Well if the family posted an actual hourly rate, not a between x-y dollar amount, etc., then I would just assume the rate posted was all that they were willing to pay regardless.
I wouldn't apply for that position unless you are willing to work for less than what you usually work for.
I highly doubt someone will meet an amazing nanny, then up the pay rate because she was so incredible. Even if Mary Poppins herself flew in w/her umbrella I don't see this happening.
I don't think it is a good job for you already due to the lower pay rate. If I was you, I would keep searching.
Good luck!
