I have enclosed a sample "motivation letter" below. I assisted a young man from Germany during the summer of 2007. Please note, I have changed the universities and dates, although the time was still during the summer / fall 2007.
As I looked through our correspondence, I noted that this was his 26th revision. Is it perfect? No. Is there still room for improvement? Yes. Was it good enough to get him admitted to his chosen program? Yes, he was admitted quickly.
His initial draft was poor. Twenty-six revisions helps tremendously. As you read through his letter, you can see from his credentials and accomplishments that he is very smart. However, even extremely bright people need to think through their letters carefully.
During our correspondence, I emphasized that he needed to be specific. Notice that nothing is vague. There is detail and meaning in almost all sentences. Notice, too, that his letter is confident. I am pleased with the effort and determination he put into his letter, and even more pleased he was accepted to follow his dream.
I hope his letter helps you create your own letter.