Q: New iPhone keeps shutting down

I recently got a brand new iPhone 5. When I put it to charge the very first time, the battery logo showed it was charging but the battery percentage didn't proceed above 20%. When I switched off the phone and restarted it, the battery percentage appeared fine. However, the problem persisted after that. Each time I charged my phone, it would get stuck at a specific percentage and neither go up nor go down. Furthermore, I started to experience another malfunction. My phone started shutting off by itself randomly. I would be using it and suddenly the Apple logo appears and screen goes blank, before restarting again, all by itself. This has started occurring very frequently, and it has reached a point where I am unable to use the phone and I have put it in my cupboard. I need help really quick because it's a two-week old product and it shouldn't be behaving this way.