What's the name of The belt in the front of the engine and how much does it cost

that would be the Serpentine Belt. depending on the engine size that wasn't included in your question,if it's a 4 cylinder it's around $30.00...if it's a 6 cylinder it's around $40.00 for a good belt.belt routing diagram is under the hood.unless the belt is very old,find out why it's coming apart,or the new one will do the same thing.