Stocks extended their rally Tuesday after the Federal Reserve's latest take on the economy raised hopes that the central bank's string of...

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NEW YORK — Stocks extended their rally Tuesday after the Federal Reserve’s latest take on the economy raised hopes that the central bank’s string of interest-rate increases is coming to an end.

The Dow Jones industrial average rose 51.15 to 10,871.43.

Microsoft, one of the 30 Dow stocks, slipped 25 cents to close at $27.91 a share. Boeing, also a Dow stock, added 10 cents to $69.10.

Broader stock indicators also moved higher. The Standard & Poor’s 500 index added 6.38 to 1,261.23, and the Nasdaq composite index gained 11.89 to 2,253.56.

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Minutes from the Fed’s Open Market Committee meeting Nov. 1 showed policymakers remained worried that high energy prices would spark widespread inflation, all but guaranteeing more rate increases. Yet the Fed also said it would remain sensitive to economic data and conscious of what those rate increases would do to a slowing economy, which investors treated as a signal that the Fed could end increases in the next few months.

The release of the minutes turned the market around, lifting the major indexes out of losses and giving new life to Wall Street’s November rally.

“This is really what we needed to keep this rally going,” said Scott Wren, equity strategist for A.G. Edwards & Sons. “The Fed seems to be recognizing that there may come a time to stop raising rates, and that’s very good for stocks.”

Crude oil rose for a second straight day in anticipation of a cold Thanksgiving weekend in the Northeast. A barrel of light crude settled at $58.84, up $1.14, on the New York Mercantile Exchange.

If oil continues to rise through the winter heating season, that could combine with interest rates to slow the economy faster than expected and prevent stocks from continuing their rise through 2006.

“The rise in oil prices and concern over the Fed’s interest-rate policy are very troubling to the market,” said Hugh Johnson, chairman and chief investment officer of Johnson Illington Advisors. “That’s going to present a challenge to this rally.”

Wall Street also received good news from the National Retail Federation, which said holiday shopping could be stronger than first forecast this year. The retail sector held up well on the report, with Wal-Mart adding 58 cents to $50.20 and Target gaining 15 cents to $55.07.