How to convince my parents to send me to boarding school?

I really want to go to this boarding school about two hours away from where I live. The problem is, whenever I ask, my parents shoot me down immediately. They say that 1) it's a lot of money. Yes, I understand that, but there's always financial aid. While we're not poor, my family doesn't exactly have $50,000 lying around 2) There's nothing wrong with the high school in my district. Yes, actually, there is. With budget cuts and a high student population, I can't exactly get one on one attention, which is what I need. The classes are pretty good, but with boarding school I get can get as much help as possible because of small class sizes. 3) It's too far away and we can't come and save you every time you need us. I also understand this. Being away from home helps me to become independent and not to always rely on my parents.

No matter what I say (including the things written above), they never even consider boarding school. Not even for a second. All I really want is my best shot, the chance to apply. Grades and intelligence are not a problem and I feel very confident that I could pass the SSAT to get in. I have not harassed my parents about boarding school, but I have researched it and mentioned it multiple times and I really think they're going to yell at me any moment for doing so. Any ideas on how to get them to consider letting me apply and, if I get in, (hopefully) allowing me to go?