Indeed, this year’s tuition at Columbia Grammar and Preparatory ($38,340 for 12th grade) and Horace Mann ($37,275 for the upper school) is higher than Harvard’s ($36,305). Those 41 schools (out of 61 New York City private schools in the national association) provided enough data to enable a 10-year analysis. (Over all, inflation caused prices in general to rise 27 percent over the past decade.)

The median 12th-grade tuition for the current school year was $36,970, up from $21,100 in 2001-2, according to the national association’s survey. Nationally, that figure rose to $24,240 from $14,583 a decade ago.

With schools already setting tuition rates for the 2012-13 school year — Brearley’s is $38,200 — parents at Horace Mann, Columbia Grammar and Trinity are braced to find out whether they will join families at Riverdale Country School in the $40,000-a-year club.