(personal prediction that 30minutes of exercise will increase my life expectancy by 4 years)
If you assume that you have, oh, 3 hours a day free time, living an extra 4 years means that you have an extra 1/2 year of free time.
As exercise is taken from your free time, this is only a good deal if 30 minutes a day for the rest of your life totals to less than 1/2 year. 30 minutes is 1/48 of a day, so 30 minutes over a year is 1/48 of a year. This means that if you expect to live any longer than (1/2) / (1/48) = 24 years, you should not exercise.
Of course, other factors come into play (if your life expectancy increases, your extra years may be spent retired, on the other hand, you're more likely to be ill in those extra years, etc.)
And the less free time you have, the less exercise helps, because you gain less (each year of additional lifespan provides you with less extra free time) but you lose just as much (since your exercise comes out of your free time).
(if your life expectancy increases, your extra years may be spent retired, on the other hand, you're more likely to be ill in those extra years, etc.)
I'd expect most of the life expectancy-increasing effects of exercise to also shift the age at which you'll get ill by almost the same amount, while hardly affecting the age at which you'll retire, so I'd guess most of the extra time would indeed be while you're retired but still healty enough.
The question is - am I doing enough exercise?
I intend to provide a worked example for you to work alongside with your own calculations and decide if you should increase or decrease your exercise.
The benefits of physical activity are various and this calculation can be done for one or all of them; some of them include: