Wise paid $3,347 for the car, happy to have a convertible. It wasn't until she was on the road, with other drivers honking and flagging her down, that she realized what she had.
"I felt like a movie star," she said.
Fifty years and 9 million Mustang sales later, Wise was on hand Thursday to celebrate the unveiling of the 2015 version of the iconic pony car. With her was the original Mustang convertible, which still sits in her suburban Chicago garage.
Wise was 22 and freshly out of Chicago Teachers College when she decided to buy a car to commute to her new job as a third grade teacher. She went to Johnson Ford and asked for a convertible, since her family already owned two other Ford convertibles.
"I thought I deserved a convertible," she said with a laugh.
The manager didn't have any on the floor, but took her into a back room and pulled a tarp off the new Mustang. It was April 15 - two days before the car was officially supposed to go on sale - but he offered it to her anyway.
"It was sporty. It was perfect. It went zoom zoom," she said. She got $400 for a 1958 Chevrolet she traded in.
Wise taught for three years before getting married and moving to South Carolina with her husband, Tom, who was in the U.S. Navy. But they kept the car, which has been fully restored.
The car now sits in their Park Ridge, Ill., garage next to a 2013 Ford Escape. It made the four-hour trip to Dearborn on a trailer, but the Wises still take it on shorter journeys, including a trip last year to Indianapolis so it could take a few laps on the Indianapolis Motor Speedway.
"It's incredible that it's still such a popular car," Wise said.