Going to the gym is not going to save you on lifetime health care costs. You'll live longer, that's for sure, but you won't save money because you'll consume health care in those extra years alive. Everything we know about prevention indicates it is cost neutral or cost increasing.
Can you cite a source for this, because my personal experience of working in healthcare with seniors could not be more different than what you are claiming.
There’s plenty of evidence that in the short term people who are active have lower healthcare costs than people who are inactive, but that is different from that being true over a lifetime. They’re also generally observational studies, which means they show an association but not causality.
This article shows that functional health status at 70 doesn’t make a difference in lifetime healthcare costs over the rest of their lifetime. I’m not saying you shouldn’t exercise to improve your health and live longer, just that the healthcare cost savings argument is largely a myth. Lots of years in good health cost as much as fewer years in poor health.
http://www.nejm.org/doi/full/10.1056/NEJMsa020614
There are no good studies of physical activity on lifetime healthcare expenditures, but our experience with decreasing smoking rates is similar.
http://www.nejm.org/doi/full/10.1056/nejm199710093371506
Finally, an overview of why prevention generally doesn’t save money.
https://mobile.nytimes.com/2018/01/29/upshot/preventive-health-care-costs.html?referer=https://www.google.com/
Here is the problem with the base blanket statement you made based on what I read from the first source.
The "healthier individuals" are spending roughly $136,000 while the "less healthy" spend $145,000. So only a roughly 6% reduction in healthcare costs. EXCEPT
The healthier individuals are spending that sum over roughly 14.3 years ($9500 per year) while the less healthy are spending that sum over 11.6 years ($12,500 per year).
I therefore conclude, while you only save 6.2% over the span from 70 to death by being more healthy this raw numbers hides the fact that your "stash" to cover the averaged annual expenses is $237,500 in the healthy case vs $312,500 in the less healthy case or a 32% increase in retirement stash size (given that you don't know when you will die so you stick to the 4% rule because there is still a potential to live for 30 years at age 70).
The only thing that I would say is potentially problematic about my quick go at reading the fist article is that I am not accounting for the ramping of costs that occurs in the later years as the costs are not necessarily averaged out on a per year basis with the higher cost institutionalization coming at the end.
Now, what about the subjective "quality of life" measures from being in "better shape". (their definition for the less healthy individual is "a person with a limitation in at least one activity of daily living").
