Financial Intelligence - Counterintuitive Pattern 3: The Explosiveness of Exponential Growth

Counterintuitive Pattern 3: The Explosiveness of Exponential Growth




The surprising rapid growth of exponential change is covered in most finance books. It deserves special attention because all financial growth is essentially exponential. Before exploring the financial world, let’s understand why exponential growth goes against human intuition.

In nature, most things grow (or decline, which is negative growth) in a linear fashion, meaning the change between consecutive events is mostly consistent. For example, as seasons shift from summer to winter, days become shorter by a few minutes each day. When temperatures rise, the average temperature increases by a few degrees over time. As the rainy season approaches, river surfaces expand by a few metres. After observing these linear changes for hundreds of thousands of years—where the difference between yesterday and today, and today and tomorrow, is always the same—our brains have evolved to predict changes based on this linear model. This linear model is almost always accurate, which is a primary reason why the human species has survived until today.

In nature, instances of exponential growth occur but are usually fleeting before reverting to linear growth. For example, when describing how quickly a single-celled microorganism can grow, we illustrate it as “if a 1 picogram (10^-12 gram) bacterium doubles every minute, in 133 minutes, the bacterium will weigh more than Earth.” In reality, we have never seen the Earth covered with bacteria because the exponential growth phase (doubling every minute) can only last a short time. Once the bacteria reach a few hundred grams, nature cannot supply resources like food, sunlight, or oxygen (if it is an obligate aerobe) at such a rapid rate to sustain exponential growth. The growth will naturally shift to linear. Another example of natural exponential growth is a nuclear reaction. When a heavy nucleus (like uranium-235) splits, it releases 2 to 3 neutrons. Each neutron can hit another nucleus, causing more neutrons to be released. This is typical exponential growth in terms of energy and particle release. If this chain reaction continues for a significant period, events like the Chernobyl disaster in 1984 or the Hiroshima bombing in 1945 occur. There are estimated to be 1.8 trillion tons of uranium-235 on Earth, so why don’t we see dramatic exponential growth like in 1945 or 1984? It’s simply because the exponential growth phase is very short in nature. Due to the density of uranium-235, the radiative decay transitions to linear growth quite quickly. In summary, because of natural limits, rare cases of exponential growth are almost impossible for humans to observe before they transition to linear growth.

In finance, growth is often exponential rather than linear, which challenges our brains that have evolved to perceive things linearly over thousands of years. Examples of exponential financial growth include: 1) Investments, where returns are calculated as a percentage of the initial amount. 2) Macroeconomic indicators such as GDP, CPI, and inflation rates, which are also percentage-based and show exponential growth when the rate of change stays constant. 3) Taxation, usually based on a percentage of the base amount. If wealth is continually taxed this way, we can see negative growth in an exponential pattern. Unlike nature, finance faces fewer limits, allowing exponential growth to go on for a long period, creating notable differences from linear patterns. For example, a $1000 personal loan with a 3% monthly interest rate will grow to $2000 in 2 years, and to $5891 in 5 years. Things in nature can hardly grow at 3% over five years, but loans can.

To fully understand the counterintuitive nature of exponential growth and enhance financial intelligence, let’s explore beyond the notion that ‘nature is leaner, so exponential growth is unnatural.’ How does our mind perceive exponential patterns, and why can it be inaccurate? Let’s use a concrete example to illustrate. Instead of relying on calculations, try using intuition to answer: what are the 10th and 100th numbers in the following pattern?




$100, $110, $121, $133….




Most people, if they answer quickly enough, will find the 10th number is between $200 and $220, and the 100th number falls between $10,000 and $15,000. However, as we slow down and reflect, we see this actually follows an exponential growth pattern with a 10% increase. Thus, the 10th number is $100 * 1.1^{10} = $259.37, and the 100th number is $100 * 1.1^{100} = $1,378,061. This reveals why exponential growth can be counterintuitive. Our brains tend to look at the pattern of the first few elements and make assumptions based on that. For exponential growth, the initial pattern is misleading because it doesn’t reflect larger changes later on. For example, the difference between the 1st ($100) and 5th elements ($146) is $46, but between the 95th ($777,879) and 100th ($1,252,782), it is $474,903—more than 10,000 times larger than the first difference. When we glance at the first few numbers, our brains think, “Oh, just adding around $10, and we get the next one.” That’s why it feels like the 100th element is between $10,000 and $15,000, not $1,378,061.










Having explored why exponential growth is counterintuitive, the next step is to address this challenge to improve our financial intelligence. The most effective way is to memorise common exponential growth patterns, so we can use these patterns as tools for perception and decision-making, rather than relying solely on instinct. For example, let’s memorise the 10% growth pattern.



- 10% growth compounding 3 times is 133%.

- 10% growth compounding 5 times is 161%.

- 10% growth compounding 7 times is 194%.

- 10% growth compounding 10 times is 259%.

- 10% growth compounding 20 times is 6.72.

- 10% growth compounding 50 times is 117.

- 10% growth compounding 100 times is 13780.




We need to memorise it to the point that, just as knowing that 3 times 9 equals 27, we can quickly state that a 10% growth compounded over 7 periods results in roughly a 200% increase. This way, we can use this knowledge as a foundation for our thinking. For example, if you’re offered a 10% per annum finance option for a new car, you can quickly see that if you choose this option and repay it over 7 years, you’re essentially paying twice the current price. While there are principal repayments, inflation, and other factors that complicate car loan scenarios, the core idea stays the same.