How do I convince my parents to let me go to a boarding high school?

I have been working on trying to convince them for about a year, now. I am in 8th grade now. They are letting my little sister go to boarding school because she's "too smart" for every nearby day school. She doesn't even want to go to boarding school unless I go with her. But I know I'm not smart enough to go to Mary Baldwin College. I need to convince them ASAP because application deadlines are almost here. But, they won't let me even apply and turn down an acceptance. I also can't go to the school that is a LOT cheaper than MBC, but also 1/2 an hour away from MBC. What do I do? How do I convince them that boarding school is what's best for me?