"Respectfully yours" is an appropriate closing for a letter to a known person. This closing is a way for writers to make their writing more personal by moving the level of formality down a notch from the typical closings of "regards" or "sincerely."
Closings vary in their level of formality. Writers can show thought by carefully choosing an appropriate closing word or phrase to conclude a letter. For a business letter, a formal closing conveys a sense of seriousness and professionalism. Options include "sincerely" along with elegant two-word phrases like "yours truly." Sometimes, the optimal closing is dictated by the specific purpose of the letter. "Best wishes" is appropriate for letters to a specific person where some form of encouragement is warranted. To conclude a letter designed to express thanks for an action performed by another person, a writer might close by using "with thanks" or "with appreciation."
General-purpose letters to an individual lend themselves to a variety of closings. Options available to writers range from "best regards" to "respectfully yours." Of utmost importance to a writer, regardless of whether the communication is print-based or electronic, is ensuring the closing is both complimentary and professional. In e-mail, abbreviations such as "KR" and "Rgds" in place of "Kind regards" or "Regards" convey a lack of professionalism.