Which one of the following letters would be considered formal

3 a letter of application

An example is:
When seeking approval from a manager, the most appropriate and professional manner of requesting for a time off is, I would like to request a 15-day leave of absence starting December 13, 2011.  It's straight to the point stating what your request is, the number of days leave and the start date of leave.  It can then be supported by other statements.  We can put the whole letter this way:

Dear Manager,

I would like to request for a 15-day leave of absence starting December 13, 2011.  I think this is the best time to take a break as I will be flying back home to spend my Christmas vacation with my family. That will also give me enough time before Christmas to buy gifts for my friends and loved ones. 

Rest assured, any deliverables will be done prior to the start of the requested date of leave.

Hoping for a positive response.

Thank you.

Therefore goldie is an animal