I think $12 an hour is very reasonable... I have paid about the same and even less for sitters and I have 2 boys 1 and almost 3. If you sitter is OK with it dont rock the boat. If you want to give a Christmas bonus, maybe that is the way to go...
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Also..just to put it in perspective, she is likely doing this for extra income and not as her only source of income (otherwise she would need to work full time). Take into consideration her skill set, education, and the service she provides. She would only make $8-9 if she worked at McDonalds. $12 an hour is equivalent to $25,000 a year (if full time). So you pay about $6000 a year for your nanny.
I know a lot of responses said they pay more, but i think it depends on you and your family income - paying that kind of money out of your take home pay is a lot (unless you or your husband make REALLY good money).
I think being fiscally responsible is important and if you can afford $12 and your sitter is making some money to contribute to her family, I think it is a good for both of you. Dont let other people pressure you into paying too much. Talk to your nanny about it, or offer her a raise or bonus every year - perhaps that will also incentivize her to stay with you longer.
Good Luck