Legally Binding Contract or Not?

Assume that you are in Week 5 of your Legal Environment and Contract Law class at Peru State College.  Your professor posts the following message on the discussion board:

"Dear Students,

I would like to see each of you do well in this course and complete it successfully.  To give you additional incentive, I promise to pay $100 to every student who earns an A grade for the course.  After all grades are posted, I will send a money order in the amount of $100 to the home addresses of those students who have earned an A. Please be sure to provide your home address on your final exam paper, so that I can send you the $100 I have promised.  Good luck!  Work hard in this course!

Sincerely,
Your Professor"

Assume that you earn an A in the course, but you have never received the $100 you expected.  When you email your professor about it, she says that it was not a legally binding contract and that you cannot enforce the payment of the $100.

Choose the side of the student or the professor and make the most convincing argument you can about why the $100 payment is or is not legally enforceable.  Remember to consider all of the elements of a legally binding contract and consider whether they are or are not all present in this scenario.

Let the arguments begin!