Colleges and universities announce a certain price for tuition, but based on financial aid calculations, they often charge a lot less. The difference is the "institutional tuition discount rate." The National Association of College and University Business Officers (NACUBO) has just released a report with the average discount rate for 2015-16 based on a survey of 401 private nonprofit colleges (that is, not including branches of state university systems and not including for-profit colleges and universities), along with and how that rate has been evolving over time.
The two lines in the figure imply that the level financial help a student receives as a freshman, when making a choice between colleges, is going to be more than the financial help received in later years. Beware! More broadly, a strategy of charging ever-more to parents who can afford it, while offering ever-larger discounts to those who can't, does not seem like a sustainable long-run approach.