Private U.S. colleges, worried they could be pricing themselves out of the market after years of relentless tuition increases, are offering record financial assistance to keep classrooms full.

The average "tuition discount rate"—the reduction off list price afforded by grants and scholarships given by these schools—hit an all-time high of 45% last fall for incoming freshmen, according to a survey being released Monday by the National Association of College and University Business Officers.

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