I tested out kabal's idea here, and I think it could work either way, but both paragraphs have engaging openings...

Throughout the past five years, I’ve spent a lot of time in the hospital. Five years ago, my brother was hit by a car that severely damaged leg. He spent months in the hospital, followed by an exhausting rotation of surgeries and doctors’ appointments. Soon after, my father suffered a number of strokes, the last of which left him with serious brain damage and two-week stay in an intensive care unit. Through my countless visits, I began to grow comfortable at the hospital. Moreover, I found myself in constant admiration of the nurses that worked there. The nurses I met were incredibly intelligent, industrious, and always helping co-workers, patients, and visitors.

In my third year of college, I realized that these nurses were everything that I had envisioned for myself. Then I came to a frightening conclusion: I no longer wanted to study finance, the major I had been pursuing for the past two and a half years (The "third year of college" reveals this already. How long had you been interested in business before that?). Slowly, I had grown discontent with my studies, losing interest in schoolwork that failed to resonate with my changing goals. I no longer wanted to work in business; instead I wanted to work in a setting that allowed me to have a direct impact on the lives of others. After researching the profession more thoroughly, I decided that I would like to go into the field of nursing.

In regards to nursing, my short term goals are related to education. I place an emphasis on education because I believe it is the vehicle that allows us to move forward in our lives. That being said, in the near future I hope to attend an accredited nursing program where I can receive an encompassing education through rigorous coursework and gain the knowledge and skills necessary to become a competent, vigilant nurse in a variety of clinical settings. (I know that this is your goal, but everyone applying to nursing school has this same goal. What are you most interested in learning (subjects, skills, personality characteristics you want to develop)?)

In consideration of my long term goals, I must say that I don’t know what I hope to achieve. I say this not because I am an impulsive, reckless young adult, but rather because I do not know where I’d like to be or exactly what I’d like to be doing in ten or twenty years. (You can emphasize your willingness to devote yourself to healthcare and say that you're open to trying any and all areas of nursing, but I think your readers would like to see a little focus too. Even if it's just whether you want to work with children or adults, in America or overseas, in a school/nursing home/hospital/doctor's office, or whether you want to be a nurse that helps thirty people in a day/really gets to know the same two or three patients.)