Why does my iphone 5 keep turning off??

Since downloading iOS7 my iphone 5 has kept shutting off at anywhere from 40%-15% battery power, and not turning on again until i put it on charge. The other day, just having the phone on it went from 40% to 7% and then shut off within 7 minutes..help??

I have a year still left on my contract and now can barely use the phone at all.