The MAGIC of Exponential Growth and Compound Interest

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I’d like to start with a quote that states how compounding is really an extremely powerful concept. If you’ll read the whole article, I am sure that you will agree on why it brought Albert Einstein to say that:

Compound Interest Is the Eighth Wonder of the World. He Who Understands It, Earns It … He Who Doesn’t … Pays It.

While I am sure you heard about compound interest before, I’d like to talk a little bit more on the concept of exponential growth behind it.

Exponential Growth

Exponential growth patterns appear in nature in different fields, like biology and physics, and they are a key to understand both today’s technological progress and also boost your finances.

It is a kind of pattern that you see when the change of a given quantity over time is proportional to the previous value of that quantity.

To make it easy and understandable (and also funny and astonishing), we are going to play this little game where we pretend to cover a distance in two different scenarios:

  • Scenario 1: 1 step = 1 meter (linear steps)
  • Scenario 2: 1 step = double the previous distance (exponential steps, just the first step is 1 meter)

Here is the game:

  • How far you would be after 15 linear steps?

The answer is pretty easy: 1, 2, 3, 4, … after 15 steps I would be 15 meters away.

Ok, now let’do the same calculation taking into account a distance that doubles at every step. Let me ask you this:

  • How far you would be after 15 exponential steps?

Try it now!

Do you find it harder? If you are human I guess so!

It’s definitely not easy and it is absolutely counterintuitive. The fact is that we can’t really estimate the end result.

While on a linear path we can easily understand and estimate the future trajectory, we don’t get the same sensation with the exponential trends.

Here is the answer: after 15 exponential steps you would find yourself 16.384 meters away, that is more than 16 km!

  • 15 linear steps → 15 meters
  • 15 exponential steps → 16.384 meters

The result is impressive, but what surprises me more is the simplicity of this concept.

It’s not complex, it does not involve hard math, it’s not rocket science (even though the exponential trend “skyrockets”), and yet we don’t naturally grasp the implication of a trend like this.

We Are Bound to Think in a Linear Way While Compounding Works Exponentially.

The result is that we underestimate final results, fooling ourselves into a misleading interpretation.

Exponential change is the rule in today’s world. The fact that we can’t easily predict exponential growth doesn’t mean that it’s not taking place. The opposite is true.

Predicting exponential growth is not intuitive, but If we take a closer look at some facts in the real world, we can realize that this is the rule, not the exception.

Technological Progress

In today’s world, the rate of change and innovation has never been so high.

The merge between different branches of science and technology, boosted by the massive digitalization, made technological progress exponential.

If you stop for a while, it is easy to realize that we had more technological and scientific progress in the last 2 decades that the last 200 years.

Here is a picture that I found on a course by Marginal Revolution University that speaks for itself.

Source: Marginal Revolution University — The hockey stick of human prosperity

I don’t know how it feels to you, but to me it sounds really incredible what we managed to achieve in the last few decades and how fast and deep technological progress advanced.

The major element of this change are exponential technologies.
Those can be described as technologies which power and potential increase every year at an exponential rate or the cost drops in half (or both).

To get a practical idea of what I mean by that, check out this example on disruption in the energy sector.

You will see how fast the efficiency increased and cost dropped, so much that at the in a matter of 20 years we found ourselves with solar energy to be the cheapest source of energy, cheaper than coal.

Exponential technologies are a real thing, and they are here. Some areas in which it is likely that you will see exponential developments over the course of your life are:

  • Networks and sensors
  • ICT
  • Artificial intelligence
  • Automation and robotics
  • Digital manufacturing
  • Virtual reality
  • Solar power generation
  • Medicine
  • Molecular biology
  • Genetics
  • Food production
  • Nanomaterials
  • Transports
  • Renewable energy

It is really an exciting future and I can’t wait for it to happen! It’s already happening today.

This picture from Tim Urban’s amazing blog Wait But Why that sums up everything I said until now and what are our perspective for the future:

Credit — Tim Urban,

Let’s move on to the second core part of this article: compound interest and finances.

Now that you got an idea of how powerful and important is an exponential trend, we are going to see how compound interest applies to money and finances and how you can make it work in your favour.

Compound Interest And How To Boost Your Finances

What if I told you that few simple and easy actions taken today, like saving $5 or $10 per day, can turn into amazing result over the course of 30–40 years?

