Élite high schools
Which schools raise the scions of the English aristocracy, Hollywood film stars or Russian oligarchs? Britain is the cradle of the boarding school. Some of these are very prestigious - and very expensive. A year at Eton, which educated several UK prime ministers (including the current one, David Cameron) and government ministers will set you back 32,000 GBP.
Other famous names from around London include Harrow, Charterhouse, Rugby and Winchester. But you can find élite schools in every region of the UK. For example Scotland has Fettes College in Edinburgh (where another recent PM, Tony Blair, was educated). Another highly prestigious school in Scotland is Gordonstoun, linked to several members of the royal family. Exceptionally, this one is actually not a very old instition, it was founded in the early 20th century by the same person who founded the prestigious Schule Schloss Salem in Germany (see below).
UK boarding schools don't cater just to the British. For example ever since Boris Yeltsin sent his grandson to Eton, sending their offspring to UK schools has become something of an obsession among the Russian top politicians and businessmen. Incidentally, this is one reason why diplomats joke that relations between Russia and the UK can never become too icy - that's hardly possible while half of the Russian élite keeps their children in the UK. The oldest or the most expensive of course doesn't automatically mean the most academically productive. If you look at the ranking of UK independent schools by the daily The Independent based on A level results (UK diploma exams), you will see that the most prestigious schools have actually been overtaken by many lesser known ones. However, the old schools still do provide some of the best education in the world. They also tend to attract high calibre teachers, whom they pay very well. And not just the teachers. The headmaster of Eton, for example, has a salary higher than the prime minister.
You can find many expensive boarding schools in the US as well, even though their tradition is not as long as that of their British counterparts. Probably the most famous is Groton School in Massachusetts, which also nearly tops the list of the most expensive schools.
However, if you are looking for the most expensive high school of the world, you need to head back to the old continent. The Swiss Institut Le Rosey collects an annual 99,000 CHF per pupil (82,000 euro). Slightly less expensive are other Swiss super-schools: Collège Alpin International Beau Soleil, Aiglon College or Geneva's Collège du Léman.
Interestingly, even though neighbouring Germany has a tradition of very good state schools, it also houses one of the most élite private schools in the world, Schule Schloss Salem, whose graduates include many members of European aristocracy as well as several famous intellectual figures. The school was founded by the educator Kurt Hahn, who also founded Gordonstoun in Scotland and later was one of the initiators of the project of United World Colleges, the association of highly international schools scattered around the globe.
You don't always have to be stinking rich to study at these places. Especially some of the top British boarding schools also offer relatively generous scholarships and thus enable a few of the lucky and bright ones to rub shoulders with the royalty.