She had to be married before her “next” birthday. There was never an age stated. Trust me, I know this movie like the back of my hand. Also I have the production book, which quotes in “Aladdin - The Making of an Animated Film” book from 1992. It reads: “Our original plot line for Aladdin had the Sultan saying, ‘Jasmine, the law says you must be married by your sixteenth birthday.’ That was the original story concept and it stayed for quiet a while. Then Jeffery started to worry about what kind of message we would be sending all the fifteen-year-olds in the world—that it’s okay to get married before your sixteeth birthday? Of course Aladdin is a fairy tale and presumably happened along time ago, but he thought it would be better to change the line to, ‘married to a prince by your next birthday.’ “We added ‘a prince’ as well, because Jeffery is usually pretty strong about, ‘We’ve got to spell out what the situation is.’ So we made it very clear that Jasmine has to be married by her next birthday—which ever birthday is it—to a prince.” (Mark Henn, page 41). So she was originally going to be sixteen, but they cut that out due to the message. Thus, Jasmine doesn’t have an age.