While your everyday life doesn’t change that much, your future self will certainly thank you. Actions as simple as this one can really make you financially rich at the end of the day without any particular effort or skill.

When it comes to personal finance and our journey to financial independence and retirement, compound interest can either be your greatest ally or your greatest enemy. This depends on how you use your money and how you use your debt.

Although personal finance can feel intimidating or complicated, the real basics can be summed up in the following two concepts:

  • Save part of your income
  • Consistently invest that amount over time

That is really so simple. Yes the concept is simple and easy to understand, the challenge if you want to reach the end result is to actually do that.

Let’s make it clear with a parallel: everyone knows how to lose weight. They know the steps, what to do and not to do. If you won’t to lose weight is not hard to know how to do it, it may be hard to get yourself to do it.

When it comes to finances and investing for the long-term it is exactly the same situation. There are several books on this topic and you can easily find all the information that you want online. Maybe one of the shortest and most concise book out there is The Automatic Millionaire by David Bach.

However, when providing examples about compound interest, many authors usually use an interest rates of 10% to do their calculation.
I don’t believe that 10% is something you can rely on for your passive investments. To make 10% every year, for maybe 40 years, you must be a top investor.

We are going to consider a scenario that is much more realistic, more prudential and definitely consistent with financial markets long-term returns.

The historical average annual return adjusted for inflation of the S&P 500 is 7%. This was calculated over a very long period of time (comparable to your lifetime). Your actual returns also depend on when you enter the market and future economic scenarios (in which we could see a crash soon).

So, consider a 5% annual interest rate, and suppose that you save $10/day and at the end of each and every month you consistently invest the $300 amount you saved for the very long-term. These are the results:

1 year → $3,699.01 
 2 years → $7,587.26
 5 years → $20,486.83
10 years → $46,778.79
15 years → $80,520.79
20 years → $123,823.89
30 years → $250,717.91
40 years → $459,713.57

After 40 years you end up with near half-a-million dollars. The great thing is that you put in capital for $144,000.00 and earn $315,713.57 of interests.

Remember, this is a conservative scenario, if you manage to save more or achieve higher returns, you can definitely do much better.

If you want to play with different amounts, interest rates and years, find out one of the many calculators online, here’s one. Here are some other examples of the results that you could achieve under different scenarios:

$150/month ($5/day) at different interest rates
40 years at 5% → $229,856.79
40 years at 7% → $396,018.72
40 years at 10% → $ 956,517.04

$300/month ($10/day) at different interest rates
40 years at 5% → $459,713.57
40 years at 7% → $792,037.44
40 years at 10% → $1,913,034.07

$500/month (less than $17/day) at different interest rates
40 years at 5% → $766,189.29
40 years at 7% → $1,320,062.40
40 years at 10% → $3,188,390.12

Too good to be true? No, not at all. Just $10/day or so, consistently saved and invested, that’s it.

Now, I am sure that you agree with me on how much it would costs to you NOT TO DO it. But stop for a moment and ask yourself the following question:

What’s the Cost of Putting in Place This Strategy Today?

Seriously. How hard is it to put away $10/day? We all have some kind of useless expense that we make and that we could easily cut them off without changing our lifestyle.

Or, you may think it this way: everyday, you keep for you 1 hour of your paycheck.

By doing that, you are following one of the major pieces of financial advice that is to pay yourself first. It’s no wonder that you always hear that.

You don’t make it with $10? Save $5! Chances are that you’ll end up with a good amount anyway.

Accumulate Wealth Through Compound Interest Is AUTOMATIC, but It Requires a Lot of Consistency in Your Actions

Time and consistency really make the difference. Starting today is very easy, there are thousands of ways to start investing and even if you are not willing to learn how to invest, you can still rely on mutual funds and index funds for that purpose.

If you’d like to know more on that, check out those articles:

The concept of compound interest applied to money is that over time your money begins to make you money. Every year you earn additional interest on the whole capital, that includes the interests of the previous year.

The result of that is an exponential growth pattern: as times goes on your money grows bigger and bigger, the higher the interest rate, the faster it will grow.

The key here is consistency. Taking advantage of this incredibly powerful mechanism puts you on the fastlane to become significantly richer in the years to come.

The Earlier You Start, The Better.

Do You Think Is It Worth It?

This article is for informational purposes only, it should not be considered financial advice. You can read the full disclaimer here.

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