If the guy with $36,000 invested it and made just 7% per year (less than the S&P average), he’d pull in $2,500 and the fellow starting at 65 would only gain $4800 - $2500 = $2,300 per year.
The guy who waits gets a raise each year (the eventual SS payment is higher), so the calculation is less. Indeed, people who counsel waiting note that it’s like getting a 2.8% risk free (or as risk free as the US Government is) bond (your payout increases). Most mathematical analyses I have read say the “break even” point is somewhere around 81 years old by waiting. So (if that is true) take it early if you are in poor health, have a questionable family health history, or can’t live without it. Otherwise wait.
But wait! I have argued (and done so myself) that the money will have little practical value to me when I am 88; I will probably be in a nursing home, and if it’s anything like my father’s or father’s-in-law, they make you pay full price until you run out, then they take your pensions and social security as full payment until you die. I guess it would be nice to give the home another $400 a month, but I think I can use that money better now myself.
I am able to live, do things, travel, play in the workshop now in my 60’s. I am unlikely to be able to do that in my 80’s. It’s not just the “time value of money”, it’s also the “enjoyment value of money.”
I took it at 62, even though I didn’t really need it.