U.S. stocks finished higher on Tuesday, with all three major indexes rising 4 percent or more, after the U.S. Federal Reserve said it will keep interest rates exceptionally low until 2013. In world markets, European stocks ended mixed, as the FTSE 100 in Britain rose 1.9 percent and the DAX in Germany fell 0.1 percent. Asian markets ended lower, with the declines led by the Hang Seng in Hong Kong falling 5.7 percent. Meanwhile, the U.S. Treasury Department plans to sell $72 billion in bonds this week. Its first auction was held Tuesday, during which the government sold $32 billion in bonds. The Dow Jones industrial average rose 429.92, or 4.0 percent, to 11,239.77. Boeing, Alcoa, Pfizer were among the biggest gainers on the index. The broader Standard & Poor's 500 index rose 53.07, or 4.7 percent, to 1,172.53. The technology-heavy Nasdaq composite index rose 124.83, or 5.3 percent, to 2,482.52.