At the end you should sign off with "sincerely yours" or any other related salutation. If you are writing a letter of intent for graduate school then it would have a different content. First of all letter of intent would start with your name, address, contact number and email address. After you have mentioned the date, you should then add a salutation like "Dear Sir/Mam".
Buyer accepts offer and signs it, where offer acceptance is binding depends of the legal jurisdiction. For example English and common law differs slightly from American uniform commercial law on matters of offer acceptance and when performance becomes binding on an offer. The seller can also reply with a pro forma invoice. In fact a pro forma invoice can serve as quote and offer, becoming a more or less binding purchase order upon buyer acceptance and signing. Pro formas are used more in smaller FCL trades, and not in larger bulk trades.