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(Adds three-year auction results, updates prices) By Karen Brettell NEW YORK, June 7 (Reuters) - Long-dated U.S. Treasury yields tumbled on Tuesday after Target Corp. warned about excess inventory and said it would cut prices, boosting bets that the worst of inflation may be in the past. Yields hit a 3-1/2-week high overnight on concerns that the Federal Reserve will continue to aggressively hike rates as it battles persistently high price pressures that are rising at their fastest pace in 40 years. But Target’s warning that it would have to offer deeper discounts to clear inventory as inflation takes a toll on demand, also indicates that consumer price inflation may improve. “Target basically announced a summer sale today, which will probably have other retailers following along,” said Lou Brien, a market strategist at DRW Trading in Chicago. “Maybe you are seeing some people hedging their positions a little bit because of the foreshadowing that Target gave on retail prices.” Benchmark 10-year note yields fell seven basis points to 2.970% after reaching 3.064% overnight, the highest since May 11. Two-year note yields were little changed on the day at 2.733%. The Fed is expected to hike rates by 50 basis points at each of its June and July meetings, though analysts are debating whether the U.S. central bank could pivot to a less aggressive stance in September if the economy shows signs of weakening and inflation eases. Consumer price data on Friday is expected to show that inflation remained elevated in May, though core consumer prices, which exclude the volatile food and energy sectors, likely ticked down on an annual basis. The core consumer price index (CPI) is expected to have gained 5.9% on the year, after an annual rise of 6.2% in April, according to the median estimate of economists polled by Reuters. Breakeven rates on five-year Treasury Inflation-Protected Securities (TIPS), a measure of expected average annual inflation for the next five years, fell to 3.05% on Tuesday, from 3.08% on Monday. The United States Treasury Department saw soft demand for a sale of $44 billion in three-year notes, the first auction of $96 billion in new supply this week. The notes sold at a high yield of 2.927%, around a basis point higher than where they traded before the sale. The bid-to-cover ratio was the weakest since March at 2.45 times. The government will issue $33 billion in 10-year notes on Wednesday and $19 billion in 30-year bonds on Thursday. June 7 Tuesday 3:00PM New York / 1900 GMT Price Current Net Yield % Change (bps) Three-month bills 1.235 1.2561 -0.003 Six-month bills 1.705 1.7437 -0.005 Two-year note 99-142/256 2.7326 -0.001 Three-year note 99-142/256 2.909 -0.031 Five-year note 98-92/256 2.982 -0.053 Seven-year note 98-96/256 3.0099 -0.067 10-year note 99-48/256 2.9699 -0.068 20-year bond 98-164/256 3.3439 -0.074 30-year bond 95-56/256 3.1219 -0.069 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 35.25 -1.75 spread U.S. 3-year dollar swap 18.25 0.00 spread U.S. 5-year dollar swap 5.25 0.00 spread U.S. 10-year dollar swap 7.75 -0.50 spread U.S. 30-year dollar swap -21.50 -1.00 spread (Editing by Bernadette Baum and Chizu Nomiyama)