CAMBRIDGE, Mass. — Harvard University has received a record 39,044 applications for next fall’s freshman class, a nearly 5 percent increase over last year. The university attributed the rise to efforts to reach out to lower income students. This year, nearly a quarter of applicants had their application fees waived due to financial hardship. Director of Financial Aid Sally Donahue said applications have soared in the past decade since the university launched a financial aid program that charges students based on family income. A fifth of current undergraduates are from families earning less than $65,000 a year.