I never had to write such a letter here in Germany... i went this week to try to apply, but the only problem is that they only start with applications from September 3... si i have to wait until i have moved in the city where the university is to apply....
The only time i had to write that kind of letter was when i applied for sound engineering in Belgium... there is an entrance exam, and in the end the uni only chooses very few people on all those who apply. One Uni only takes 10 people each year, on 100 that apply for the exam, and the other takes 100 on maybe 200 applyants or more....
I had to fill in papers stating my musical ans movie style tastes, and otehr questiosn about arts. It was a pain in the ass to do because the sound engineering schools in belgium are more into cinema than music...
so i had to lie a bit and pretend i liked to watch movies a lot. In one of the schools it worked and i was accepted for the oral exam after the written part (only 40 people were chosen for this). But then i didnt make it because i unfortunately said that i would have prefered to be a profesional musician.
In the other school, the people that made the oral exam were sadistic, and you coudl feel that they considered you as some piece of crap. So it mase me loose control of myself and couldnt answer anything good... they were like "if you dont like to watch TV, you wont ever work in a TV studio? huh??"... WTF, it is not because you dont like to watch TV that you wont accept to recrod shows... its not the same...
And those schools usually accept faster people who already have some experience and have some recording stuff hat home... Dumb... because recording equipment is really expensive and not all people can afford it. And if you go to school, its for learning... so it doesnt matter in teh end.
For your paper, i think you should exaggerate on some things a bit, but not too much so that it still stays believable. Or say things like "the way of thinking of the school is the same as mine blahblah", "i have always done good until now and believe that this uni is going to help me a lot when i start working later" . Thats only some suggestions, i dont know if they would really work.