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Annie (Quvenzhané Wallis) is a little girl with such a big personality that even New York can hardly contain her. Nothing gets her down, including the mean-spirited rants of her foster mom, Miss Hannigan (Cameron Diaz). And not for a second does Annie believe that she’ll never be reunited with her parents, who left her behind when she was a baby.

Such optimism deserves a reward, and it comes in the form of Will Stacks (Jamie Foxx), a cellphone magnate who aspires to be mayor of the Big Apple. When his campaign adviser Guy (Bobby Cannavale) insists that taking Annie into his home would be good for his poll numbers, Stacks reluctantly agrees. Before long, Stacks is spending more time than he might have imagined with Annie and her new dog, Sandy. Annie also bonds with Stacks’ business colleague, Grace (Rose Byrne).

But the foster kid’s newfound happiness is threatened when Guy joins forces with Miss Hannigan.

“Annie” is loosely based on the classic comic strip, “Little Orphan Annie,” and the hit Broadway musical that it inspired. It’s an appealing song-and-dance romp that’s just right for the charismatic Wallis, who earned a best actress Oscar nomination for the 2012 indie flick, “Beasts of the Southern Wild.” Regardless of what’s required of her — comically, dramatically or musically — her star quality shines through.

Director and co-writer Will Gluck (“Easy A”) is a bit slow to get things going but has smartly modernized Annie’s story. References to Twitter and Google turn up, Sandy is named for the hurricane, and Stacks is a stand-in for munitions tycoon Daddy Warbucks.

Foxx engagingly brings off Stacks’ transition from full-time capitalist to surrogate dad. Diaz initially comes across as more shrill than mean but eventually settles into her role, deftly balancing ditziness and desperation. And Cannavale and Byrne are perfectly cast.

“Annie” is not a great movie musical — but it’s a fun time at the movies.

What “Annie” • Three stars out of four • Rating PG • Run time 1:58 • Content Mild language and rude humor