A two-page letter Paul McCartney wrote longhand to Prince many years ago with the salutation “Dear Princely person” sold at auction for nearly $15,000.

RR Auction of New Hampshire said the letter from the former Beatle was estimated to go for no more than $4,000 when it first went up for sale and fetched $14,822 last week from an undisclosed buyer who came out on top after “pretty ferocious” bidding on the last day, said Robert Livingston, executive vice president at the auction house.

The letter to Prince, who died in April at his Chanhassen home, apologetically requests a donation toward McCartney’s establishment of the Liverpool Institute for Performing Arts. The school opened in 1996 and is still in operation.

“Hi there! I know how hard it is to always be getting letters that ask for some favour or another, so it was no easy for me to accept the job of Lead Patron for a Performing Arts School to be located in my hometown, Liverpool. … So now I’m writing to ‘friends and all good people’ to try and interest them in the scheme. … Now the hard part. A donation from you would be a great boost to our project, and I know your involvement in some way would be a thrill for everyone concerned.”

McCartney went on to suggest that Prince could “come and teach a class some moves!!”

The letter includes McCartney’s signature at the top and closes with “Cheers, and love,” a smiley face and another signature.

The auction house said it could not determine whether Prince sent anything toward McCartney’s project, noting that the “vast majority” of the Prince’s charitable gestures “were gifted anonymously.”

The letter came to the auction house from a collector who wants to remain anonymous, Livingston said.

“You don’t see Paul McCartney letters of that length hardly ever,” said Livingston, whose auction house has handled many of his handwriting samples in the past and “had no problem authenticating” its true origin.

McCartney played two nights at Target Center in early May and said from the stage on Day 1 that he was dedicating the show to Prince and included on his playlist the Purple One’s “Let’s Go Crazy” — complete with a properly hued glyph on the video screen.

McCartney mentioned that he had seen Prince in concert several times in London and had experienced Prince onstage in a small club on the most recent New Year’s Eve.

“Minneapolis, Prince,” Sir Paul declared and paused. “Prince, Minneapolis. It goes together.”