By Christopher Rugaber And Josh Boak WASHINGTON (AP) — Inflation rose last month to its highest level since February as President Donald Trump’s sweeping tariffs push up the cost of a range of goods, including furniture, clothing, and large appliances. Consumer prices rose 2.7% in June from a year earlier, the Labor Department said Tuesday, up from an annual increase of 2.4% in May. On a monthly basis, prices climbed 0.3% from May to June, after rising just 0.1% the previous month. Worsening inflation poses a political challenge for Trump, who promised during last year’s presidential campaign to immediately lower costs only to engage in a whipsawed frenzy of tariffs that have left businesses and consumers worried. Trump has declared that the U.S. effectively has no more inflation as he…