How do i convince my parents to get me violin lessons?

I'm 13 and I really want to learn how to play the violin. I love the sound that it makes, so I got some information on where to buy one and get lessons. But when I told my mom about it she said $75 an hour is too expensive for lessons and she doesn't want to be paying that kind of money for something I'll get no benefit out of. She says that if I invest that money in an academic program, or a drama cl to improve my self-esteem or athletics it would be ok. However, she wouldn't spend that money on an instrument especially since it won't help me later in life. I told her I could be committed to it and practice everyday. She says I should be committed to school and take an instrument in college.There's still my dad to convince and he's a little bit more supportive but I'm afraid of his reaction to the price. How do I at least convince him?