I will be babysitting soon and have no idea what to charge. The children are 4 and 7. It will be most likely 8-9 hours a day. 5 days a week and when school starts I was asked to take the boy to school and pick up. The school is about 2 miles from my home. Is there a hourly rate or weekly rate to go by?

Call a few daycare centers and see what they are charging. I was paying $110 per week 15 years ago for one child and I had to use my lunch and break times to go get my daughter and run her to and from school myself.

The cheapest full-time babysitting around here is 125 a week per child. One lady charges 175 a week for the first child and 125 for the second.

whatever you charge...first make sure that you are going to be comfortable with that fee...after it's set.. it's hard to change it...we watch our 4 grandsons in our home M-F (11+ hours a day) plus transport the eldest to and from school...give baths, do laundry, make sure homework is done and transport to swimming, football, soccer, baseball practices...if they weren't our grandkids...they couldn't afford us..for all we do.

Varies by where you live, whether these are relatives or friends or neighbors or just a job. If I was the parent, I would expect to pay less on a weekly basis than I'd pay for an evening (which is now about $6 per hour in my area.)
In California, you are supposed to have a license to care for more than two unrelated-to-you children in your home. Be sure you check your homeowner's (and auto, if driving the kids) liability insurance to see that you are covered in case of injury.

Ask other working mothers how much they pay for baby sitting such as what you will be doing. Get two or three answers, then sit down and discuss this with the parent(s) of these children. And I'd suggest that a signed statement that this sum is what is what all agree with.
And what about food, who pays what for that? Is either of them allergic to anything? Make sure that is spelled out.
What about emergencies? You should have some sort of signed statement allowing you to take them to a doctor till one of the parents can be located and come to where the child is.

Wow a lot to think over. I will call daycares tomorrow and check with insurance company as well.

If you are going to charge less that a daycare would, I would make it part of the deal that you still get paid even if they take a sick day, personal day or vacation day from work. That is what I did when I did home daycare. That way you still get paid if the children dont come. It worked well for me.

I did home daycare until last Dec for the under 6 crowd my rates were $450, the under 2 crowd was $575 a month. I didn't really take care of school aged children but before and after at the schools in my area provided by YMCA is $189. Check with your state for regulations. Good luck.

Get "it" in writing & you need to know what your state's laws are concerning being lisenced. Do you need to keep as many records as here in IL? Call some of the other ads in the newspapers, too. Home daycare may be at a different rate than someplace like Kindercare. I did home day care for 14 yrs.