WASHINGTON, July 30 (Reuters) - U.S. consumer spending surged in June as vaccinations against COVID-19 boosted demand for travel-related services, but part of the increase reflected higher prices, with annual inflation accelerating further above the Federal Reserve"s 2% target. Though personal income barely rose last month, other data on Friday showed wage growth in the second quarter was the fastest in 13 years on an annual basis. That, together with rising household wealth and ample savings should keep consumer spending strong, though rising COVID-19 infections pose a risk. "The overall trend of healthy-to-strong growth will continue into next year," said Scott Hoyt, a senior economist at Moody"s Analytics in West Chester, Pennsylvania. "Downside risks remain large. The return of shutdowns from increased infections is unlikely, but cannot be ruled out. There are also upside risks, especially given all the extra saving since the spring of 2020." Consumer spending, which accounts for more than two-thirds of U.S. economic activity, rebounded 1.0% last month after dipping 0.1% in May, the Commerce Department said. Economists polled by Reuters had forecast consumer spending rising 0.7%. Nearly half of the population has been vaccinated against COVID-19, allowing Americans to travel, frequent restaurants, visit casinos and attend sporting events among services-related activities that were curbed early in the pandemic. Spending on services advanced 1.2% last month. The broad increase was led by spending at restaurants and hotels. While spending on goods remains strong, the pace has slowed amid shortages of motor vehicles and some household appliances, whose production has been hampered by tight supplies of semiconductors across the globe. Demand is also shifting to services from goods. Amazon.com Inc (AMZN.O) on Thursday said sales growth would slow in the next few quarters as customers venture more outside the home. read more Spending on goods rose 0.5%. Spending on long-lasting goods decreased 1.5%, reflecting a decline in motor vehicle purchases. Outlays on nondurable goods rose 1.8%. The data was included in the second-quarter gross domestic product report published on Thursday. Consumer spending grew at a robust 11.8% annualized rate last quarter, accounting for much of the economy"s 6.5% growth pace, which lifted the level of GDP above its peak in the fourth quarter of 2019. read more With demand outpacing supply, inflation is rising. The personal consumption expenditures (PCE) price index, excluding the volatile food and energy components, rose 0.4% in June after advancing 0.5% in May. The so-called core PCE price index was lifted by increases in prices of airline tickets, used cars as well as hotel and motel accommodation. In the 12 months through June, the core PCE price index shot up 3.5%, the largest gain since December 1991, after rising 3.4% in May. The core PCE price index is the Federal Reserve"s preferred inflation measure for its flexible 2% target. "Price pressures are centered on areas that are having struggles during reopening. Some of those areas are simply reflating to pre-pandemic prices; others should see prices come down as they adjust capacity and work out supply chain issues," said Will Compernolle, senior economist at FHN Financial in New York. "Even with modest monthly increases in PCE prices for the next year, year-over-year readings will be high for a while." Consumers are taking note of higher inflation, which is eroding sentiment. Stocks on Wall Street were trading lower. The dollar rose against a basket of currencies. U.S. Treasury yields fell. WAGES RISING The U.S. central bank on Wednesday kept its overnight benchmark interest rate near zero and left its bond-buying program unchanged. read more Excluding inflation, consumer spending rebounded 0.5% in June after dropping 0.6% in May. The bounce back in the so-called real consumer spending last month puts it on a higher growth trajectory heading into the third quarter. Personal income gained 0.1% in June after dropping 2.2% in May as transfers from the government declined. The saving rate fell to a still-high 9.4% from 10.3% in May, which should underpin spending as the flow of government money dries up. Households accumulated at least $2.5 trillion in excess savings during the pandemic. Record-high stock market prices and accelerating home prices are boosting household wealth. Wages are also rising as companies compete for scarce workers. In a separate report on Friday, the Labor Department said its Employment Cost Index, the broadest measure of labor costs, rose 0.7% last quarter after gaining 0.9% in the January-March period. That raised the year-on-year rate of increase to 2.9%, the largest gain since the fourth quarter of 2018, from 2.6% in the first quarter. Wages and salaries rose 0.9% after shooting up 1.0% in the first quarter. They were up 3.2% year-on-year, the largest rise since the second quarter of 2008, after increasing 2.7% in the first quarter. Wage gains were led by the leisure and hospitality sector. The economy is facing a shortage of workers, with a record 9.2 million job openings at the end of May. About 9.5 million people are officially unemployed. Lack of affordable child care and fears of contracting the coronavirus have been blamed for keeping workers, mostly women, at home. There have also been pandemic-related retirements as well as career changes. Republicans and business groups have blamed enhanced unemployment benefits, including a $300 weekly check from the federal government, for the labor crunch. "We should be prepared for labor supply constraints that keep solid upward pressure on compensation costs in the second half of 2021," said Oren Klachkin, lead U.S. economist at Oxford Economics in New York. "Better health conditions and reopenings will only gradually equalize the imbalance between strong labor demand and the limited supply of workers."