PHOENIX — The U.S. Mint began pouring 500 million Arizona quarters into circulation on Monday.

 But don’t expect to find anywhere near that number. Ed Moy, director of the federal agency, said the experience his agency has had with the 47 prior state quarters is that only about a third of them wind up in general circulation. The other two thirds, he said, are hoarded by collectors.

 That’s not a bad thing, Moy said. In fact, just the reverse is true.

 “When the Federal Reserve orders these from us, they pay us 25 cents for a quarter,’’ he explained. But it costs the Mint just about a dime to actually produce the coins.

 “So that 15-cent difference is a profit that we return to the taxpayers at the end of every year,’’ Moy said.

 That translates out to just under $50 million for the Arizona quarter alone.

 Monday’s official release at the Capitol mark the end of  process that began three years ago when Gov. Janet Napolitan selected coin collectors, state officials, educators and even some elementary school students to figure out what the Arizona coin should look like.

 That panel reviewed more than 4,200 design suggestions from across the state before coming up with five finalists. These were sent to the U.S. Mint which produced the actual drawings.

 Napolitano, who got the final word, decided to conduct  a nonscientific online poll, eventually choosing the one that gained the most votes: A picture of the Grand Canyon and a saguaro cactus, with the motto of “Grand Canyon State’’ in between. That placement was not accidental but instead designed to show that the signature cactus can be found nowhere near the canyon.

 The other options included one with just the canyon, a second with a more prominent saguaro and the canyon in the background,  picture of John Wesley Powell’s expedition through the canyon, and a coin depicting the Navajo code talkers during World War II.

 It actually took some time to choose those five finalists.

 The Arizona State Quarter Commission reviewed various suggestions both for content and, for lack of a better word, “draw-ability.’’

 The coins had to be able to depict the scene given both the limited size of the quarter and the restrictions on how high or deep the stamping could be.

 And some ideas were rejected for political or other reasons.

 For example, one commission member suggested a Hopi kachina might be an effective way to represent something unique to Arizona. But that idea was jettisoned, not only because it meant singling out one tribe but also because of the belief that there were still a lot of raw feelings about the partition of Navajo and Hopi lands and the forced relocations.

 And a suggestion to use Mission San Xavier del Bac, south of Tucson, was dismissed because it remains an active Catholi church.

 Even the decision to select Powell making his way down the

 Colorado River as one of the finalists was fraught with concerns over political correctness. Committee members insisted the inscription should say that Powell was “exploring’’ the Grand Canyon, because American Indians might take offense at th suggestion he “discovered’’ what they knew was there all along.

 Congress approved a law in 1997 ordering the Mint to produce quarters for each of the 50 states in order of their admission to the union. The first was issued in 1999; Arizona, as the 48th state, is followed only by Alaska and Hawaii whose coins will be issued later this year.

 The new coins should be available immediately at some banks.

 Several hundred people wanting to be first lined up to purchase two rolls of the brand new quarters at the $20 face value.

 Anyone else who wants two-roll sets can either wait for the banks to get them in or order directly from the Mint. But that wil tack on another $12.95 in postage and handling for each two rolls.

 And 1,000-coin bags also are directly available from the mint fo $309.95, with your choice of whether you want quarters produced at Denver or Philadelphia.