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).
If your intent is to persuade the recipient in some way, whether it's to invest money, give you a reference, hire you, partner with you, or fix an issue, create a compelling case for your cause. If, for example, you want the reader to sponsor a charity event, identify any overlap with their company’s philanthropic goals. Convince the reader that helping you would be mutually beneficial, and you will increase your chances of winning their support. Keep your closing paragraph to two sentences. Simply reiterate your reason for writing and thank the reader for considering your request.