iPhone5 shuts down at 20%-30% battery since new IOS7 was installed
Ever since I installed the new IOS 7 operating system the day it premiered, not only do I have battery issues in which it drains quickly (seems to be a common occurrence) but now if I am using the phone (app, imsg, etc) when it gets down to about 30%, sometimes 23% the phone completely shuts off as if it was at 0% battery life (I say that exact number because it's been at exactly 23% on a few occasions where the phone shut off). The icon pops up that looks like a drained battery with an indication to plug it in, and when I plug it in the phone turns itself on immediately and then works fine. I was told to reset it, hard reset it etc, all of which I tried and to no avail. I have spoken with someone from Apple and they are telling me I need a new battery. The phone is just over a year old (so of course, they won't cover the battery replacement even though the issue started about two weeks ago and it's now two weeks past it's 1 year warranty), and I highly doubt it's a coincidence that the battery is suddenly acting up after the new operating system update. Is anyone having this same issue? Helpful comments would be appreciated. Thanks :)
iPhone 5, iOS 7.0.2