Expressing Moore's Law with the Compound Interest Formula
In 1965, Intel co-founder Gordon Moore predicted that "the number of transistors on an integrated circuit doubles approximately every two years." This prediction, known as "Moore's Law," has served as a guiding principle for the semiconductor industry. Expressed using the compound interest formula, doubling every 2 years means the annual growth rate r is (2)^(1/2) - 1 ≈ 0.414, equivalent to approximately 41.4% annual interest.
To appreciate how extraordinary 41.4% annual growth is, compare it to the financial world. The S&P 500's long-term average return is approximately 10% per year. Warren Buffett's lifetime return is about 20% per year. Moore's Law growth rate of 41.4% is more than double Buffett's. Intel's 4004 processor in 1971 had 2,300 transistors. Apple's M4 chip in 2024 has approximately 28 billion. That is roughly 12.17 million times more over 53 years. Calculated as compound interest, this is equivalent to compounding at about 38% annually for 53 years.
The 'Performance Compounding' Moore's Law Created
The essence of Moore's Law is not just the increase in transistor count. As transistors shrink, power consumption drops, operating speed increases, and manufacturing costs decrease. In other words, consumers have enjoyed "performance compounding" every year in the form of "more powerful chips at the same price."
Consider the concrete numbers. In 1980, achieving 1 gigaflops (1 billion floating-point operations per second) of computing power cost approximately $32 million. By 2020, the same computing power cost about $0.03. Over 40 years, the price dropped by a factor of roughly 1 billion. Annualized, that is approximately a 52% price decline per year. Your smartphone possesses computing power that far exceeds 1980s supercomputers. This is the result of 40 years of accumulated "technology compounding" through Moore's Law.
The Limits of the Law - The Day Physics Stops Compounding
Moore's Law cannot continue forever. Transistor miniaturization is approaching the physical limit of atomic dimensions. The most advanced process as of 2024 is 3 nanometers, roughly 15 times the diameter of a silicon atom (approximately 0.2 nanometers). Further miniaturization causes electrons to tunnel through gates via quantum tunneling effects, rendering transistors non-functional.
In practice, Moore's Law "doubling period" has been lengthening in recent years. Until the 2000s, doubling occurred approximately every 2 years, but some analyses suggest it has stretched to 2.5-3 years since the 2010s. In compound interest terms, 41% annual growth has declined to 26-32%. Still remarkable, but the universal law that "exponential growth eventually decelerates" applies here too. In the investment world as well, high-growth companies' growth rates eventually slow. The deceleration of Moore's Law is a grand-scale example of the limits of exponential growth.Books on the semiconductor industry provide a deeper understanding of the technical background behind Moore's Law.
Next Actions - Applying Technology Compounding to Your Investments
Moore's Law teaches investors two lessons. First, the exponential evolution of technology has the potential to exponentially boost the earnings of companies that harness it. Fields where increased computing power directly creates value - cloud computing, AI, autonomous driving - benefit most from Moore's Law. Second, exponential growth always has limits. The ability to detect decelerating growth rates and judge the inflection point from growth stock to mature stock determines long-term investment returns. Periodically check whether the growth rates of technology companies in your portfolio are slowing down.