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NEW YORK — Stocks closed at their highest level of the year Tuesday as investors welcomed the latest signal from the Federal Reserve that it will move slowly to raise interest rates.

Big names, including Apple and Microsoft, led technology stocks higher as the market made its biggest gain in two weeks.

Stocks rose after Fed chair Janet Yellen confirmed that the reserve isn’t in a hurry to raise interest rates. Her remarks boosted all corners of the market, and the price of gold rose along with stocks. Bond prices also rose and yields sank.

“A little bit of self-doubt started to enter the trading public’s mind,” said Sam Stovall, U.S. equity strategist for S&P Capital IQ. “She reassured investors.”

The Dow Jones industrial average rose 97.72 points, or 0.56 percent, to 17,633.11. The Standard & Poor’s 500 index gained 17.96 points, or 0.9 percent, to 2,055.01. Aided by the gains in tech stocks and in small cap stocks, the Nasdaq composite index climbed 79.84 points, or 1.7 percent, to 4,846.62.

Stocks were trading slightly lower before Yellen’s remarks, but they moved higher after the text of her comments was released.

The price of gold climbed while bond yields fell and the dollar weakened. The yield on the 10-year U.S. Treasury note slid to 1.80 percent from 1.89 percent. The euro rose to $1.1295 from $1.1200. The dollar slipped to 112.75 yen from 113.28 yen. Gold rose $15.70, or 1.3 percent, to $1,235.80 an ounce.

Apple climbed $2.51, or 2.4 percent, to $107.70 after the FBI dropped its legal efforts to force Apple to break into the iPhone used by radicalized Islamic terrorist Syed Farook, who along with his wife killed 14 people and seriously wounded 22 in San Bernardino, Calif., in December.

Microsoft added $1.17, or 2.2 percent, to $54.71. Information technology company SAIC advanced $5.33, or 11.5 percent, to $51.88 after its fourth-quarter profit was far larger than analysts expected.

Utility and telecommunications stocks, which pay hefty dividends similar to bonds, also traded higher.

Financial stocks made only small gains and lagged the market. They are able to charge more money on lending when interest rates are higher, so the Fed’s low-rate policy has hurt the sector. So has the weakening price of oil, because investors are worried that loans to energy companies won’t be repaid.

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