iPhone 5 shuts down with plenty of battery life left

I have been having some serious iPhone problems lately. I upgraded to iOS 7 when it first came out and only had a few issues, now more recently I am having problems, especially with the battery. My battery meter seems to be inaccuriate or the battery itself is jacked. My battery seems to drain very quickly even when I am not using my phone. I have done all the tricks to save the battery; turned off Bluetooth, turn off auto refresh for backgroud apps, turned off the motion screen, no dymanic background, etc. However my battery still drains quicker than normal. Lately my phone completely shuts itself off and shows me the dead battery icon even though I have anywhere between 20 and 40 left on my battery. When I plug my phone back in after it dies the battery icon shows a different and yet higher battery life then what it was at when it shut off. I have also noticed that my phone shuts off after I use my camera. THAT part is really annoying.

Is this an iOS 7 issue or is there something wrong with my phone? I have insurance on my phone so I can have it replaced, but the cost to replace my phone is more than if I were to get a new and DIFFERENT phone altogether.