Officials at George Washington University, responding to protests against a proposed sharp increase in tuition, have come up with a plan to protect students against any future tuition increases: Pay four years in advance.

The plan, similar to ones already in effect at a small number of private colleges, would require a payment of $24,400 next fall -- four times the proposed yearly tuition of $6,100.

To make such a lump sum affordable for middle-income families, GW president Lloyd Elliott said, the university is trying to make arrangements with other colleges in the District to sell tax-exempt bonds to raise money for student and parent loans at below-market rates.

At present no other college in the Washington area offers such an advance payment, guaranteed-tuition plan, and yesterday none said they have plans to do so. But officials at George Washington said they thought it might be helpful to students who can't qualify for need-based financial aid -- now about half of GW's student body.

An advanced payment plan was originally proposed by the George Washington University Student Association, which yesterday praised Elliott's proposal even though it was slightly different from their own.

"You can call it a victory. You can call it appeasement. But we think it's quite monumental," said Marc Wurzel, a junior who has been one of the leaders of the protest against a tuition increase.

At a meeting Thursday, Elliott and other senior administrators who make up the university budget committee also agreed to scale down next fall's proposed increase from $1,250 to $1,200, which is still a 24.5 percent hike.

The increase and the advanced payment plan now await formal action by the university's board of trustees, scheduled for mid-January. The trustees are expected to approve Elliott's recommendations.

Officials said the sharp tuition increase is needed to help erase an operating deficit of $6 million since 1981 that was caused partly by an unexpected 5 percent drop in enrollment.

Robert Shoup, a GW budget officer, said a guaranteed tuition paid four years in advance might be attractive to parents if they thought tuition increases ahead would be greater than what they could earn from money market funds, which now pay about 8.5 percent, or some other investment.

"A great deal depends on what kind of interest rate we might be able to arrange on loans," Shoup said, "and what the tax implications of that are."

At Washington University in St. Louis, the first college to offer an advance payment program four years ago, about 10 percent of undergraduates use the plan. Most of them get loans, which the university offers from its endowment at 13 percent, said Robert Leider, author of a widely used guide on student aid. However, at the University of Southern California, which helps to arrange loans at commercial rates, just one percent of students use the plan.

Leider said guaranteed cost plans have also started recently at Case Western Reserve University in Cleveland and at Averett and Lynchburg Colleges in Virginia. Earlier this week Brandeis University near Boston announced it would offer such a plan next fall.