The iPhone4 was introduced in Juny 2011. So there is a good chance yours is less then a year old and still under warranty. Back to the Apple shop then.
Batteries in an iPhone can't be replaced by the user. So even if there is no more warranty, it's back to the Apple shop.
Kees
Apple phone charging 100% full unplug the charger got left 20 percent will shut down ??

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