“Dear Mr. Kent: I am writing to inform you that we have not yet received your rent payment for this month.”

You work in the management office of an apartment building. One of the tenants hasn't paid his rent yet for this month, and the payment is 10 days overdue. You're writing a letter to warn him to pay his rent immediately. You start the letter:

Dear Mr. Kent:

I am writing to inform you that we have not yet received your rent payment for this month.

Dear Mr./Ms. (Last name),

When you're writing formal letters or e-mails, the most common way to start them off is with:

• the word "Dear"
• the title of the person who you're writing to ("Mr." or "Ms.")
• the person's last name
• a comma (",") for less formal letters or a colon (":") for more formal ones

For example:

Dear Ms. Yokoyama:

Dear Mr. Traven,

But you shouldn't address all letters and e-mails this way. Most personal messages just begin with "Hi (first name),". But you should use the more formal greeting above in these situations:

• You're writing to a customer who you don't personally know.
• Your message might involve some legal action.
• You're applying for something like a job or admission to a school.

I am writing to inform you that (clause)

This is a phrase that people use at the beginning of a very formal letter or e-mail. For example, if you're writing a letter to inform an employee that you are firing them, it might start:

I am writing to inform you that we will not be renewing your contract for 2011.

In addition to "that...", you can also say "I am writing to inform you of (something)". For example, if you want to quit your graduate school program, you could write to your academic advisor:

Dear Professor. Kind,

I am writing to inform you of my decision to withdraw from the program.

As you may be able to tell, "I'm writing to inform you..." is often used for formally announcing some kind of bad news.

(something) has not yet (done something)

The meaning of the phrase "we have not yet received your payment" is the same as "we have not received your payment yet". But "not yet (done something)" is a more formal version.

There's a famous example of this phrase from history. In a battle during the Revolutionary War between America and Britain, a captain in the American navy was told to surrender by the British. He replied:

I have not yet begun to fight!

This means "I haven't even started fighting yet!" The captain was telling the British soldiers that he would not give up.

Here's another example. In a nature film about a family of bears, the narrator might say:

The cubs have not yet reached maturity, so they continue to stay very close to their mother.

Narrators in documentary films sometimes use formal English like this.

payment for (a time period)

People are supposed to pay their rent each month. If you pay your February rent a month early or a month late, you're still paying "for" February, although you may be making the payment "in" January or March.