My iPhone 5s won't charge to 100%?

I got my iPhone 5s last Christmas (so it's not even a year old yet) and I've taken good care of it but it won't charge to 100% anymore, even overnight. If I leave it on overnight, it'll just charge to 99%. I thought the cable was the problem so I bought a new cable but that didn't fix the problem so I'm assuming its the phone.
Any ideas?
Would Apple replace it if I took it to them?
Any other information will be greatly appreciated.

Take it to an Apple store before your 1 year warranty expires?

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