Is it appropriate to use 'eagerly' while ending a formal e-mail

Nowadays, I always use the following phrase when I am ending formal email;

I eagerly await for your response.

Regards,

I've seen this phrase somewhere, kind-of a formal e-mail and I am using it since then instead of always saying I look forward to your response.

I would like to know if it is suitable to use that phrase for formal email.

It really depends on how eager you wish to seem. If you don't mind coming off a little strong, it's fine. But you could convey nearly the same level of enthusiasm by simply saying "I look forward to hearing from you." That is only if using eagerly would make you seem too desperate.

Yes, this would be acceptable, however I would change it a bit.

I eagerly await your response.

I would say this is completely acceptable. I have used "I await your reply eagerly" in formal letters also, although obviously not when I wanted to be snotty.