iPhone says "out of battery" with 96% left?

Hi, I've been having this problem with my iphone since the day I got it, it turns off with around 90% battery left and I can only use my Iphone whilst plugged in. Loads of people online have been having this problem with different versions of the Iphone as well so I know it must not be this specific devise, they're saying it's the IOS 7 but there's no way this can be proved so I've put that theory to the back of my head. There are some solutions online but none that are a major success, people have been saying to change the battery but many people have had no luck with that? Also my phones not in warranty so I don't really want to do this and spend £50 on a battery and gain no benefit from it. I've tried turning off the signal (which was another theory) but yet again, no luck. What usually happens is I'll turn my phone on, charge it to 100% go on an app or browse the web and it would turn off I'll press the lock button and the 'drained battery' logo would come up and it sort of go in that cycle? I've tried many other websites to this answer but no luck, please help?!