(Note: for answering this question I need the assistance of a person
whose mother language is English. Thank you.

Is it correct whether you reply to the following email/letter as
specified below?
(Suppose that the email/letter is from a company where you have
applied for a job. The reply is your reply to that email/letter):

The email/letter:
"...and of course I will keep you posted. Kind regards."

The reply:
...
"...I look forward to hearing from you. Kind regards."

The specific question is: as the writer of the first letter stated "OF
COURSE, I will keep you posted...", isn't the ending "...I look
forward to hearing from you..." a bit "demanding" or "anxious" for the
reply? Or, on the contrary, both are usual and common expressions, the
latter perfectly suitable to reply to the former? I am not absolutely
sure if the reply "...I look forward to hearing from you." in this
case is right, because there is a chance that the expression "...of
course, I will keep you informed." indicates a bit of "tranquilizing"
or "relaxing" effect to the reader, which may not match with the "I
look forward...." reply.
Would you please ellaborate your reply?
Regards,
Tom