**Martin Verbic** @marteensart

Medical student

4 min read

# Compound Interest: The Most Important Equation In History

## Equations are a way of understanding and explaining the world around us. But the most important one to truly understand is the compound interest equation. Easy to understand, broadly applicable, and capable of achieving remarkable results.

*A short view into a fascinating equation, a principle, and its application to everyday life.*

Equations are a way of understanding and explaining the world around us. They range from simple and easy to understand, to very complex that are on average almost impossible to understand. But they help us in daily life to achieve great things in science, economics and elsewhere. However, an equation that recently caught my attention is the compound interest equation, which is why I'd like to make a case for it being the most important in history.

Business Insider came up with a list of 17 Equations That Changed The Course Of History. These 17 equations range from the simplest, such as the Pythagoras's Theorem, Logarithms to the more complex such as the Fourier Transform of the Black-Scholes Equation. The most famous one, of course, being Einstein's Relativity equation.

However, the equation we really should pay attention to is the compound interest equation. Even Einstein famously said that the compound interest equation is the most powerful force in the Universe. He went as far as to say that it's the 8th wonder of the world. Use it to right and you'll benefit from it a lot. Use it wrong and it will play against you for years to come. It goes like this:

A=P(1+r/n)^{nt}

Where:

- A is the amount after applying interest rate.
- P is the amount of the initial investment.
- r is the interest rate expressed in decimal.
- n is the number of times interest rate is applied (number of cycles).
- t is the amount of time the investment is invested for.

What exactly is interest rate? It's the amount a lender charges for the use of assets expressed as a percentage of the initial principal [2]. Or in simpler terms, how much, for example, a bank pays you for lending them a certain amount of money to on a yearly basis.

The foundations of the compound interest equations date back to ancient Rome, where law severely condemned it. In the 14th century, however, an Italian merchant, Francesco Balducci Pegolotti, was the first one to provide a table of what happens when 100 lire is invested for 20 years for interest rates of 1% to 20% [1].

The first true literature on compound interest equation followed in the 17th century. Richard Witt published a book called *Arithmeticall Equations,* which was entirely devoted to the compound interest formula, whereas former resources only discussed it in brief [1].

For me, the reasons that this equation is the most important equation in all of human history are three. First, it's **easy to understand and implement, **it's** broadly applicable, **and with its help, anyone can **achieve remarkable results.**

## Easy To Understand And Implement

Understanding compound interest is not especially hard. On the other hand, understanding, for example, the Black-Scholes Equation is almost unthinkable for an average human not diving deep into economics and mathematics. The value of something will grow exponentially each time the interest rate is applied. That's something called a cycle. That same interest rate is then applied in the next to that value and so on. The amount of something multiplies exponentially with every cycle. The true benefits, however, show themselves only when thinking about it in the long run. The implementation is just as simple. Applying the fact that small, steady and frequent increases lead to big results can be applied in the fields such as knowledge, skills and investing. This tells another thing about it - it's broadly applicable.

## Broadly Applicable

It's everywhere you look. Investing small amounts of money consistently over a long period of time will save a lot of money. Bacteria divide based on a very similar principle. Radioactive decay works exactly the same way but in the opposite direction. The "interest rate" of the human population in the modern era has been around 1.1% every year, thus making it exponential (to some point of course).

The principle of compounding knowledge can be thought of in the lines of the compound interest equation. Learning and absorbing valuable knowledge, constantly upgrading it with new knowledge from other areas, combining areas together and enriching each of them is the compounding amount here. That's in terms of width, but it's almost exactly the same with the depth knowledge. The previously acquired knowledge forms a template and a pillar for future knowledge.

## Achieves Remarkable Results

As stressed before, compound interest formula achieves remarkable results, but only in the long run. Investing money in the stock market, which on average grows 8% annually, will give you a large sum of money after a certain period of time. For example, 100 euros after 10 years in the stock market (where average interest rates are 8%) turns into 215.9 euros. It doesn't help you much to leave it there only a year. Similarly, it doesn't help you to have it in your bank account, where its value stays exactly the same. Investing is not even the only field. Think of the human body, for example. Your body, contains about 37.2 billion cells [3]. It used to be 1. And even though this exponential growth ends somewhere, as the exponential decline of the number of your cells balances it, it's still quite a result to increase in number for 37 billion during the growth phase.