Grocery prices fell in April as overall inflation cooled. Milk prices dropped 0.8% while egg prices declined 7.3%.

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Justin Sullivan/Getty Images

Grocery prices fell in April as overall inflation cooled. Milk prices dropped 0.8% while egg prices declined 7.3%.

Justin Sullivan/Getty Images

Inflation slowed last month, offering a note of relief to cash-strapped shoppers after three months of bigger-than-expected price increases.

Consumer prices in April were up 3.4% from a year ago, according to the Labor Department, a smaller annual increase than the month before. The cost of living rose 0.3% between March and April. Rising rents and gasoline prices were partially offset by falling prices for groceries, including household staples such as eggs and milk.

“Core” inflation, which strips out volatile food and energy prices, was 3.6% in April — the lowest reading in three years.

Could the Federal Reserve cut interest rates soon?

If inflation continues to moderate, the Federal Reserve may be able to start cutting interest rates later this year — a prospect that cheered investors and triggered a stock market rally.

Still, the central bank is likely to be cautious about cutting rates until it’s confident that prices are under control.

“We did not expect this to be a smooth road,” Fed chairman Jerome Powell said Tuesday, before the inflation report was released. “We’ll need to be patient and let restrictive policy do its work.”

Powell acknowledged how frustrating the extended period of high prices has been.

“You tell people that inflation is coming down and they think, ‘I don’t understand that. The price of all the things that I buy hasn’t come down.’ And they’re not wrong,” Powell said at a conference in Amsterdam. “Particularly people at the lower end of the income spectrum are very hard hit by inflation from the start, which is why we’re so strongly committed to restoring price stability.”

Signs some consumers are maxed out

There are signs that some consumers are hitting their limit. Retail sales were flat in April, according to the Commerce Department, although spending at gas stations rose 3.1%.

Although wages have risen faster than prices over the last year, some families are relying on credit cards to cover their monthly bills. Nearly one in five credit card users has maxed out his credit limit, according to a report Tuesday from the New York Federal Reserve Bank.