The LOI as it is now used is a misunderstood application of poorly informed brokers and traders. A more proper application based on established custom and practice in International trade, going back even to the old medieval "Law Merchant" (Lex Mercantilis) is: Buyer requests a quotation _ in modern usage this is an RFQ/Request For Quotation _ NOT an LOI. Seller may then reply with a Quote. Buyer confirms receipt of quoted prices, and requests an Offer.
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".