Iphone battery problems

I normally charge my iPhone 5s, version 9.3.1) to 100%, before going to sleep. I have found the following problem:

Next morning, the battery indicator indicates the battery at , say 40%.

When I then plug the phone into the charger, the phone suddenly turns off, and the battery indicator, on the otherwise blank screen, shows a 2% charge?

Something wrong with the battery, or the charge indicator?

Any suggestions?