WASHINGTON — The Federal Reserve’s preferred measure of inflation changed little in September, likely easing the way to a widely expected interest rate cut by the central bank next week.

Prices rose 0.3% in September from August, the Commerce Department said Friday, in a report that was delayed five weeks by the government shutdown. It matched the increase recorded during the previous month. Excluding the volatile food and energy categories, core prices rose 0.2% in September from August, the same as August, and a pace that if it continued for a year would bring inflation closer to the Fed’s 2% target.

Compared with a year ago, overall prices rose 2.8%, up slightly from 2.7% in August. Core prices also rose 2.8% from a year earlier, a small decline from the previous month’s figure of 2.9

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