I am WritingI' m writing
Words - Is the use of "I'm writing to" in an e-mail regarded as too informal or old-fashioned?
This may be considered somewhat old-fashioned, but more specifically, it is formally to use "I am writing to". There is definitely a feeling that the writer and the receiver do not have a strong connection. Indirect use is used to establish a courteous detachment in both oral and verbal communications.
At some point, the addressee of the note knows that you have written it. The words "I write" do not contain any additional information, but these words show a courteous distancec. "I' m writing to tell you that you won the first prize." He or she has written the note and sent it, which means they want to tell me.
"I' d like you to know you won the first prize." "You' re a winner of the big prize." I' ve always written'Dear' until one of my teachers tells me that I'm too formally; now I write'Hi' and save'Dear' for more form.
"I' ll write to you" is also very formally.
phrase - Is "I write to keep you informed" unpleasant or out-of-date?
At least as VonC suggests, the base structure is a bit shaped. However, I think "I write....." is somewhat unofficial in relation to "I write....". - with the more official "....to let you know...." and it turned out that the mating "I am writing to let you know...."
is much more frequent than "I am writing to let you know...." by 8,840 to 5,960. Conversely, "I am writing to let you know...." is in fact more frequent (around 17,900 to 14,000) than OP's (mixed informal/formal) "I am writing to let you know....". What is the point of initiating or writing a correspondence with me?