But investors warmed to the Fed news, and the Dow made a bumpy, steep climb for the final stretch of trading. That included a 640-point swing from its lowest point of the day to its highest.

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The Dow closed at 11,239.77, up 4 percent. The S&P 500 finished up 4.7 percent and the Nasdaq composite index up 5.3 percent.

The yield on the 10-year Treasury bond briefly hit a record low, 2.03 percent, and finished at 2.26 percent. Investors have bought U.S. debt, driving yields down, even after S&P stripped the United States of its top-of-the-line credit rating last week.

Interest rates on consumer loans, including adjustable-rate mortgages, car loans and credit cards, are often based on Treasury rates. So mortgage rates, which are already among the lowest ever, could go even lower.

Low interest rates for two more years could make the stock market a better bet because bonds will return less money. That appeared to be at least part of the reason stocks rallied so much after investors had a chance to digest the Fed's statement.

Some analysts also attributed the late-day rally to wording in the Fed's statement suggesting it might take further steps to stimulate the economy in the future.

The stock rally came after two and a half weeks of almost uninterrupted declines. Those were fueled first by uncertainty about the federal debt ceiling, then by concerns that the U.S. economy is headed for a new recession and about out-of-control European debt.

When it came late Friday, the downgrade only added anxiety. On Monday, the first day of trading after it was announced, the Dow fell 634 points. Even counting Tuesday's gains, the Dow is down 11.6 percent since July 21 — almost 1,500 points.

The price of gold continued its seemingly unstoppable climb. It set a record price of $1,782 an ounce. Some investors see gold as a safe bet because its value isn't tied to a particular nation, like a currency or government bonds, or to companies, like stocks. The price of gold has more than doubled since the recession began in 2007.

The Fed's announcement of a two-year timeframe for any rate increase underscored a stark reality: A sluggish economy and painfully high unemployment have become chronic.