Okay your iPhone has a battery issue. This may be from overcharging or damage to the phone. If it is from overcharging, you can replace the battery. You can either do it manually, I know they have kits and things online.
They sell those on amazon. Or you can go to the apple store to see what they will do about it. Try not to just walk into an apple store without an appointment. Here is the URL,
for the apple website where you can make a reservation. Make a Genius Bar reservation- if you have not been in an apple store before- it is the bar usually located in the back of the room. Note: the nearest apple store may vary- there are only 3 in my nearest city- I live in the suburbs. Each is an hour away for me- so they may not all be close. The person there will determine to either ask you to replace it, or try to fix it.
They are very good with customer service.
I am not affiliated with Apple in any way shape or form. I am only a 14 year old computer nerd who uses Apple's technology.
Try using youtube also for tips on how to replace a battery, if you choose to do that. Messing it up may result in breaking the phone- just saying- that is why I also put in the apple store- they know what they are doing.
How are you closing "all programs"? The most likely problem is you think they are closed and they aren't. Double click your "home" button at bottom center of phone. Screen will shrink and any open apps will appear in a row along the bottom of screen. Press and hold any app that appears until you see a red "-" at the top of app. Press red "-" on each app to actually close it completely. If you've never done this, every app you've ever opened is running in the background and draining your battery. Even the girl who sold me my iPhone didn't know how to do this, so it's usually the problem when people think they have a bad battery. If you already do this occasionally, you may in fact have a defective battery.