Understanding of Introduction to the basic elements of a contract: mutual assent, consideration, capacity, and legality. Please read the following case and prepare the analysis discussed at the end of the case:

Fred Flintstone is a 16-year old student at Bedrock High School. Bedrock is a small town in rural Washington. Fred recently purchased a used bicycle at the Bedrock Thrift & Save for $29.95. The bicycle is seven (7) years old and is in fair but workable condition. Wilma, age 35, lives next door to the Flintstone family in Gravelly Court - a Bedrock suburb. Wilma owns Bedrock Antiques & Collectibles, a small antique store specializing in rare and collectible sporting goods. Wilma saw Fred riding his bicycle. Wilma was pretty sure that Fred's bicycle was a rare collectible. She had only seen one other like it and that one sold for over $500 at auction. Wilma complimented Fred on his bicycle and asked him about its age and condition. Fred said, "Its about seven years old and seems to work okay." Wilma said, "I'll give you $100 for your bicycle." Fred replied, "I wasn't thinking of selling it, but that seems like a good price, so I'll sell you my bicycle." Wilma pulled a crisp $100 bill from her wallet and handed it to Fred. Fred then gave his bicycle to Wilma. The next day Fred deposited the money into his bank account and began looking for another bike.

Does a contract exist between Fred and Wilma? Discuss whether each of the elements of a contract-mutual assent, consideration, capacity, and legality-exists in this case.