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Microsoft this morning released a new version of Office 365 for businesses and said the paid subscription service has become one of the fastest-growing businesses in the company’s history — now used by 20 percent of its largest customers, up from 15 percent a year ago.

This is the latest step in the company’s move to expand beyond traditional licensed software for Word, Excel, PowerPoint, SharePoint and many other Office programs. With the new release, Microsoft announced a series of new Office 365 business subscriptions ranging from $144/user per year to $180/user per year.

The new packages include features designed to help IT departments to better manage Office 365 settings inside companies.

Microsoft is aiming to fend of rivals including Google, which touted its own growth on the eve of the Office 365 update, saying that more than 5 million businesses are now using Google Apps. The price for the premium Google service is $50/user per year. Google is holding its first Enterprise Global Partner Summit this week, and says its community of apps resellers doubled in 2012 to more than 600.

Microsoft didn’t give specific customer numbers but announced three new enterprise customer wins: the Hamburg Port Authority, Midroc Europe and Sephora USA, who join existing business customers including the state of Texas, Toyota, Tesco, Barilla America and the International Federation of Red Cross. Microsoft said the number of small and midsize businesses using Office 365 has grown by 150 percent over the past year.

Ed Bott of ZDNet has a detailed look at the Office 365 business subscriptions.

Microsoft in January expanded Office 365 with a new subscription for consumers.

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