iPhone 5 Battery Drains While On Charger
So I charge my iPhone 5 overnight. I plug it in to the wall charger that came with the phone before I go to sleep. It fully charges too 100% and switches from the lightnin bolt to the plug. But then it seems to discharge while still on the charger with no use. A few days ago I woke up to it (after being charged overnight) at 96%. At first I didn't think much of it and thought maybe it was a fluke. Then this morning my alarm went off and I woke up to it (also after charging overnight) 100% and DID NOT UNPLUG IT, simply turned on the screen to see my notifications, locked the screen then hopped in the shower. Came back about 20 minutes later and it was at 97%. It had not been taken off the charger at all. I noticed that when i checked the percentage while it was on the charger and at 97%, that rather than having the lightning bolt indicating it was still charging from 97 % it had the cord plug (which I believe indicates its fully charged which 97% is not) so I thought that was weird. Please help. Thank You!
iPhone 5, iOS 6, Battery