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SAN FRANCISCO — Sales of iPhones, including the new, big-screen iPhone 6 models released last month, helped carry Apple to a record-breaking quarter, with $8.5 billion in profit, the company said Monday.

The company’s profit for its fiscal fourth quarter was 13.3 percent higher than the same quarter a year ago. Revenue over the quarter was $42.1 billion, up from $37.4 billion in the same period last year.

Overall, Apple sold 39 million iPhones over the quarter, a significant bump from the 33.8 million it sold in the same period last year.

“Our fiscal 2014 was one for the record books, including the biggest iPhone launch ever with iPhone 6 and iPhone 6 Plus,” Timothy D. Cook, Apple’s chief executive, said in a statement.

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The revenue was above the expectations of Wall Street analysts. They had expected revenue of $39.9 billion, according to a survey of analysts by Thomson Reuters. Apple’s $1.42 per share profit also exceed analyst expectations for $1.31 a share.

Year after year, iPhone sales have steadily grown, even though overall sales of smartphones are slowing in developed markets, including the United States and parts of Europe. To achieve growth, Apple recently made a series of aggressive moves with the iPhone.

Last year, Apple for the first time released two new iPhone models instead of just one. Last month, Apple again released two new iPhones, this time with bigger screens.

On top of that, Apple has teamed up with phone carriers in important markets, particularly China. Late last year, Apple reached an agreement to start selling iPhones with China Mobile, the largest carrier in the world, with about 800 million subscribers.

The larger iPhone 6 and iPhone 6 Plus smartphones received a strong reaction early. In the first weekend the new iPhones went on sale in September, Apple sold 10 million of the devices, up from the 9 million new iPhones sold last year on their opening weekend.

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