The total cost for a year at Georgetown University will climb this fall to about $8,500 -- the highest in the Washington area, but much less than the $10,550 cost at Harvard, the nation's most expensive university, according to a report issued yesterday.

Throughout the country, average total costs for students at private four-year colleges have gone up 10.3 percent from the last academic year, the College Board reported. The board is an association that coordinates entrance exams and financial aid applications at colleges across the United States.

The figure is less than the country's 14.4 percent inflation rate over the past year but considerably more than the average 8.1 percent cost increase at public universities, which are keeping tuition and other student costs relatively low through government subsidies.

For example, at the university of Maryland costs for in-state residents living in dormitories at College Park will rise by only about 5 percent next fall to an estimated $3,742. The bill includes $884 for tuition, $2,150 for room and board, and an estimated $750 for books and personal expenses.

At the University of the District of Columbia, tuition and required student fees will rise to $199, an increase of $30 or almost 18 percent but still by far the lowest in the Washington area.

All of UDC's students are commuters. Their total cost for attending the college, including transportation, books and food, will come to an estimated $2,122, according to the college scholarship service, a branch of the College Board that compiled the new statistics.

In the Washington area, the estimated total costs for students living in dorms at other colleges are as follows: American University, $8,277; Catholic University, $7,300; George Washington University, $7,050; Howard University, $4,700; and University of Virginia, $3,800.

The totals include estimates for five basic items: tuition and fees, room and board, books and supplies, transportation, and personal expenses.

In contrast to the $199 charged at the University of D.C., tuition and fees at the area's other mainly commuter colleges are: George Mason University, $888; Montgomery Community College, $792; Prince George's Community College, $470; and Northern Virginia Community College, $342.

At the public colleges, all the figures are for students living in the county or state where the college is located. Usually, non-residents pay much more. For example, the extra charge for non-D.C. residents next fall at UDC will be $1,250.

The figures in the report are used for computing grants and loans under scholarship programs. They will be published in September in a College Board publication "The College Cost Book," which can be used by prospective students for comparison shopping.

Kenneth Kohl, financial aid director at Georgetown, said that despite its relatively high cost, Georgetown had more applications than ever this year for its freshman class.

Through loans, jobs and grants, Kohl said, the university can make sure that every student admitted can afford to attend. But with costs rising, he said, loans are getting larger and students are expected to earn more during the summer and at part-time jobs during the school term.

Whether a student actually attends a particular university still depends, only partly "on what a family thinks they can pay," said Kohl, who is a former associate U.S. commissioner of education for student financial assistance.

"The other factor is the educational respectability of the institution," Kohl said, "that intangible -- the quality of education. That's why Harvard has no trouble getting 10 grand."

According to the new College Board report, Harvard's undergraduate tuition next fall will be $6,490; room and board, $2,680; and books, transportation, and other expenses, an estimated $1,380.

The only other college in the report that surpasses the $10,000 figure is the school of engineering at Columbia University, which will cost an estimated $10,240.

All other Ivy League colleges will cost close to $10,000. Others costing more than $9,000 include Johns Hopkins, Boston University, Sarah Lawrence, and the Massachusetts Institute of Technology.

Altogether, 28 colleges out of the 3,200 included in the College Board survey will cost more than $9,000 next fall. All 28 are private institutions. s

Overall, the four-year private college reported anticipated average expenses of $6,082 for dormitory students, compared to just $3,409 at public four-year colleges.

Among two-year colleges, the private ones average $4,592 in total costs for dormitory residents, compared to $3,123 at colleges that are publicly-supported.

The cost of commuting to all types of colleges averages from $400 to $700 less than living on campus.

Richard Dent, executive director of the college scholarship service, said that despite their higher costs "the good private colleges still are attracting large applicant pools." But he added: "There are signs that things are starting to slow a bit and will slow some more in the next few years."

Both public and private colleges, he said, managed to hold cost increases below the rate of inflation by limiting pay raises to their faculty and other employes to about 7 or 8 percent, and also by postponing maintenance or dipping into endowment.

"A lot of them are doing everything they can to hold down costs," Dent said, "but it's hard."

According to a national survey by Alexander Astin of the University of California at Los Angeles, students and their parents pay on average 56 percent of all college expenses. The remainder comes from government and private financial aid programs, including loans, which have grown sharply in the past year as federal guarantees and interest subsidies have expanded.

Nationwide, student aid totaled $14 billion during the past academic year, the college board said. Only 19 percent of it came from private grants.About 17 percent was from government-guaranteed loans, 7 percent from state aid, and the remaining 57 percent from U.S. grants.

Eventually, the federal government may well put a limit on education benefits," Dent said, "and that's going to cause a serious problem."

If college costs increase over the next decade as rapidly as they have since 1970, expenses at the high-cost colleges will approach $20,000 a year by 1990, the scholarship service predicted.