I use my android smartphone for this purpose. I do push-ups, pull-ups, squats, and sit-ups coupled with supermans in a four day cycle different muscle group every day. That's less than 10 minutes every day. The smartphone apps calculate how much you should rest between sets and how many you should do the next cycle based on how many you did and how difficult it felt.

If you do every muscle group every day that might be better for your cardiovascular health, but expect to gain strength and muscle stamina much slower. Your muscles need to get some rest too. Most apps aren't designed for no resting. The exercises don't target every muscle group possible but if your goal is just to stay healthy I think they're balanced enough for that purpose. If they start to feel too easy, add some free weights or make your posture more difficult. If you don't have a pull-up bar home and don't want to buy one, find one outdoors.

For cardiovascular benefits I would recommend aerobic exercise. It doesn't really matter what it is, as long as you get your heart rate high enough often enough. If you want to make sure the exercise doesn't become too anaerobic (would become more difficult to do often) but don't want to buy a heart rate monitor, try breathing only through your nose and slow down if that becomes too difficult. You might start with brisk walking, but over time even running while breathing this way should become effortless.