1 and 3 are correct. Option 3, using the present continuous, is the more common and natural expression. It tells us what you are feeling at the moment, and is used in spoken and written English. Option 1, using the present simple, is mainly used as part of a concluding formula in more formal written communications. We don't use this form in spoken English. Options 2 and 4 are wrong. The verb following 'look forward to' is ALWAYS a gerund (+ing form). It is incorrect to use an infinitive, even though many fluent English speakers who have otherwise perfect grammar make this mistake. I hope that answers your question.

I'm not a native to give you an accurate answer but in my experience the third one is correct. 1. the phrase "to look forward to" goes with something/ doing something (you can look for this phrase in Oxford or Cambridge dictionary) 2. The present continuous tense used to show that you're still in the middle of waiting for the reply/answer (you haven't done yet)

Hi Irrel, Both forms are use, number 1 and 3. They are basically the same. Or at least the difference is so subtle that it might be too confusing and not worth it to get into it. Just use it as a set phrase to show that you are waiting for the other person to act at the end of a formal letter.

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