iPhone battery goes flat and restarts every few minutes

My iPhone 5c (running 9.2.1) instantly goes flat after the battery drops below 80%, Then I press the power button once and it shows the low battery icon, Then I press the power button a second time and the phone restarts, after I unlock my phone the process repeats again. I was wondering if anyone knew if this is a software issue or if my battery has just become old and I need to get it replaced (I bought my iPhone about a week after release).

Thanks, Jack