Apple Inc.’s customers have downloaded more than 40 billion applications from the company’s App Store, with almost half occurring last year as use of the iPhone and iPad surged.

More than 2 billion apps were downloaded in December, a record, Cupertino, California-based company Apple (Nasdaq: AAPL) said Monday in a statement.

Apple, with now more than 775,000 apps available for its iPhone, iPad and iPod Touch devices, said it has paid more than $7 billion to the developers of those applications.

Apple launched its app store in 2008. The store hit the 10 billion downloads mark in early 2011. In March 2012, Apple announced that more than 25 billion apps have been downloaded.

The 40 billion milestone does not include updates or re-downloads.

Apple is counting on apps to help woo consumers who are choosing amid an increasing array of lower-priced tablets from competitors, including Google Inc., Inc. and Microsoft Corp. Apps can also help the iPhone compete against feature-laden phones from Samsung Electronics Co. and Nokia Oyj.

The growth in app-store users from 435 million in September, as well as the surge in downloads from 35 billion in October “could help allay some recent demand concerns,” Will Power, an analyst at Robert W. Baird & Co., wrote in a research report today. He rates the shares outperform with a target price of $750.

Shares of Apple slipped 0.6 percent to $523.90 at the close in New York, a third straight day of declines after a 31 percent increase last year. Barclays Plc cut its price estimate to $740 from $800 in a research report yesterday, while maintaining an overweight rating.

“Expectations are actually low and getting lower,” Ben Reitzes, an analyst at Barclays, wrote in the report. “Many investors fear iPhone sales will be relatively flat this year and that there will be no move into TV that moves the needle.”