This blog post calmly examines how compound interest functions as a tool for growing assets, while also exploring why it can easily lead to exaggerated illusions and misconceptions, using real-world examples and calculation logic.

Can you really trust compound interest?

This is the story of S, who is currently planning to invest. After following several investment-related accounts on social media, S frequently encountered advice emphasizing the concept of ‘compound interest,’ often described as the most attractive approach in investing. Every explanation of funds or stocks mentioned compound interest. As someone who supports ‘long-termism,’ S felt this aligned well with their investment philosophy, promising long-term, stable returns.
A few days ago, they clicked on an account recommended by an algorithm. There, they found friendly consultations on compound interest-related products. Titled “Turn $10 into $100 in a Month!”, it introduced an easy investment opportunity. The explanation was simple: Invite acquaintances to purchase items on the platform. Those acquaintances would then invite others to buy items. Each time a purchase occurred, a fixed commission would be paid to you. The commission per order wasn’t large, but the calculation was that if everyone invited just one person per day to make a purchase, the commissions would exceed $1,000 within a month.
Listening to this explanation, I thought to myself, “That’s ridiculous. Something’s off here,” but I couldn’t pinpoint exactly what the problem was. Is ‘compound interest’ really that powerful?

The Three Fundamental Principles of Compound Interest

Before explaining what compound interest is, there’s a crucial story we must address. First, let’s hear the tale of ‘Archimedes and the King’s Chess Match’.

The king, a skilled chess player, enjoyed challenging others. One day, he proposed a chess wager to the visiting mathematician Archimedes. However, even after playing all day, they couldn’t decide a winner. Delighted, the king asked Archimedes:
“If you win, what would you desire?”
Archimedes looked at the kingdom’s grain storehouse and replied:
“If I win, place a grain of rice on each square of the chessboard.”
Seeing the king’s puzzled expression, Archimedes added,
“Place one grain on the first square, two grains on the second, four grains on the third, and so on, doubling the amount on each subsequent square.”
The king thought it was a wager worth taking. His granaries were full, and the chessboard seemed very small. He readily accepted the challenge.
In the end, Archimedes won the match. When it came time to fulfill the promise and deliver the grain, however, the entire stockpile in the kingdom’s granaries was insufficient to fill every square of that small chessboard.

So how much rice did the king owe Archimedes? If we place one grain of rice on the first square, the second square gets 2 to the power of 1, the third square gets 2 to the power of 2, and so on. The Nth square gets 2 to the power of N-1.
Since a chessboard has 64 squares, the number of grains of rice required for the final 64th square is 2 to the power of 63, or 9,223,372,036,854,775,808 grains.
However, this is only the amount for the final square. The total number of grains of rice needed for the entire chessboard amounts to 18,446,744,073,709,551,615 grains. Calculating the weight of one grain of rice as approximately 0.016 grams, one kilogram of rice contains about 62,500 grains.
Based on this, the required amount would be approximately 295.1 billion tons.
According to data from the Food and Agriculture Organization of the United Nations, the total annual global food production in 2019 reached about 2.7 billion tons. In other words, Archimedes demanded enough grain for over 100 years of global food production for a single chessboard.
As this story shows, compound interest doesn’t intuitively resonate. It’s easy to think like the king, “What difference could one grain of rice possibly make?” Its power isn’t immediately apparent. Yet its true value emerges where we fail to foresee.
Things difficult to grasp intuitively are hard to distinguish clearly in the short term. That’s why most people pay little attention. But if you can see what others overlook, that’s where the difference in skill emerges. This is the ‘magic of compound interest.’ Though its effect seems minimal at first, over time it produces results beyond imagination.
Compound interest isn’t just a numbers game. It’s a philosophy for approaching investment. If you want to achieve results through compound interest, there are three essential elements you must keep in mind.
First, the principal.
The most crucial starting point when growing money is the size of your initial investment. The scale of the compound interest that accumulates later depends entirely on how much your principal is. Investing $1 and seeing it grow 100-fold still only yields $100, but investing $100 and achieving the same 100-fold return results in $10,000. Applying a 1,000-fold increase here would grow the asset size to $100,000. The true allure of compound interest lies not in the rate of return itself, but in how the outcome changes exponentially based on the size of the principal. Therefore, the larger the starting point, the more significant the transformation compound interest creates.
Second, the rate of return.
The king’s chess wager doubles each time, equating to a 100% compound interest rate. Such returns are difficult to expect in real-world investing. However, even with a low rate of return, a massive difference emerges over a long period.
For example, investing $10 at a 20% annual return yields approximately $2,370 after 30 years—237 times the original amount. Even slight changes in the rate significantly alter the outcome. A 15% annual return yields about 16.37 times the original after 20 years, while a 20% annual return yields about 38.3 times— That’s nearly double the difference. Extending this to 50 years, a 15% annual return yields about 1,083 times the original amount, while a 20% annual return yields about 9,100 times the original amount, widening the gap even further. Ultimately, the core focus for investors is the rate of return.
Third, the time period.
The length of time applied to compound interest is also a decisive factor. A 20% annual return yields roughly 6 times the principal after 10 years, 38 times after 20 years, and 9,100 times after 50 years. Notably, the rate of return growth becomes significantly more pronounced as the investment approaches maturity. In a 50-year investment with a 20% annual return, the returns generated in the final 5 years alone are approximately double the total returns accumulated over the preceding 45 years. This effect is often called ‘time’s friend’.
The process of accumulating wealth is neither a sprint nor a marathon. It is a much longer battle requiring decades of patience. Even with a small starting capital, combining sufficient patience with stable interest can lead to victory in this long race.

