NEW YORK—Wall Street stormed higher Tuesday as investors, optimistic following stronger-than-expected earnings from two big investment banks, were also galvanized by the Federal Reserve’s decision to cut interest rates by three-quarters of a percentage point. The Dow Jones industrial average soared 420 points, its biggest one-day point gain in more than five years.

Many investors were expecting the Fed to cut rates a full point, but appeared to overcome their early disappointment, especially since a 0.75 point cut is still substantial. The central bank’s benchmark fed funds rate is...

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