When Casey Ravitz graduated in June from Poly Prep Country Day School in Brooklyn, she’d spent 14 years in three different private schools in New York City. For eight of those years, she’d kept weekly appointments with a $100-an-hour Manhattan tutor.

“I had a lot of friends who were being tutored, too,” said Miss Ravitz, 18, an investment banker’s daughter who moved to Chicago in August to attend DePaul University. “My last tutor wouldn’t let me get away with anything. She was the most helpful person I’ve ever met.”

In New York, where tuition at some private schools will top $30,000 this fall, parents are spending thousands of dollars more on one-on-one instruction. Some teens need extra coaching — which can cost more than $500 an hour — to get through chemistry or Kafka. Others seek help to nab the A’s required for a seat at Harvard or Princeton universities, says Lisa Jacobson, 47, who started Manhattan-based Inspirica Ltd. in 1983 and now employs more than 100 tutors.

About 75% of private high school graduates in New York have had some tutoring, said Sandy Bass, editor of Private School Insider, a New York-based newsletter published five times a year. Rising demand for socalled homework help, which is distinct from prepping for the SAT college entrance exam, has led the city’s tutoring companies to add teachers and services.

Some are also jacking up prices. On Manhattan’s Upper West Side, Allison Baer, 32, who has a doctorate in psychology from Columbia University, charges $225 an hour for helping clients as young as 12 with writing skills. Miss Baer had more business in this year’s first half than in all of 2005, she says, and will raise her fee by 20% in October.

The boom in tutoring is powered in part by Wall Street bonuses, which have been at record levels in the past three years. Bankers at securities firms such as Goldman Sachs Group Inc. and Merrill Lynch & Co. cashed a record $21.5 billion in bonus checks last year, according to the New York state comptroller’s office.

There’s fierce competition for spots in elite high schools and colleges as the today’s teenagers create their own demographic bulge. From 2000 to 2004, the number of children aged 10 to 19 in Manhattan jumped 18.7% to 128,817, according to U.S. Census data. The city’s 87 independent schools, meanwhile, had 42,320 students in 2005, 11% more than in 2000, the New York State Association of Independent Schools said.

When it comes to pressuring kids to achieve in school, New York is the epicenter, said Lloyd Thacker, a former admissions officer at the University of Southern California and founder of the Education Conservancy, an advocacy group based in Portland, Oregon. “Tutoring is the symptom, and the fact there is so much of it says there is a sickness,” he said. “If past trends hold up, it’s likely to spread.”

Miss Ravitz, an only child who grew up on the Upper East Side, was first tutored as a 7-year-old at Trevor Day School on West 88th Street. By the time she graduated from Poly Prep, she’d had three more tutors. One helped with essay writing; another, called in when Ravitz was struggling in 10th grade French, steered her to B+’s in the class, she said.

“The tutors were able to help her to buckle down,” Miss Ravitz’s mother, Debbie Dunn, 52, says. Her daughter’s final Poly Prep report card, with two A-‘s and one B-, hung on Mrs. Dunn’s refrigerator as she helped her pack for college.

Many private schools have loaded their curricula with university-level courses that demand hours of homework from students every night.

At Horace Mann School in the Bronx, for example, an honors physics class that covers mechanics, thermodynamics, electricity and magnetism focuses on teaching students how to prepare scientific papers. At Saint Ann’s School in Brooklyn, one 12th-grade English class studies novels by Honore de Balzac, Fyodor Dostoyevsky, Henry Fielding, Vladimir Nabokov, Thomas Pynchon and Virginia Woolf.

“The pressure is real,” said Edith Spiegel, whose daughter, now 20, was tutored while attending the Dalton School on the Upper East Side. Mrs. Spiegel, 58, who taught in New York’s public school system for 29 years, said the stigma attached to tutoring when she was a child has faded. “When my friends got tutored, we thought of them as stupid,” she said. “Now, we need our kids to be as smart as they can be.”

Ivy League Tutors Inc., with offices on Manhattan’s Madison Avenue, has instructors trained specifically to help students at Riverdale Country School in the Bronx complete a single 11th-grade course, Constructing America. The class combines advanced placement material in both history and English, said Ryan Chang, 26, who founded the company three years ago and holds a bachelor’s degree from Columbia University in economics and creative writing.

About 16 kids used the service to get through Constructing America in the spring term, he says. Fall-semester students started booking in July.

Mr. Chang, whose instructors charge $125 to $250 an hour, said competition is driving growth for his business, which now has about 100 clients and 20 tutors. “Parents are worried that if they aren’t doing it, it’s a disadvantage to their student,” he said. Lately, he’s been turning away those who want to start their seventh-and eighth-graders on SAT preparation. The test is given in the 11th grade.

Individual instruction has ramped up all over America in the past five years, especially in California, Illinois and Texas, said Sandi Ayaz, executive director of the Lakeland, Florida-based National Tutoring Association. Her organization is based in a state where home-schooled students are spurring demand for tutors. NTA membership, which includes private tutors, companies and others involved in administering educational services, jumped 62% to 4,900 this year and has risen almost sixfold since 2001, Ayaz said.

In New York, the price and quantity of tutoring surpasses other regions of the country, she said. “New York is on steroids, as usual,” she said. Elsewhere, homework help goes for about $15 an hour from a college student and $25 from a graduate student.

Manhattan tutoring companies ratchet up their prices by offering extra services. Inspirica, which bills $225 to $525 an hour, offers seminars on school admissions and has three full-time employees just to deal with parents’ questions, Mrs. Jacobson said. Instructors are hired for their teaching ability, and trained how to behave professionally when they give lessons, whether in a client’s Manhattan apartment, on a yacht or in a vacation home in the Hamptons or in Europe, she said.

Brig Boonswang, 34, a former investment banker at Donaldson, Lufkin & Jenrette Inc., offers teens the use of a 42-inch flat-screen TV, one of Microsoft Corp.’s XBox 360 video game consoles and a fridge stocked with Red Bull energy drinks at his tutoring shop on East 95th Street. Some teens drop by four times a week and may stay hours beyond their one-hour, $250 session, he said.

Mr. Boonswang, who has a bachelor’s degree in mathematics from Columbia, began tutoring as a career in 2001 after talking to Stephen Spahn, chancellor of the Dwight School on the Upper West Side, at a cocktail party. Mr. Boonswang says he was unemployed after a Brazilian Internet company for which he’d helped raise $2 million went bust.

In April 2005, he was joined at Boonswang Group by Rachel Magid, 28, a 2004 graduate of Harvard Business School. The partners now employ 10 part-time tutors and aim to have the same number working full time and revenue of $3.5 million in five years. “The parents would rather us deal with the kids and the homework,” Miss Magid said.

Mr. Boonswang said his job is much more rewarding than banking ever was. Buoyant kids text-message him after receiving good grades and sometimes seek his support as late as 2 a.m., he said.