbling banks, plus AIG, General Motors and Chrysler, was never disbursed. About $385 billion in cash had been handed out as of Sept. 30, according to the Government Accountability Office.

Almost $204 billion has been paid back to the government, and the fund has made $28 billion more on interest, dividends and profits on investments in companies like Citigroup. About $180 billion is outstanding, most of it with pieces of AIG, auto companies and small banks.

The Congressional Budget Office estimated in November, the fund, the Troubled Asset Relief Program, will wind up costing taxpayers $25 billion.

The government sold the last of its stake in Citigroup in December. The transaction was smaller, but similar in structure, to the unwinding of the federal stake in AIG: The government converted its investment into common stock and sold it publicly. The government owns about a third of the common stock of GM and is paring that down gradually as well.

Most of the large banks have repaid their bailout amounts in full.

AIG first announced its repayment plan in September. Since then, the company has worked to raise cash to pay back the government by selling parts of itself around the world.

On Thursday, it agreed to sell its 98 percent stake in Taiwan’s third-largest insurance company. Before that, it took Asia’s AIA Group life insurance company public, raising $20 billion. It raised $16 billion by selling American Life Insurance Co. to MetLife.

The pace at which AIG moved toward ending its government involvement surprised Kevin Ahern, a credit analyst at Standard & Poor’s, who raised the insurer’s rating from junk status to a more respectable BBB+ last month.

Ahern said that while AIG may have given up some of its jewels to raise cash, it has offered the government “a simpler path to exit its stake.”

The bailout of AIG had been expected to result in massive losses, but the Treasury Department now believes it will book a multibillion dollar profit. AIG stock has nearly doubled over the last year as the company sold off assets and trimmed its business.

The AIG rescue was complex. The government still has $20 billion tied up in shares of MetLife and AIA. And the Federal Reserve still holds many of the $50 billion worth of complex derivatives that it took off AIG’s books.

How much the government makes or loses on those other parts of the AIG rescue will determine whether it comes out in the black on the overall bailout of the insurer.

AIG itself is today a much smaller and less flashy company than it once was. It was undone by its financial products division, which bought and provided insurance on risky investments that got other financial companies in trouble.

The financial products division held $2 trillion in assets in September 2008. It had little more than $500 billion at the end of September 2010.

Today, the company is mostly a global property and casualty insurer and a U.S. life insurance business. And it still has work to do to rebuild its reputation.

“Both of the core businesses are less profitable now than they were before the crisis,” said Bruce Ballentine, lead analyst for AIG at Moody’s, the corporate ratings company.

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AP Economics Writers Christopher S. Rugaber and Martin Crutsinger contributed to this story from Washington.