Prince George's County officials, who have struggled for 13 years to come up with a plan for desegregating their schools that a court would approve, are now faced with a fiscal predicament that may well become an annual challenge: They have to find the money to pay for the solution.

Prince George's School Superintendent John A. Murphy's magnet-school plan has won the general support of the school board, parents, the NAACP and, at least tentatively, U.S. District Judge Frank A. Kaufman.

And local and state officials are optimistic about their ability to marshal the $8.7 million needed to start the program this fall.

Mention the four years after the first one, though, and they become less sanguine. Prince George's, which has a legal cap on its property-tax rate, can only hope to pay for desegregation by turning to the state and federal governments, officials said. The cost of the five-year plan, Murphy has said, could be $30 million.

For the first year, school officials hope to get $4 million from a federal magnet-school grant. About $1 million will come from parents whose children use the schools after regular hours, at a cost of $27.50 a week. The rest will come from county coffers, though county officials think they can get reimbursed from the state.

County officials are allocating county money to set up the program on the assumption that the cash spent will be returned to Prince George's coffers in the form of increased grants from the General Assemly.

"I truly and honestly believe that these are not monies that should be borne by the people of Prince George's County," said State Sen. Thomas V. Mike Miller Jr., the head of the county's state Senate delegation.

But it is unlikely, he added during an interview last week, that state legislators who are facing reelection battles in their home districts next year will be eager to come up with money for the five-year program, which will benefit only one jurisdiction.

"It will be very difficult to obtain the money from the state, and if we do, I think the only way we'll be able to is on a year-to-year basis," Miller said.

Speaker of the House Benjamin L. Cardin is more optimistic about the chances of longer-range funding for the county's schools. "If [Prince George's elected officials] have a united delegation, then I think the chance of state aid is high," Cardin said recently in an apparent reference to the county delegations' occasional differences with the Glendening administration.

"Education funds have always been a partnership with state and local funding," Cardin said. Prince George's, he said, could benefit from a revision of the state education aid formula that would provide for a special payment to Prince George's much as it now does to the city of Baltimore.

The dollars needed, he said, "although substantial, are not substantial in [the context of] the state budget."

Murphy has proposed establishing six schools the first year geared to talented and gifted students, and six others offering before- and after-school day care, hoping to attract students from throughout the county. School board members have said the magnet plan will go forward, though they may appeal the federal desegregation order that prompted the proposal.

School officials estimate the plan's cost by using a formula of other school departments across the country. Under that yardstick, the cost for magnet schools averages about 10 percent above normal per-pupil expenditures, once the magnet program is in place, according to Edward M. Felegy, an assistant school superintendent.

In Prince George's, where an average of $3,040 is spent annually on each student in the 105,500-student system, that would mean added expense of about $400,000 for the nearly 1,400 students who are expected to participate the first year.

John Wesley White, the county's chief administrative officer, said that costs after the first year will have to be nailed down more firmly before the county can appeal to the state for money. Miller agrees.

"You can't commit to long range funding for something that is in its embryonic stages," Miller said.

Even traditional adversaries of the school superintendent and school board acknowledge the fiscal difficulty the system now faces.

"At the moment they have zero money," said Paul Pinsky, president of the Prince George's County Educators Association and a supporter of the magnet concept. County teachers, he said, who have long complained about low pay and large classes, cannot afford to begrudge anyone the money to be spent on desegregation.

"We need many millions of dollars," Pinsky said. "To fight over half a million dollars [here or there] is like people fighting for the last crumbs on a sinking ship."