Want to tutor younger kids, will their parents let me?

I have been thinking of starting up a small tutoring business instead of getting a part time job somewhere. Just like posting up a brochure or advertisement with my name and number. I am a straight A student and have helped a lot of my fellow high school students... especially in math. I am even in an Advanced Program; but for some reason, I don't think parents would want me to tutor their kids. I don't think i could guarantee them improving in anything because it all depends if the kid really wants to learn and pay attention. Places like Sylvan say that if they could to Sylvan they will improve in one grade level, but Sylvan cost 40$ an hour and they could just be saying that to get people to go. I would only charge 10-15$ for hour and say if they wanted 10 sessions it would be a bit cheaper. Do you think those are good rates? If you have a kid would you consider it? Or to anyone that doesn't, do you think that this is reasonable? I am aiming for grades 4-7.