Hearts have broken across New York this week, and not by Valentine’s Day dates gone bust. New York City private schools have been sending out notifications -- yes, no and the dreaded wait list -- and by many accounts, it has been a tough year to win a coveted seat at some of the city’s top schools.

But for those who have, there’s a downside to victory: the bill. As we predicted a few weeks ago, tuition numbers are topping $40,000 at some schools, whether they present it that way or not.

Topping the charts, once again, is Riverdale Country School, where prekindergarten to grade five will cost $40,750 and grades 6 to 12, $42,000.

“Riverdale is beautiful, and we love the school,” said one mother whose daughter was admitted for kindergarten. “But is it $45,000 beautiful? It’s a lot of money.” (She and her husband are still trying to decide between Riverdale and their local public school.)

At the Ethical Culture Fieldston School, tuition came in just under $40,000, at $39,525. But that number doesn’t include books for students in the middle and upper school, putting the real tally above $40,000.

At the so-called Hill schools in Riverdale, there’s another not-included expense: busing. At Riverdale and Fieldston, transportation runs between $2,000 and $4,000 a year per child, depending on where families live.

Manhattan does not appear to be brimming with bargains, either. At Columbia Grammar and Preparatory, where prices include all fees and books, the scale starts at $38,190 for prekindergarten and rises to $40,140 for 12th grade.

Bad as the numbers may seem, some heads of school are emphatic that they are trying to cap costs. Dominic A.A. Randolph, Riverdale’s head of school, said that tuition increases have moderated in the past two years, with increases of only 4 to 5 percent. In the 1990s and early 2000s, that figure was 6 to 7 percent a year.

“Since we are a tuition-driven school, the increase is correlated directly with increases in faculty salaries, benefits, financial aid and the running of a large school facility," he said. (Read here Mr. Randolph’s breakdown of how one tuition dollar is spent.)

Damian Fernandez, the head of Ethical Culture, said the price increase at his school was the lowest percentage increase in more than a decade. He also said that the school has been trying to cover costs in the tuition for items like school trips.

The tuition at some schools skated in just under $40,000. At Trinity School, kindergarten to eighth grade will cost $38,810; 9th to 11th grades, $39,125; and 12th grade, $39,625 (fees of $1,700 for lunch, $75 for the Parents Association and $500 for graduating seniors are included).

And then there were those that looked good at first -- relatively speaking, of course -- until you did the math.

At the Chapin School, tuition will run $36,500 for the 2012-13 school year. But that number doesn’t include fees and books, which can run between $1,300 and $4,600. If books are $4,600, the total costs come to $41,100.

Chris Palmer contributed reporting.