District high school students can strike driver education from their fall class schedules because the Board of Education has scrapped the popular course to save money.

But while the school system will save almost $750,000 a year by cutting the program, parents will have to pay higher auto insurance rates for their teen-age drivers and the police department will face the annual loss of $1 million in federal funds.

The course is only one of the latest cuts the board has made to reduce its budget for the fiscal year that begins Oct. 1. More than a thousand staff positions, including 714 teacher jobs, 24 in driver's education, have also been eliminated.

Since 1965, most insurance companies have offered a 10 percent discount on car insurance to parents whose children pass a school's driver education course. That discount can mean savings of $50 to $100 for a family which carries the standard policy and whose child has a good driving record.

According to spokesman for the Government Employees Insurance Company (GEICI), the District's largest car insurance company, the standard policy for a District family with a 16-year-old son and one late-model car would rise from $712 to $811 if the child cannot take driver's education in school.

District residents whose children attend private and parochial schools also enjoyed the reduced rates if their children took the class on Saturdays or during the summer. Commercial driving school classes do not now qualify teen-agers for the discount, according to the Insurance Information Institute.

Since the driver education program was started 31 years ago, an estimated 110,000 students have taken the course, according to Frank Bolden, director of the school's physical education and safety department.

But parents aren't the only ones who will feel the pinch.

Before the school board voted to cut the program on June 13, city transportation officials warned that it could threaten almost $1 million in federal highway safety funds that the District recieves each year.

For the past few years, the city has spent more than half of those funds for a police department program to crack down on drunk drivers, speeders and jaywalkers. The strict enforcement program, officials say, was a major factor in lowering the city's traffic death rate to 50 fatalities last year, the lowest number since 1913.

Federal transportation officials said they were unsure whether the city would continue to receive the funds. Under law, jurisdictions that recieve the grants must have school driver education programs.

Aside from the financial implications, the program's demise also affects teachers and students.

"I think they did an injustice when they cut the program because a lot of these kids are not going to college and they need to know how to drive to get a job," said Virgil White, 69, who has put more than 2,000 youths behind the wheel since the start of the program.

"This is no frill," he added. "A lot of these parents don't want to teach their kids" and when they do, they teach bad habits, he said.

White started in driver's education with 40 students and a World War II vintage Ford with a manual transmission.

Last year at H.D. Woodson High in (Northeast, White was one of three instructors who used sophisticated driving simulators equipped with dashboards, brakes, steering wheels and signal lights. Students were shown films to simulate driving and learned to make turns, pass other cars, accelerate, stop suddenly and park.

An adjoining room held 40 computer terminals that posed driving problems to students and let them enter the answers. Incorrect answers were then explained.

The teachers had two cars -- a 1980 Pontiac Grand Prix and a 1980 Honda.

The board's decision will leave the school system with more than $600,000 worth of equipment that has been installed, at federal expense, in most city high schools over the last 10 years.

Even as the board was dismantling the program in June, workmen were installing $100,000 worth of new driving simulation equipment at Roosevelt High School, according to school officials.