Is compound interest easy money?

Following this logic, it might seem like all you need to do is put in a little principal and wait. It can feel like making money while lying down. But reality isn’t that simple.
Charlie Munger, while viewing compound interest as a crucial investment tool, stated:

“You must understand the magic of compounding and also accept its difficulty.”

Actually enduring this ‘difficulty’ is never easy. Here’s why:
First, maintaining stable returns is extremely difficult.
The compounding example calculated earlier assumes a consistent annual return rate. However, the real economy fluctuates periodically. A single major fluctuation could wipe out all the compounding gains accumulated before it in an instant.
In extreme cases, a single year could see a 100% loss. Even after accumulating compound interest for 49 years, a total loss in the 50th year renders all prior effort meaningless. Even if the loss isn’t 100%, a 50% or 30% loss significantly undermines the multiplier effect of compounding. Therefore, in long-term investing, stability tends to be valued more highly than high returns.
Second, time can be both a friend and an enemy.
Compound interest requires sufficient time to demonstrate its power. This means sacrificing present satisfaction for future gains. While valid from an asset accumulation perspective, the choice between present happiness and future achievement is personal. Even if investing $10 today could yield $100 million in 100 years, its meaning is limited if you won’t be alive to see it.
Third, the multiplier effect of compound interest may not be as large as imagined.
For example, when China first began its reform and opening-up, households earning over $2,000 annually were considered wealthy. What if those wealthy individuals had invested their entire $2,000 fortune in a compound interest product promising “50 years, 1,000x return”?
Even if that asset grew a thousandfold to 2 billion yuan in less than 50 years, by today’s standards, it would hardly qualify as upper-class wealth. It wouldn’t even be enough to buy a single home in Shanghai.
This is because the “50 years, 1,000-fold return” figure looks impressive, but when converted to an average annual return, it amounts to only about 15%. Moreover, China’s economic growth rate during the same period far exceeded this return.

Compound interest has no direct relationship with returns

The crucial fact is that the method of calculating interest does not determine the size of investment returns. Articles or advertisements praising compound interest often exaggerate the difference by simply comparing compound and simple interest. But in reality, this isn’t the case.
If you invest $1,000 and receive $1,440 after two years, the total profit is $440. Calculated as simple interest, the rate is 44%, while as compound interest, it’s 20% per year. Only the calculation method differs; the actual profit is the same.
The reason compound interest appears more advantageous than simple interest only applies when the rate of return is predetermined. However, in reality, the rate of return is not set beforehand; it is calculated after the final profit is realized. In other words, the rate of return does not determine the profit; the profit determines the rate of return.
Therefore, whether it’s compound or simple interest is not the fundamental issue. What matters is how much profit the investment vehicle generates.
The key metric here is the Internal Rate of Return (IRR). IRR evaluates investment profitability based on future cash flows, allowing comparison regardless of investment amount, duration, or calculation method.
IRR inherently operates on an annual compounding basis since it annualizes returns. Therefore, one should never judge investment profitability solely by the stated interest rate; always verify the actual annualized return using IRR.

The Hidden Trap of Compound Interest

Compound interest reflects the time value of money and is undoubtedly a valid tool if long-term investments can be maintained. However, blind faith in it can lead to falling into the trap of compound interest.
As mentioned in the story, investment products structured around recruiting acquaintances require particular caution. If they promise over $1,000 in profit within a month, it’s no different from the King’s Gambit in chess. Even a one-month calculation shows this figure would require recruiting the entire global population. Yet many still fall for this illusion of compound interest.
Recent cases of auto-loan platforms luring consumers with “no deposit required” and “no interest” slogans follow a similar pattern. They tout daily interest calculations, but the structure actually requires repayment of both principal and interest. Calculated using IRR, this equates to a high-interest loan exceeding 10% annually.
The myth of compound interest is ultimately a marketing creation. It’s just a well-packaged image. In this world, there may be “money you lose while lying down,” but there is no such thing as “money you earn while lying down.”