It is established etiquette by the Joint Chiefs of Staff, United States Department of Defense, the U.S. Army, the U.S. Navy, and the U.S. Air Force that the closing “Respectfully yours” be reserved for the President of the United States (according to U.S. Army standards, this also extends to the first lady and the President_elect).
Business writing varies from the conversational style often found in email messages to the more formal, legalistic style found in contracts. A style between these two extremes is appropriate for the majority of memos, emails, and letters. Writing that is too formal can alienate readers, and an attempt to be overly casual may come across as insincere or unprofessional. In business writing, as in all writing, you must know your audience.