Could Jeff Bezos afford a swimming pool of gold coins like Scrooge McDuck? An in-depth analysis.
This afternoon I found myself wondering how unrealistic Scrooge McDuck’s iconic swimming pool of gold coins was, so I sat down, pulled out a pencil and paper, and worked out the math.
First, I needed to figure out how big of a swimming pool to use. I settled on using the dimensions of the pool down the street from me growing up, which I estimated to be 18m x 7m x 1.5m (a little on the small side for pools, but deep enough in some places that it has a diving board and long enough to reasonably swim laps in).
Okay, so we have our dimensions. When we multiply those together, we get 189 m^3. I’m going to go ahead and convert that into cubic centimeters (1.89*10^8 cm^3) for ease of future calculations.
Next we need to determine how much of that actual space we need to fill up. When you throw a bunch of loose coins in a box, they don’t take up 100% of the space of the box. I tried to look up packing efficiency of coins, and found estimates ranging from 55%-75%, so I took the average of those (65%). Multiplying the total volume (1.89*10^8 cm^3) by the packing efficiency (65%) we get 1.23*10^8 cm^3.
After that I needed to figure out what kind of coins the pool would be filled with. From zooming in on pictures of Scrooge McDuck’s pool, I determined it was filled primarily with a mixture of Liberty Double Eagles and Saint Gaudens Double Eagles, priced at $1459.47 and $1470.47 respectively. I assumed an even distribution, averaged the prices, and rounded the value to $1465/coin.
Other information this website gave me about the coins was the mass (33.4 grams each) and the composition (they were both 90% gold, 10% copper). I looked up the density of gold to be 19.3 g/cm^3 and the density of copper to be 8.96 g/cm^3. Multiplying those by their proportions you get the density of the coins to be (.1)*(8.96 g/cm^3) + (.9)*(19.3 g/cm^3) = 18.27 g/cm^3
If we were to fill the pool with coins, then, the mass of those coins would be (1.23*10^8 cm^3)*(18.27 g/cm^3) = 2.25*10^9 grams. Since the mass of each coin is 33.4 g, we can divide our answer by this to determine how many coins it would take to fill the pool, (2.25*10^9 g)/(33.4 g/coin) = 6.74*10^7 coins.
The last step is to multiply the number of coins by the price per coin to give us the total cost of the pool (6.74*10^7 coins)*($1465/coin) = $98.7 billion.
Jeff Bezos has a net worth of $111.4 billion. So yes, he could afford it with money to spare.
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