Anything that you'd use in an informal communication is inappropriate for a business letter. This includes slang, text_speak, emojis, and anything off_color or casual. If you're used to communicating mostly with friends, family, or even co_workers you've worked with for a long time, an appropriate closing for a business letter will probably feel pretty stilted at first. Don't worry about it – your colleague or business associate won't feel that way when he or she reads your correspondence. What seems unnatural to you will feel respectful and polite to the recipient.
In these days of email and instant messaging, letter writing is becoming a lost art, and especially the formal letter. I’m pretty sure that formal letter rules are still taught in schools, but very little of it sticks. If you’re an executive or other high_ranking person within an organization, you can probably rely on your secretary or assistant to handle the niceties of letter writing, but for everyone else, knowing how to write a strong letter ourselves is important.