NEW YORK — Stocks surged to multi-year highs on Thursday after the Federal Reserve announced an aggressive plan to stimulate the economy, encouraging investors to dive back into the market.

The Dow and the S&P 500 both closed at their highest levels since December 2007, while the Nasdaq ended at the highest since November 2000.

Major market names were big winners, with Apple Inc , the most valuable U.S. company, ending at an all-time closing high and No. 2 Exxon Mobil, closing at a four-year high. Nearly 600 shares on the New York Stock Exchange and Nasdaq touched 52-week highs on the day.

The Dow Jones industrial average ended up 206.51 points, or 1.55 percent, to 13,539.86. The Standard & Poor’s 500 Index closed up 23.43 points, or 1.63 percent, to 1,459.99. The Nasdaq rose 41.51 points, or 1.33 percent.