The government will receive preferred shares that pay an 8 percent dividend and warrants to purchase additional shares in return for the money, the department said.
Treasury also said it will lend up to $1 billion to General Motors so that the company can purchase additional equity that GMAC is planning to offer as part of its effort to raise more capital.
The assistance is part of a larger government effort to aid the auto industry and is on top of the $17.4 billion in loans the Bush administration agreed to provide to the industry Dec. 19, a Treasury Department official said.
Analysts had speculated that if GMAC didn't obtain financial help it would have to file for bankruptcy protection or shut down, which would be a serious blow to GM's own chances for survival.
When GM's sales plunged 45 percent in October, the company said the inability of its credit arm to lend money had cost it as many as 60,000 sales, reports CBS News business correspondent Anthony Mason.
GMAC now says the bailout money will allow it to "resume close to normal levels of financing" effective immediately. The company has lowered its minimum credit score from 700 - on a scale of 800 - to 621 allowing tens of thousands more potential buyers access to credit.
That should give GM more customers, but even with $13 billion dollars in government bailout money, the world's biggest automaker doesn't have much time, Mason reports.
"The money they've been given only takes them through the end of March," says Angus McKenzie, editor of Motor Trend magazine. "And we still have to figure out how we're going to keep these companies viable, solvent. That hasn't been resolved yet."
Last week, the Federal Reserve approved GMAC's application to become a bank holding company, which made it eligible to receive money from the financial rescue fund. The Fed's approval was contingent on GMAC raising additional capital.
Separately, GMAC said late Monday that it has accepted all the bonds tendered in a debt-for-equity swap that was also part of its capital-raising efforts. The company released few details about the results of the swap.
GMAC "intends to act quickly to resume automotive lending to a broader spectrum of customers," the company said in a statement.
The company's goal is to reach $30 billion in capital, the majority of which would come from the debt-for-equity exchange. GMAC has struggled to get bondholders to convert 75 percent of their debt into equity of the company and has yet to say whether it has met its goal.
The Treasury Department's investment in the company does not mean it is "passing judgment" on whether GMAC has met the Fed's requirements to raise additional capital, the official said.
GMAC, meanwhile, said the government's $5 billion investment was completed Monday. The $1 billion loan is still in progress, the Treasury official said.
The Treasury Department said after initially bailing out the auto industry earlier this month that it had committed the first $350 billion of the bank bailout fund, and said Congress should release the second half.
But in several cases the Treasury hasn't actually spent all the committed funds, and the department will use money that hasn't yet been spent to fund the investment in GMAC, the official said. For example, the department allocated $250 billion for a program to inject capital into banks, but has so far spent only about $162 billion of that amount.
General Motors' partial ownership of GMAC has kept the finance arm lending to dealers and car buyers, even as credit from traditional banks has dried up. If GMAC went bankrupt, other institutions would be unlikely to step in to replace the credit lost by GM's dealers and customers.
GM owns 49 percent of GMAC, while the rest is owned by private equity firm Cerberus Capital Management.
As part of its order last week approving GMAC's application for bank-holding company status, the Federal Reserve said GM will reduce its stake to less than 10 percent of the voting and total equity interest of GMAC. Cerberus, which led an investment group that bought a 51 percent stake in GMAC from the automaker for $14 billion in 2006, will reduce its stake in GMAC to no more than 33 percent of total equity.