When do you use a period between the letters in an abbreviation?

One places a period at the end or each letter (for initialized abbreviations) , i.e.,, U.S.

If the abbreviation is the shortening of a longer word, one places it at the end, i.e., apt. for apartment., or appt. for appointment.

U.S.A. is a correct abbreviation for the United States of America.
USA is a correct abbreviation for U,S.A..

Using periods is more formal and/or old-fashioned, but perhaps more correct or at least more specific.

Understood.