We paid $50 per day (not hourly, but averaged 8-9 hours/day) for 1 child. Now that we have 2, we pay $75 per day.
Athough it was a daily rate, we agreed from the beginning that this was for a standard workday - basically between 8AM and 6PM on weekdays, although the exact number of hours varied day by day. If it was outside of those times we paid $10 per hour. So, for example, if she worked 9AM-7PM because of a late meeting, we paid $50 for the day plus an extra $10 for staying an hour past 6:00.
We also agreed in advance that if we cancelled her for the day, we still paid her (because it wasn't her choice that she didn't work that day). If she cancelled on us for the day, either in advance or at the last minute due to illness, then we did not pay her (because we had to pay for backup childcare).
ADDED: There is a big difference between you and a daycare center. Centers are often open longer hours, they have back-up childcare on-hand, so if a teacher calls in sick, someone else steps in and the parent doesn't have to have her own backup plans. Daycares usually provide a structured curriculum (mine even has a curriculum for the infant room). They are licensed and accredited. They have toys, cribs, and other baby gear on hand, and don't ask the parent to provide it. They have to buy very expensive insurance. So yes, there are a lot of reasons why daycares are often more expensive than a nanny. I'm also guess that $289 per week was for 5 days, and you are only taking care of the baby 3 days.
And, the question you didn't ask the daycare - how much do they pay their teachers? They may charge $289 per week, but I can guarantee the childcare providers who work there don't bring home $289 per week. Even those who have have in-home daycares don't actually make the full amount that they charge, because they too have other administrative expenses. Likewise, even a nanny, which is often through an agency, has to pay the agency a fee.