First paragraph: My name is (state name) and I am a resident of (state address). Currently, I am pursuing my Major in (subject) at the (name of university). It has always been my dream to study at (name of university). (This para is introductory where you give the basic information about yourself and grab the attention of the recipient).
Second paragraph: The purpose of writing this letter is to express my intention of pursuing (name of programme) at the (name of the university). (Here you can briefly mention your qualifications and reasons for choosing this institute. Be sincere and enthusiastic about your subject and the place where you want to apply).
Third paragraph: I will look forward to hearing from you for the same. (Conclude the letter by rounding off your desire to study in this institute and also adding why you feel you deserve to study there).