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While the body of the letter is responsible for passing on the intended message of the writer, the fact remains that the salutations are what give it character. Just like your words can express your mind, but your body language expresses your words. The closing of a letter is the body language of the letter.

New Contacts

Closing salutations for new contacts need to be kept formal and slightly distant in business letters. This is done to avoid eagerness from showing in the letter. The safest bet in these cases is to use the traditional closing phrases. These types of closing regards are best for sales mailers and mass mailings. Advertisement letters are also best closed with these (as I call them) 'safe' phrases.

Sincerely
Yours Sincerely
Yours Faithfully
Respectfully yours
Faithfully yours
Yours truly

Regular Contacts at Same Hierarchical Level

In case of contacts whom one is regularly in touch with, and at the same hierarchical level, the closing paragraphs can be friendlier in nature. This is because, the regular contact develops a bond, and the same hierarchical level allows the conversations to be less formal. More so, keeping the friendliness also ensures loyalty to an extent. However, one needs to ensure that professionalism is maintained. These are best used to keep the informality in the letter, whilst maintaining its professionalism. Let's just say, the letter went for a business meeting with a friend.

Kind regards
Best regards
Regards
Warmest regards
Many thanks
With appreciation

Regular Contacts at Different Hierarchical Levels

If the recipient of the letter is at a higher or a lower hierarchical level, the closing statement will differ. In most cases while closing the business letter, if the levels are different, either way, the remark becomes more formal. Writing a closing paragraph for a higher or lower level recipient is the same as it would be for a new contact. This is to maintain the difference in status and to keep the fact that the communication is strictly professional, in clear view. In fact, in many cases higher level senders tend to end the business letter without a complimentary close, with just their name. This works at intimidating the recipient to a certain extent. It works well as a negotiation tactic as well.

Casual Closings

In spite of the fact that the letter is a formal one, these days people prefer to keep the salutations informal. This is for ease of communication. If the communication is informal and "easy", the business flow tends to be smoother. More so, a client will prefer to stick to a friendlier provider. To maintain this "friendly" relationship, the following closings are also used.

With love
Cheers
Adios
Enjoy!
See ya soon
Have a great day

These days, due to excessive use of emails, letters are often kept shorter and to the point. As such, it is important to keep a standard format of closing the letter. There is an option with most email providers like Google, etc., wherein you can set and save your closing and email signature. This way, your closing will be maintained despite the contents of the letter.