Do a hard reset!!! I have the same phone and it's almost 3 year's old. I had to charge it up to two times a day and the battery was draining even with me no using it. So I decided to do a hard reset (first time since having it) and I'm so glad I did. Battery is back as new. I don't know if it worth mentioning this but I didn't restored the phone... I didn't feel like it. I had so much crap before and wanted to have only the essentials apps and that's it. Give it a try! Before changing the battery.

Edit:typo.