Week 5 Day 1: A Penny or a Million?

A penny doubled daily for 30 days becomes $5,368,709.12. More than five times the million dollars. Almost nobody picks the penny because our brains cannot intuit exponential growth. We see a penny and think 'worthless.' We see a million and think 'rich.' But the math says the penny is worth 5x more.

Here is the day-by-day breakdown that makes it visceral. Day 1: $0.01. Day 5: $0.16. Day 10: $5.12. Day 15: $163.84. Day 20: $5,242.88. Day 25: $167,772.16. Day 30: $5,368,709.12. Notice what happens: for the first 20 days -- two thirds of the journey -- the penny has not even reached $6,000. It looks pathetic compared to the million. Most people would give up at this point. But in the final 10 days, it goes from $5,000 to $5.3 million. The explosive growth is back-loaded. This is exactly what happens in real investing: the first two thirds feels disappointing, and the final third is where the magic happens. Everyone wants the magic. Almost nobody has the patience for the first two thirds.

The penny doubling problem is a classic illustration of exponential growth bias -- the systematically documented tendency for humans to underestimate compound growth rates. Stango and Zinman (2009) demonstrated that individuals with higher exponential growth bias hold more high-interest debt and save less, suggesting the bias has real financial consequences. In controlled experiments, people asked to estimate 30 doublings starting from 1 cent typically guess between $1,000 and $100,000 -- off by a factor of 50 to 5,000. The actual formula is straightforward: 0.01 * 2^29 = $5,368,709.12. But the human brain processes this as 0.01 + 0.01 + 0.01... (addition) rather than 0.01 * 2 * 2 * 2... (multiplication). We are addition machines trying to understand a multiplication universe.