My 14-year-old babysits. She is CPR certified and has taken the babysitting course through Central DuPage Hospital. She doesn't actually have a set fee she charges. She takes what she gets, and people pay her between $5 and $10 an hour, depending on the number of kids.
Once she is older and can drive herself, I think people will pay her more. The going rate around here really is $10. I paid that years ago when I had babysitters for her. I always believed that if you paid well, sitters would keep coming back... and that way I always had a sitter if I needed one. I never did have a sitter tell me what she charged. They always took what I gave them.
I think $10 sounds a little steep for a 13-year-old. I think $8 sounds more reasonable.