It is, but it doesn't mean what most of the answerers here seem to believe. Peter seems to be the only person here who understands the meaning of the word 'duly'. 'Duly' is not an outdated or formal variant of 'truly', 'sincerely' or any other adverb used an an intensifier: 'duly apologise' is NOT an merely old-fashioned way of saying 'sincerely apologise'. As Peter has explained, 'duly' means 'as is required, expected or appropriate'. We would generally use 'duly' to refer back to the circumstances which make it clear that an apology was required. For example, "He explained how hurtful my remarks had been. I realised my mistake and I duly apologised". This means that it was appopriate for me to apologise. I hope that helps.

No, "duly" does not mean "truly" or "sincerely." https://www.dictionary.com/browse/duly?s=t https://learnersdictionary.com/definition/duly Here, it means we were required to apologize / it was the right thing to do, so we apologized. And there's nothing old fashioned about it.

Hello Ovtolevks! I agree with the other answers but I would like to add that it would definitely depend on the context - who you are apologizing to, why you are apologizing and what you are apologizing for. If it is just an apology to a friend, then I would say "we are truly sorry" If it is an apology to a client or customer and you are apologizing on behalf of your company then I would say "we apologize sincerely..". You could also say it like this "Please accept our sincerest apologies for....." - this is a more formal way of saying it and is also super polite and respectful. I hope that helps!

Yes authentic but very formal and mostly used on older official documents, or spoken by older speakers, sometimes. In normal English it would be "I truly apologies" if apologising to a friend, or when apologising for something you did to/that upset a lot of people

I think Lyne and I said it was very formal, not used too much in daily speaking is not outdated. And you would often see it in official documents. We all all saying the same thing with different words.