Why does my phone turn off with 90% to 80% battery life?

[Ur_Face2014]

It started cutting off randomly around 15%, then 20% to 30% and not a week later it is randomly shutting off my phone between 80% and 90% and it will turn back on load up to the AT&T white logo screen then turns off again. I have to plug it in then turn it back on. After it is plugged in it shows the battery as 80% full and will turn back on and then once it is loaded you can unplug it and it will last until 50% then it dies again. Not sure if this is a battery issue or a software issue.

I have a Samsung Galaxy S4, it is about a year old and recently it updated itself (As in I didn't let it, it just did it) to Android 5.0 Lollipop.

 

[B. Diddy]

Look at your battery graph--is there a sudden steep dropoff of the battery curve right before it shuts off? That could be a dendrite in the battery. http://forums.androidcentral.com/ambassador-guides-tips-how-s/479461-guide-my-battery-shot.html. I'd try a new battery.