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An afternoon report, however, that the government was in the midst of crafting a plan to assume banks’ bad debt led to a late-day surge in stocks. The Dow rose 410.03, or 3.86 percent, its biggest percentage point gain since October 2002.

“If a solid plan is put in place, it’s definitely going to be a positive in easing the pain,” said Stephen Carl, principal and head of equity trading at The Williams Capital Group. He added, though, that “it depends on how it’s structured.”

Wall Street’s whipsaw week saw a massive loss Monday, a rebound on Tuesday, another drop Wednesday, and the rally on Thursday.

The dollar rose against most other major currencies in Friday trading. Gold prices fell. Light, sweet crude for October delivery rose $1.44 to $99.32 a barrel on the New York Mercantile Exchange.

Advancing issues outnumbered decliners by about 8 to 1 on the New York Stock Exchange, where volume came to an enormous 1.38 billion shares.

The Russell 2000 index of smaller companies rose 23.51, or 3.25 percent, to 747.32.

Overseas stock markets soared. Japan’s Nikkei stock average jumped 3.8 percent, and Hong Kong’s Hang Seng index surged 9.61 percent. In Europe, Britain’s FTSE 100 surged 7.88 percent, Germany’s DAX index jumped 4.90 percent, and France’s CAC-40 rose 7.95 percent.

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