BY RYAN GAVIN, CFA PORTFOLIO MANAGER
Human brains are naturally wired to process linear growth. We instinctively grasp steady,
predictable increases – like a savings account growing by the same dollar amount each year or
a tree growing by a consistent number of inches each season. However, when growth follows
an exponential trajectory, our intuition struggles to keep up. Small changes that seem
insignificant at first can snowball into massive shifts, yet we tend to underestimate their long-
term impact. This cognitive blind spot can make it difficult to fully appreciate the power of
compounding in finance and investing.
The difference between linear and exponential growth
Linear growth is straightforward: A quantity increases by the same fixed amount over equal time
intervals. If you save $100 per month, you’ll have $1,200 after a year, $2,400 after two years,
and so on. The progress is predictable, and the total growth can be estimated with simple
arithmetic.
Exponential growth, however, follows a different pattern. Instead of a fixed amount being added
over time, the growth compounds. Each step builds upon the last, resulting in an acceleration
that quickly surpasses linear projections. In financial terms, this is the essence of compound
interest – where earnings accumulate on both the initial investment and prior gains, leading to
much greater long-term growth than simple interest.
A classic example: the lily pad problem
To illustrate why exponential growth is so counterintuitive, consider a pond where lily pads
double in number every day. If the pond is fully covered on the 30th day, on which day was it
only half covered?
The answer is the 29th day. Just one day earlier, only half of the pond was covered, and two
days earlier, merely a quarter. Even on the 20th day, after nearly three weeks of growth, the
pond would still have been more than 99% uncovered. This example illustrates the deceptive
nature of exponential growth.
Why investors struggle with exponential growth
Many investors understand that their investments compound rather than earn simple interest,
but they often don’t fully grasp how much of an impact compounding has over time.
The chart below illustrates the growth of a $100 investment. The blue line represents growth at
a 5% annual simple interest (linear growth), while the orange and green lines depict growth at a
5% and 6% annual compound interest (exponential growth), respectively. In the early years, the
differences are minimal, but by year 30, the gaps become significant.
The importance of thinking exponentially
Understanding exponential growth can be a game-changer for investors. It highlights the importance of starting early, staying invested, and allowing compounding to do the heavy lifting over time. Just as the lily pads seem insignificant until they cover the entire pond, so small, consistent gains in investing can lead to extraordinary outcomes if given enough time to compound. Recognizing this can help investors avoid short-term thinking and instead focus on the long-term benefits of staying the course.
