The trustees of George Washington University yesterday approved a 24.5 percent tuition increase for next fall, a record boost that officials said was necessary to offset a growing deficit.

The increase, which will raise annual tuition to $6,100, was approved despite vocal protests by students. But officials said the university would help students pay the higher bills by substantially increasing grants and loans.

George Washington also will establish a prepayment plan to protect students against future tuition increases if they pay for all four years of college in advance.

The bill for that would be $24,400 next fall.

"We had to raise tuition because we just can't let this deficit situation continue without threatening the long-term health of the university," said budget director William D. Johnson. "We don't like to do it. But frankly, even with the increase, when you look at our tuition rate in comparison with other similar private universities, you see that ours is still at the low end of the spectrum."

With room, board and other expenses, the total cost for a year at GW is expected to reach about $11,000 next fall. It already costs that much to attend American and Georgetown universities and more than $13,000 a year at the highest-priced private universities, such as Harvard and Stanford.

George Washington is the first private university in the Washington area to set tuition for next year. Last month, the University of Maryland announced its tuition would go up by 13 percent to $1,128 for state residents and $3,523 for out-of-staters.

Johnson said an unexpected 5 percent drop in George Washington's enrollment last fall was the principal reason for the university's deficit, which has reached $6 million in the non-medical part of the school. But he said even with a decline in college-age students and a slack economy, he expected next fall's enrollment drop to be held to 3.6 percent.

Thomas Mannion, president of the university student association, said he feared the enrollment loss would be greater than that because "more students will be priced out."

"Even if they make more loans available," Mannion said, "I can see a lot of students switching to state schools where they can get a pretty good education for a lot less money."

At George Washington's medical school, the trustees voted to reduce first-year tuition by $250 next fall from the current rate of $19,000, the highest in the nation. Second-place Georgetown medical school charges $17,500.

Despite its high price, Johnson said George Washington was having no difficulty attracting high-quality medical students and that the school was operating in the black.

Despite George Washington's financial crunch and a national inflation rate of about 5 percent, the university's new budget includes 8 percent pay raises for employes and about $1 million to fill faculty vacancies and add programs and computers.