The cassette tape was part of a lot of Beatles items put up for sale by Bruun Rasmussen Auctioneer in Copenhagen, along with 29 still photos and a copy of the school newspaper that ran the interview.
The tape, recorded on 5 January, 1970, features the married musicians speaking about being in Denmark and world peace. John and Yoko also sang "Give Peace a Chance" and "Radio Peace", which was written for a radio station in the Netherlands but never released.
The teens conducted the interview in northern Denmark at the height of the Vietnam War and the Cold War because Lennon and Ono had "a message of peace, and that was what was important to us," said Karsten Hoejen, who recorded the chat on a tape recorder borrowed from a local hi-fi shop.
"It is a small item with lots of interest," auctioneer Jesper Bruun Rasmussen said as he brought the hammer down on the winning bid.
The three surviving men who conducted the interview have not decided what to do with the money, according to The Independent.
Lennon and Ono were in the region because Yoko's ex-husband, and their five-year-old daughter Kyoko, had recently moved there.
The identity of the lucky bidder was not disclosed.
The long-lost interview tapes were discovered during a cleaning spree amid lockdown.