The following was originally a comment on a Reddit post asking about a Public Citizen tweet. The tweet, and question, are replicated below.
It's 2589 BC. The Egyptians are building the Giza Pyramids. You are immortal.
You have $0. You decide to save $10,000 every day, never spending a cent.
4609 years later, it's 2020.
You only have only one-fifth the average fortune of the 5 richest billionaires.
Tax the rich.
- Public Citizen (@Public_Citizen), February 18th, 2020
Question: "Can anyone confirm? Assuming dollars exist, and don't change in value, just going off the number of days?"
Really, this is just an attempt to explain why the rich should be taxed. It doesn't need to make sense mathematically. That being said...
From January 1st, 2589 BC to the day this tweet was posted (February 18th, 2020 AD) was 1,683,108 days. This would be $16,831,080,000 without interest, which is definitely under a fifth of the average top 5 billionaire net worth.
However, let's assume that starting in, say, 1970, our immortal friend began investing in 10-year treasury bonds, buying a new one when his last one reached maturity. After all, you wouldn't just keep this money under your pillow for a million days. How a 10-year treasury bond works is that you buy in, and you get paid interest every 6 months, with the full amount you bought in at available to you at face value once the bond "reaches maturity" (basically, in 10 years). (Originally, I started in 1790, but we don't have dates going back that far, so I'm going to assume our buddy helped Alexander Hamilton with the USA's debt issue in 1789, and Hamilton paid it back dollar-for-dollar, just to make me feel better.)
On January 1st, 1970, our immortal friend has accrued $16,647,970,000 (about 15% of Bill Gates' net worth in November of 2019). Since I'm not entirely sure how bonds work, let's err on the side of helping our buddy out. We'll treat each number as a simple interest yield p every 6 months, which will be presumably paid out to our friend once the 10 years are up. Our friend will then re-invest that money, plus the 10 years worth of $10,000 payments they've got, into another bond at that rate for the next 10 years.
On January 1st, 1970, our friend deposits $16,647,970,000 into a 10-year savings treasury note. The yield on the note would be 7.86% percent, and assuming that was all paid out and accumulated at a rate of 7.86% interest per half-year, and accounting for the $36,520,000 our buddy accumulated over this time, he has $42,855,098,840, which is 33% of Jeff Bezos' net worth. It's 1980, and our friend has over a fifth of the net worth of the richest billionaire on Earth (and probably more since Bezos' net worth presumably took a hit when he gave his ex-wife a 4% stake in Amazon).
But, to heck with it, let's see how long it takes our buddy to catch up to Jeff. in 1980, the yield was 10.5%. Accounting for an extra leap year (or some other reason 1980-1990 has an extra day), our friend has $132,887,336,404 in their hands as the '90s began. As the 90's roll around, not only has our friend hopefully invested in Apple, making them lots of money by present day, but they can sit on their hands for the next 30 years (even halting the $10k per day payments), safe in the knowledge that Jeff Bezos will be 2% short of them come 2019. (Although, they'll certainly be kicking themselves for not waiting until September of 1981's 15% yield rates.)
But let's just see how far we can go with this. In 1990, the yield rate opened at 7.94%. As the disaster of Y2K was averted, our friend would be sitting on $343,948,946,613. If sitting on their hands in 1990 would have made Jeff Bezos feel Locked Out Of Heaven, this would have made him feel Lower Than Dirt, at 61% short of our friend.
But let's see if we can make Jeff Bezos feel lower than Lower Than Dirt, by continuing this investment strategy. In 2000, the yield rate opened at 6.58%. Investing all of the money into another bond (which at this point, if I haven't made clear yet, is absolutely unnecessary), our friend would have $796,622,290,355. Jeff Bezos would probably cry since he now only has less than a fifth of our net worth (about 16%).
Let's make Jeff cry even harder. The killing blow: In 2010, the yield rate opened at 3.85%. That isn't a lot, but with our 756 billion, our friend enters the so-called "rawring twenties" with $1,410,057,973,928. Our friend becomes the world's first trillionaire by a long shot, and didn't even have to work that hard for it. Jeff, sit down before you read this, only reaches 9% of our net worth. That's right; with only investing in simple-interest bonds at the 10-year treasury yield rate from 1970 to today, our friend has so far surpassed the world's richest people of today that Jeff Bezos can barely imagine that much money in his possession.
Adding the days leading up, as Public Citizen attempts to explain why the government should tax the rich on the 18th of February, our thrifty immortal has accrued a net worth of $1,410,058,453,928.
Even with my Fermi estimationflawed understanding of how this works out,
you can't tell me that our friend wouldn't eventually have invested enough
money to get this much out of it by 2020.
Either way, all of this is a moot point, as our time traveling friend could simply pick up some priceless artifacts along the way to sell later to museums, pick up priceless art techniques to make millions teaching (who wouldn't want to study art from somebody who was taught by Vincent Van Gogh?), and also probably invest plenty of money in Apple.
1 million days is a lot, in the grand scheme of things, though it may seem small to the minds of an immortal. :)