How long would it take me to learn how to "play" the piano?

i'm 16 and want to take piano lesson for the rest of my high school, and also in college through life. i want to get good enough to play Beethoven sonata's and more. how long do you think that would take me to achieve this goal?. i'm a pretty quick learner, and always enjoy music. but i want to learn fast. what do you think i could accomplish in a year from now?