(Adds economic activity, paragraphs 5-6) MEXICO CITY, Dec 23 (Reuters) - Mexico's annual inflation cooled to a fresh record low in early December, showing little impact from a sharply weaker peso currency after the central bank hiked rates for the first time in seven years. Inflation in the 12 months through mid-December slowed to 2.00 percent, the national statistics institute said on Wednesday, well below the 2.21 percent reached in the full month of November, its seventh consecutive record low. A poll of analysts by Reuters forecast a rate of 2.05 percent. Mexico's central bank has said it expects annual inflation to end the year around 2 percent, before climbing back to around the bank's 3 percent target next year. But lackluster growth is containing price pressures in Latin America's No. 2 economy. Economic activity expanded by 0.2 percent in October compared with the prior month, its weakest showing since July, the national statistics institute said in a separate report on Wednesday. It noted industrial output and agriculture shrank. Compared with October 2014, the economy grew by 2.3 percent in the same month this year. Last week, Mexico's central bank hiked borrowing costs last week off an all-time low in a bid to stem further weakening in the peso after the Federal Reserve lifted U.S. interest rates the day before. Mexico's peso, which had tumbled to a series of unprecedented lows this year on concerns of higher U.S. borrowing costs, has continued slipping since the rate hikes last week. But the latest data underscored the so-far limited impact of peso weakness. While the depreciation of the currency has made imported goods more expensive, it has been offset by price drops, such as a big decrease in telecommunications costs. The data showed that consumer prices rose by 0.26 percent in the first half of December, helped by falling tomato and air transportation prices. The analysts' poll had forecast a 0.28 percent increase. The core price index, which strips out some volatile food and energy prices rose by 0.27, above expectations for a 0.23 increase. That took the 12-month core inflation rate to 2.39 percent, in line with expectations for a 2.39 percent rise. (Reporting by Alexandra Alper Editing by W Simon)
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