S&P 500 (man is so hard to write because of & sign) index is a weighed (by capital) average of all stock prices in the list and today it rose some 1.5%. Unfortunately i cannot find the value of the rise of the whole market cap of 62.8, all i could find was the current value of S&P, 53.3 though it should follow closely the index. (So yesterday market cap should have been something like 1.51% less).
Which means everybody who owns stock in the US market today is 1.51% richer. 62.8 trillions (last known value) by 1.5% = 945 billions. Almost one trillion have been added today to their capital out of nothing or Powel's words). One of the wonders of capitalism.
How is that possible. I mean, someone's 401k should not depend by daily market fluctuations, right?
Unfortunately, there's more to it. Biggest ten firms listed on S&P have market cap in the trillions, which count for about 40 % of the whole market cap, though their assets (real selling value) are hundreds of times less. As of today, the most "valuable" firm in the world is Nvidia, with 4.1 trillion market value which BTW rose today with 1.7%.
It is all an illusion, if not a Ponzi scheme, with the biggest listed firms being over evaluated hundreds of times (through successive daily fluctuations over the years). However, it is there where retirement money or 401 k are for most Americans. Japanese money are in real estate or whatever that is. Land.

All firms traded on the stock market do loan money especially for short term purposes and the banks loan from FED. So how much money does FED lend to banks to have such an influence on the market?

In other words, FED deals with financial crisis every 5 or 10 years, rest of the time is in standby and manipulates the market mostly with rumors many times a year if not on daily basis. BTW, could or did they do anything about the dot.com bubble of Y2K?
I guess their only purpose is keep the market over inflated so people put more of their retirement money in it.
And yeah, instead of dot com bubble we are living nowadays the AI bubble led by Nvidia.