How can I persuade my parents to let me buy a Blackberry Curve 8520?

I'm 13 and i've had my old phone (an LG KC550) for a year now, so therefore I would really love a Blackberry Curve 8520. So i've found a good contract for it, and showed it to my mum, and consequently, she said no, I can't buy it. When I asked why, she said because my sisters 18 and in University, she's got a Blackberry, so she thinks that it would be stupid letting me buy one in comparison to my sisters age. So now i'm wondering how can I persuade my mum to let me buy the Blackberry with my own money...