The cost of a college education in the Washington area--already painful to many parents and students--continues to soar despite a slowdown in inflation and cutbacks in federal student aid.

At Georgetown University, the area's highest priced college, undergraduate tuition and required fees will reach $6,890 next fall, up 18.6 percent from the past academic year.

With room, board, books and incidental expenses, total costs for a student will top $11,000 a year, Georgetown officials say. For the class of 1986, which enters in September, costs may reach $50,000 for a four-year bachelor's degree, a figure already exceeded by Harvard, Stanford, and a few other high-cost, high-prestige private institutions.

Four other universities in the Washington area--American, Catholic, George Washington, and George Mason--also have set tuition increases from about 17 to 21 percent.

At the University of Maryland and Howard the boosts are a more modest 10 and 11 percent, though they are still far above the 6.6 percent inflation increase over the past 12 months, as measured by the Consumer Price Index.

Across the country, double-digit increases in college tuition are common, according to The Chronicle of Higher Education, with increases at many colleges topping 15 percent. Although data is still incomplete, officials of the College Board said average increases nationwide may match last year's record of 13 percent for private institutions and 16 percent for public ones.

"Even though parents and students may not believe it," said Richard Berendzen, president of American University, "most of us really tried to be benevolent and we didn't increase [charges] adequately during the the very high inflation of the late 1970s. Now we have to catch up."

In addition, at some public colleges, including those in Virginia, increases in what had been relatively low tuitions are part of a deliberate policy to shift a higher proportion of costs onto students and away from taxpayers.

At many private colleges part of the increase is an effort to raise more money from well-to-do students to provide scholarships for needy ones, particularly because of cutbacks in federal aid.

"You might call this the Robin Hood approach," remarked Charles A. Deacon, admissions director at Georgetown where the university's internal scholarship funds are increasing 27 percent. "You charge more to those who can afford to pay and plow some of it back to help the others. But obviously that has its limits."

Overall, appropriations for federal aid programs are being cut 5.4 percent next fall after several years of dramatic growth. Subsidized loans will be limited to demonstrated need for families earning over $30,000.

The cuts are modest, but when coupled with higher tuition, they have increased the financial pinch of going to college, particularly for middle-income students at high-cost private schools. Also, fears that the cuts might be much greater--fanned by the heated and so far successful opposition to Reagan administration proposals for 1983-84--may have an impact on where students go to school.

So far, though, there have been just slight changes in applications and enrollment forecasts for the fall, but to some college officials the trends are worrisome.

For example, at Catholic University, where tuition is going up 17.3 percent to $5,870, applications increased 4 percent, but deposits by freshmen planning to attend are down 4 percent, compared to last year.

"The number of high school graduates is down[because of population changes] and we planned on a slight decline," said Robert Talbot, the university's admissions director. "But it's a struggle to get those deposits. I'm afraid there are a lot of students who may change their minds and go to less expensive schools."

George Washington, American, and Trinity also have smaller proportions of accepted students who say they plan to attend, though both GW and American say the quality of the students, as measured by college entrance exams, has improved.

Conversely, relatively low-priced public colleges, such as the University of Virginia, George Mason, Montgomery College, and Prince George's Community College, report a substantial increase in both applications and acceptances.

According to a Chronicle of Higher Education survey, private colleges across the country have received about 2 percent fewer applications than a year ago and public ones about 2 percent more.

Even with substantial increases, tuition at public colleges remains low because of large government subsidies. For example, at the University of Virginia, tuition will be $1,350 for state residents after a 17.8 percent increase. For nonresidents after a 23.8 percent jump it will be $3,276, still $2,000 to $3,500 cheaper than comparable private schools.

Tuition at Northern Virginia Community College is going up 45.3 percent, but at $558 a year, "It's still very reasonable," said NVCC Dean Cecil W. Shuler.

At Prince George's Community College in Maryland tuition for full-time undergraduates will be unchanged at $710 after a 21.7 percent increase last year. The University of Maryland and the state's public colleges will have tuition raises of about 10 percent after increases last year of 21 to 24 percent. But public colleges in some other states, caught in financial crises, will have much steeper tuition rises--25 percent in Minnesota, 46 percent in Idaho, and 54 percent at the University of Washington.

Despite tuition boosts elsewhere, the area's lowest-priced college, the University of the District of Columbia, is planning no increase in its $364 charge for city residents. Last fall UDC raised tuition 83 percent, but this year, the city budget is absorbing all cost increases.

Paradoxically, at Georgetown there has been a slight drop in the number of applicants requesting financial aid despite the steep rise in tuition. Admissions director Deacon said this may have occurred because some low-income students were scared off by Georgetown's cost. Another possible explanation, he said, is that some middle- and upper-income students thought aid would no longer be available for them and that asking for it might hurt their chances for admission.