How much would a person need to be Financially Independent?

No, productivity increases are factored into the price that companies charge you for their goods and services. The price you pay for goods is then analyzed and studied by the BLS. “Productivity” is essentially irrelevant, the relevant bit is what the final price of the good and/or service is that you actually pay at the store, which is then in turn a function of productivity.

You’re in college, have you not taken Macro-Econ 101 yet?

Slight hijack, but why is “perpetuity” a requirement? If you purchased annuities, you could save a few bucks most likely.

Productivity increases are the reason that wages increase by more than inflation. In the calculations in the earlier posts, I assumed that you would want to keep abreast with inflation. If you want to keep abreast with median earnings, then you will need even more capital.

You might want to bear in mind one other thing:
Your income from interest doesn’t have to last forever at the same level. Technically, it just has to be enough to provide your target income for each year between now and when you die.
So, to be conservative, I’m 27. If I have enough money to pay me the current equivalent of today’s $35,000 pre-tax for the next 73 years, that’ll be enough. There’s no real reason to require that the fund still be paying out that money the year after I die.

That is true - it is just that the OP asked how much you need to live on without dipping into the principal at all.

Another thing to take into account is that instead of putting your money into securities, you could save on rent/loan repayments by using a part of it to buy a house in cash (and bulk buy 20 years’ worth of canned meats at a super-discount price). Since rent or home loan payments are a major part of most people’s expenses, this could lessen the amount you need. And you wouldn’t need to go food shopping. So in fact you would need considerably less than the median income to match the average standard of living.

Canned meat won’t last 20 years.

You can store it for five years, tops.
http://www.fsis.usda.gov/Oa/pubs/dating.htm

However, you could buy some cattle, and pray they don’t get some disease or other…

Providing for yourself wouldn’t be the motivation for that, unless you were immortal. But it would be usefull in order to provide for your heirs. Say you want to help your children and grandchildren afford houses and college long after you have expired, but you don’t trust them to manage the money themselves so you have the executors of your estate invest in treasury bonds and dispense the funds to them accordingly.