What is the part of speech a business letter?

A business letter itself is not a part of speech. It's a form of communication - a written document.

The words within a business letter, however, are all parts of speech. For example, a sentence in a business letter might be:

"We are writing to you today to confirm your order."

Here, the parts of speech are:

* We - pronoun

* are writing - verb phrase

* to you - prepositional phrase

* today - adverb

* to confirm - infinitive phrase

* your - possessive pronoun

* order - noun

So, while the letter itself isn't a part of speech, it contains many words that are.