between
"i am looking forward to hearing from you"
and
"i look forward to hearing from you"?

i have seen these phrases used fairly interchangeably, but i find only the first one is proper.
what do you think is the proper phrase to use in a business letter?

" I look forward to hearing from you"

It is more formal. " I am looking.." suggests that the thought is not only current but occupying the mind of the writer continually ! It can even be read by the recipient as " I AM looking forward ' which conveys a degree of enthusiasm which is probably absent.

I'd save " I am looking.." for letters to my dear friend who has just returned from abroad, of course, and for my mother in law.........well, I say 'enthusiasm'....

I agree with Fred. The progressive tense almost always suggests immediacy and action, and so, in this case, more enthusiasm.

Compare the relatively calm, "I love ice-cream" which is simply a general truth, with the over-the-top and immediate, "I am loving (this) ice-cream!"

'Look forward' and 'love' might be described as stative verbs - not normally put into the progressive tense - so that, when you do make them progressive, you signify that something extraordinary is happening.