If everyone in the U.S. grasped the idea of compound interest, it might make a small dent in the number of people deeply in debt and facing bankruptcy or foreclosure. Understanding the math isn't a panacea; some find themselves in overwhelming consumer debt as a result of truly dire circumstances and others due to poor impulse control. Still, educating people about the consequences they could face can't hurt.
Teaching college students and adults about sensible money management has tremendous value, but exposure to basic principles can and should begin much earlier than that. When I was in upper elementary school, my Girl Scout troop attended a talk by someone from a local nonprofit credit counseling agency. The speaker talked about the importance of budgeting and saving. Although most of us couldn't have worked the calculations ourselves, she was able to use charts and graphs to illustrate the value of starting to save early and the costs of buying on credit and making only the minimum payments. I don't know about the other girls, but that made a deep impression on me.
There's really no reason parents and schools can't provide this information. Parents can teach about the household budget and provide their children with age-appropriate experiences handling money of their own. Lessons on compound interest can be incorporated almost seamlessly into algebra coursework. If children are exposed to sensible money management early and often, they stand a better chance of developing good habits that last into adulthood.