Aug. 11 (Bloomberg) -- The euro is likely to weaken to 130 yen by year-end after the 16-nation currency failed to rise through so-called resistance at 141.04 yen, according to Deutsche Bank AG, citing trading patterns. Resistance at that level represents the 50 percent retracement of the euro’s decline from last year’s high of 169.96 yen reached on July 23, to this year’s low of 112.12 on Jan. 21, based on a series of numbers known as the Fibonacci sequence. Resistance refers to levels where sell orders may be clustered. Since reaching January’s low, the euro has gained 22 percent versus the yen. “The European currency has strengthened too quickly,” said Koji Fukaya, a senior currency strategist at the Tokyo unit of Deutsche Bank, the world’s biggest foreign-exchange trader. “It will struggle to break 140 yen.” The euro weakened to 137.22 per yen as of 9:30 a.m. in Tokyo, from 137.36 yesterday in New York, when it fell 0.8 percent. The currency reached 138.72 on Aug. 7, the highest level since June 5, according to data compiled by Bloomberg. Europe’s single-currency will probably decline to 135 yen by the end of September, according to a Bloomberg News survey of economists and analysts. The estimate puts a heavier weighting on more recent forecasts. Fibonacci analysis uses a mathematical formula based on the theory that prices rise or fall by certain percentages after reaching highs and lows. A break of one level indicates a currency may move to the next. A failure suggests a trend may stall. Other Fibonacci points include 61.8 percent. In technical analysis, investors and analysts study charts of trading patterns and prices to forecast changes in a security, commodity, currency or index.

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