It is always a hard question for someone new to tutoring to decide what is a reasonable amount to pay. There are certainly people who have some ability, took the class and got a good grade who will offer a service. This is how I started out in high school. You can find people on Craigslist who call themselves tutors who will charge a relatively low rate. In many of these cases, these are essentially baby sitters who can do a little math and may even know less than the remaining public school instructors teaching the classes. There is a big qualitative difference between such a person and a subject matter expert (SME) who has invested his life in a topic and has additional counseling skills to help. If you hire a tutoring service like Tutor Doctor the service takes a large fee and the person delivering the service will typically bring home about $25 an hour from which they will pay self employment taxes and so make about what a deliveryman makes. Naturally you can’t get someone with high level and diverse mathematical knowledge to do this work (but you certainly can find someone to take your money!).
If you are pursuing the homeschool route and want to supplement your courses with regular meeting with such an expert you should expect to pay a professional wage. An independent contractor will certainly be giving you the best value for your money since there is no overhead administration and lower advertising costs.
UNC math and science students have been coming to me for help in Calc/Physics/Statistics/Differential Equations/Advanced Analysis and other topics that only someone with a couple of decades of experience could really help with in useful and insightful fashion. Sadly the tutoring centers generally consist of someone who merely survived the course and even your prof may be an adjunct without a great investment in the topic he is teaching and little availability.
In the Chapel Hill area, most professionals helping with students charge $60-$100 per hour. My current rates are $70/hr cash or $75/hr check or billing to trusts or accounts (or Venmo!). (Note: As of Sept. 1 the rates went up but established clients will be grandfathered at the old rate).
I do offer some sliding scales and even have pro bono for people in need. Considering the price for a private school education is $25K-$35K per year, having a once a week meeting with a subject matter expert is only $2700 at the full rate. This is a modest and local way to spend your money that gives your child time with someone with deep and passionate knowledge that is much cheaper than a private school. Another advantage of concentrated and focused learning is that it leaves you child more time for fun, play and outside time which builds their positive attitude and investigative spirit.
For independent learners at a higher level, like those studying formal logic, quantum mechanics, electromagnetism, number theory and other such topics, there are very few people with deep and long term knowledge available at all. To meet with and encourage such people is a great joy and privilege for me and one I would not really get in an academic position. I work extra hard to make sure such people get what they need and can afford it. If you are uncertain, please call and I will try to find an arrangement that works. We might be able to arrange the times to less busy ones for me at a discount so you can continue to grow in the ways that really matter.