Please analyze the following problem. Be sure to state your reasoning.

On March 1, Owner offers to sell a plot of land to Buyer for $100,000 and gives Buyer until April 1 to accept. Buyer pays Owner $1 to keep the offer open until April 1. On March 15, Buyer states to Owner "I will give you $90,000 for the land" but Owner refuses to sell for that amount. On March 31, Buyer mails a letter to Owner agreeing to pay $100,000 for the land. The letter reaches Owner on April 2. Is there a contract between the parties?