Well my ankle sprain had last over a week so I guess I gotta stop being stubborn and stop trying to keep jogging as my cardio. Are there any other exercise that is works well as a cardio exercise I could do for around 40 min.

Anything that elevates your heart rate for a protracted amount of time is, by definition, cardio. In your case, it sounds like swimming or biking wouldn't be a bad idea, at least until your ankle heals. If it keeps hurting, go see a orthopedist. You could have something much worse than a sprain