Taxpayer aid to Fannie Mae and Freddie Mac will reach $224 billion by the end of 2012, of which $55 billion will be returned in dividends to the U.S. Treasury, according to President Barack Obama’s 2012 budget released today.

By 2013, the government-owned mortgage companies will be profitable enough to “pay part, but not all” of their dividend payments from earnings, according to the budget.

The projected cost to taxpayers of rescuing Fannie Mae and Freddie Mac is at the low end of a range of recent estimates from the Federal Housing Finance Agency, the companies’ chief regulator. The agency’s analysis, issued in October, predicted a best-case scenario of $221 billion in aid and a worst-case scenario of $363 billion, including $142 billion in dividends paid to the Treasury.

The Treasury took Fannie Mae and Freddie Mac, which own or guarantee more than half of U.S. residential mortgage debt, into government conservatorship in 2008, promising unlimited aid in return for nearly 80 percent of the companies’ preferred shares. Under the agreement, the stock accrues dividends of 10 percent a year, payable to the Treasury.