Iphone 5 doesn't fully charge?

I've had the Iphone 5 for about two months now and the past few days, it did not charge to 100%. I always have it on the charger all night and for a couple days, it charged to 98%. I would unplug it an plug it back in then it would charge the rest of the way. Last night it only charged to 78%, and again I unplugged it and plugged it back in and it charged the rest of the way. I'm using the supplied charging cable and wall adapter. I have taken some advice I had gotten and let the battery drain below 20% before charging and that didn't seem to help. What is going on? I can't imagine these batteries should be doing this after only two months, especially due to the fact that iphone users have to pay a premium to own these phones and that technically, the battery is not meant to be user changeable. Any suggestions?

Hold the hold button and the circular button for about 5 seconds and the whole phone will reset. If this doesn't work, a factory reset on itunes should do it. The battery does not need replacing. One other thing you could try is to drain the battery completely, let the phone die, then recharge

I'm having the same problem with my iPhone 5. I charge it until it gets to 100% and the battery icon shows that's it is running off the the mains, but when I unplug it from the charger it's reading 98% :-/
Ever since the 6.0.2 update I've also noticed that the battery drains quite quickly compared to before, so I'd say its more of a software issue rather than a hardware one.
In my opinion IOS 6 riddled with bugs…
And for every one the fix, another turns up.
Very frustrating.

My i5 is brand new and still doesn't charge more than 75%

My iPhone 5s does not charge full to 100%, in spite of keeping it for charging for long periods. At times it stops at 50/52%, and at times it goes up to 70/72%. I'm using the Std cable provided with the device.
Bhatia