Let's assume that 4% is a SWR, and that Social Security is going to last our lifetimes.
Given this, has anyone applied these two together for those of us looking to retire in their late 40s or 50s? For example, let's say that Alan is aiming to retire at 57 and has an annual spend of 40K. This alone would say that he should save $1 million. Now assume that he also will get a annual social security payment of $5K, starting at age 62. In this case, he could set aside 5 * 5K = 25K and look at an annual spend of 35K with a 5K supplement. The first 5 years he pulls from the set aside money and after that collects $5K from social security. This would suggest that he needs a total savings of 35K * 25 + 25K = 900K, or 100K less. (This could be optimized further by looking at the invested money needed to get 5K per year for 5 years, but I wanted to keep this simple.)
Is there anything wrong with this logic? Anyone else retiring in their late 40s or 50s that is using this kind of thinking to determine your target stache? What refinements do you have to this?