The annual cost of an undergraduate education at Harvard will break the $20,000 mark for the first time next year, buoyed by a probable 5 to 7 percent tuition hike, a University spokesperson said yesterday.

Director of News and Public Affairs Peter Costa, who gave the estimated increase in an interview last night, said that exact tuition figures would probably be released March 16.

Undergraduate fees for tuition, room and board and health charges totaled $19,395 for this year. A 5 percent increase over last year's $12,715 tuition would bring the total figure next year to $20,030, excluding expected increases in nonacademic costs.

The estimated range for Harvard's tuition increase would not vary much from that of the last two years. Tuition increased 6.5 percent for both the 1988-'89 and 1989-'90 academic years.

At many other universities, tuition increased at a lower rate than in any of the last 15 to 20 years, but the price hikes continued to be well above the inflation rate.

David Merkowitz, a spokesperson for the American Council on Education, said he sees "a recent moderation in price increases" among the nation's colleges, as tuition growth comes "back down closer to the historical pattern of a couple of percentage points higher than general price increases, which has been true for 50 years or more."

Tuition at the University of Pennsylvania will climb by 6.7 percent, Brown and Dartmouth by 6.4 percent, Columbia by 5.7 percent and Stanford by 5.5 percent, officials at those schools said. These rates of increase all represent the lowest in the last 15 to 22 years, they said.

Partly in response to last year's tuition increases of around 8 percent, many college officials said they resolved to curb administrative costs in order to minimize student expenses this year.

Universities have also faced increasing opposition from students and government officials for perennially increasing tuition costs at a significantly greater rate than inflation.

In the midst of increasing public wariness of colleges' financial practices, the Justice Department last summer began an investigation into alleged anti-trust violations at 56 of the nation's top universities. The government is reportedly investigating whether colleges collude in setting tuition and financial aid packages.

Despite the public outcry and student opposition, some colleges have announced that their costs to undergraduates will shoot up at a rate similar to or greater than last year's.

Tuition at Princeton University will continue to climb at a rate of 6.4 percent, the same as 1989-'90. And MIT announced yesterday that its tuition would go up 7.1 percent, only slightly lower than last year's 7.2 percent.

Cornell University and Yale University are the only two members of the Ivy League that have announced plans toincrease the rate at which tuition grows. Cornellofficials said that that tuition will rise between7.1 and 8.6 percent, up from its 6.9 rate lastyear. And yesterday Yale announced plans to raisetuition by 8.4 percent, its highest jump in atleast the last four years.

College officials said the continued *** wascaused by escalating expenses and cuts in federalsupport for education.

"Tuition rates have risen faster than inflationbecause all of our major expense items--facultysalaries, student financial aid, libraryacquisitions and facility maintenance--have beenrising faster than inflation," said ColumbiaUniversity Provost Jonathan R. Cole