You do not specify why you think it is wrong but I can se two dangers:
BETWEEN can be implemented differently in different databases sometimes it is including the border values and sometimes excluding, resulting in that 1 and 31 of january would end up NOTHING. You should test how you database does this.
Also, if RATE_DATE contains hours also 2010-01-31 might be translated to 2010-01-31 00:00 which also would exclude any row with an hour other that 00:00.