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U.S. inflation remains much higher than anyone would like — consumers, the White House, the Federal Reserve. In September, prices stayed high, returning to a 13-year peak after dipping a bit in August.Consumer price inflation — one of the key inflation indicators — rose 0.4% in September, adjusted for seasonal swings, faster than in August but slower than in previous months, the Bureau of Labor Statistics reported Wednesday.Rising prices for food and shelter contributed more than half of this increase, while prices for new cars, household furnishings and car insurance also climbed. The index that tracks new car prices rose 8.7% over the 12 months ending in September, which marks the biggest jump since 1980.Overall, inflation stood at 5.4% in the 12-month period ended in September. Stripping out food and energy costs, which tend to be more volatile, prices rose 4% over the same period, the same rate as in August.America's annual inflation rate is the highest since the summer, which had matched the highest annual inflation rate since 2008.More expensive food and cheaper plane ticketsFood prices jumped 0.9% in September, far more than in August, as grocery store prices climbed across the board.But not everything in America got more expensive. Plane tickets, for example, keep getting cheaper: The price index for airline fares dropped 6.4% in September, after a 9.1% decrease in August.That's not great for airlines, and it's happening even though demand for travel continues to recover from the worst of the pandemic. Delta said in its earnings Wednesday that the company expected to feel price pressure from rising energy costs.Energy prices rose 1.3% last month, the fourth straight increase. Gas prices rose 1.2%, less than in the prior month. Over the past 12 months, the energy price index rose nearly 24.8% and gas increased 42.1%.