I used to be open 24/7. I've dropped basically down to 24/5 with the exception of a few existing clients. I charge hourly. I charge the same hourly rate whether the child is 4mo or 4 years, 8 months or 8 years. It's just easier. As far as the minutes thing goes, I round down to the lower 15 minute increment at drop off and up to the next 15 minute increment at pick up. If child is dropped off at 8:35 and picked up at 3:10, he is clocked at 8:30 and 3:15.
Figuring the quarter hours isn't too challenging. I use a calculator.
I also have it in my contract that I round to the nearest quarter. So, if I have a day that adds to $13.875, it's $14. I've been doing it this way for 2.5 years.
Not sure what the norm is in my area for other providers' pay, whether its hourly, daily or weekly. This works for me.
Also, parents don't pay if the child isn't here, as long as I have 24 hour notice that they won't be here. I have had a few that have the mentality "well, I'm paying for it, might as well use it." This is also part of the reason I do hourly pay.