*“The elementary mathematics of compound interest is one of the most important models there is on earth.”*

-Charlie Munger

Charlie Munger died last month. I have no doubt that he will go down in history as one of the most quotable humans of this and the last century, among other more remarkable achievements. This post is not a eulogy, however, it’s the application of one of his pithy, insightful phrases into the area of growing and profiting from expertise.

Of the three key variables of the future value of an investment—the principal amount invested (P), the rate of return (r) and the length of time (t) the money is invested—the latter is, somewhat counterintuitively perhaps, the biggest driver of results. This compounding effect of time is why the authorized biography of Munger’s partner in Berkshire Hathaway, Warren Buffett, is titled *Snowball*. Money invested over time is like a snowball rolling down a hill, starting out small but growing with time, interestingly at first and then with an awesomeness that is almost incomprehensible.

Just as the interest on money compounds over time, the interest on knowledge compounds similarly, under the right conditions. Whether we are experts at seeing (and therefore advisors) or at doing (practitioners), knowledge is the foundation of what we do and each of us wants more.

The compounding effect is not intuitive because people are not good at thinking exponentially. Consider a thought experiment. Off the top of your head, what do you think the future value of a $1 investment would be in 30 days if the value of that investment doubled every day?

Not many guess at anything approaching the right answer: just over $1 billion.* Here’s the follow-up question that many people also struggle to answer correctly. How many days does it take for the investment to reach half that amount, about $500 million?

Many intuit the halfway point of 15 days which shows that we think linearly and not exponentially. The answer, which is obvious after you hear it, is 29 days. A $1 investment (at a ridiculously short doubling period, granted) yields $500 million in the 30th doubling period—in one day—when it yielded just $1 in the first one. On day 31 the investment is worth $2 billion. On day 40 that initial dollar is worth $1 trillion, and well before a year it’s worth more money than has ever been generated in the history of humanity.

The time value of knowledge has the same effect as the compounding effect of interest. In this domain of knowledge, the principal (P) is what we know at the start of our career. Our rate of return (r) is the rate of learning—the pace at which we get smarter. Time (t) is time; it remains the same. From this we can draw two important lessons.

### Lesson One

**The first lesson is that ***P*** and ***r** ***do not have to be large when ***t*** is.**

Our knowledge base at the beginning of our career (P) is almost irrelevant. A rate of learning (r) is vital but it doesn’t have to be large when time (t) is long. We can overcome a disadvantaged starting point or a slow rate of learning with time, as long as we continue to learn. Play the long game and keep learning.

We all know people who are coasting through the last few years of their career. We can spot them not because of their age (Warren Buffett is 93 and isn’t done. Charlie Munger was still compounding just before his death at 99.) but because they telegraph that they are done. They are enjoying the fruits of their career, taking a last victory lap around the track before they head off into the Florida sunshine. That is their prerogative and it’s not my point here to marginalize someone for their choices or diminish anyone who decides their work is done, I’m simply pointing out that the compounding of knowledge is not just a function of age (t). Older people are not necessarily wiser. Older people who are lifelong learners, however, are.

### Lesson Two

**The second lesson is that the biggest gains—by far—come at the end.**

Our $1 investment went from $1 to $2 in the first period (1 day) and from $500 million to $1 billion in the 30th period of the same length. Persistence really does pay off—when you keep learning.

I have a scientist friend with whom I have the most interesting conversations because he brings his domain to bear on my business and I bring the business domain to bear on his work. He’s 74 and in his words he was retired from the age of 18 to 45. Then he went back to school, earned his PhD at 50 and proceeded to have an impact in his study area over 24 years that any of us would be proud to have in our own worlds. In a recent conversation I was marveling at the impact he’s had in the last 2 years alone, a few years after most people would have retired. He is an example of a person whose growth has been exponential instead of linear and as a result has achieved a massive amount in a short period of time—after sticking with it for a long time.

### The Tricky Variable of *r*

It’s fair to say that most people don’t get an exponential return on their knowledge and it’s probably because rate of learning (r) is the difficult, amorphous variable in our model. Unlike a rate of return on financial investments, our measures of any rate of learning are likely to be intuitive, inconsistent and plain wrong. Just as people’s ideas of what constitutes exercise changes, diminishing almost imperceptibly as they age to the point where one day they mistake walking for exercise, so too I suspect does the sense of our rate of learning.**

Here’s another thought experiment. Consider the idea of someone building a chatbot version of you. They train a narrow AI on all of the outputs of your career—your work and your thought leadership—up until 1 year ago. None of the material has been weighted, meaning the people building the model treated all your work with equal value, ignoring the fact that you learned with time, improving some ideas, surpassing, correcting and even disavowing or refuting others. What’s your reaction? Do you laugh at the idea of someone skating to where the puck used to be? Or do you bridle with rage that almost everything you know is now out there, that you’ve effectively been replaced by an archived version of you?

If it’s the latter then you’ve let your rate of learning (r) decline with age.

Okay, one year might be the right threshold for this test for a 57-year-old writer, but maybe not you. How about a chatbot based on everything you knew up until two years ago? How about five years ago? There is a point in time at which you think, “yeah, prior to that my competitors can have everything I knew. I’m miles ahead of that place now.”

I can’t tell you where that line should be for you, but I think you’ll arrive at an honest *feeling* about your rate of learning (r) by doing the thought experiment. Has your idea of learning diminished to the exercise equivalent of walking? It might be time to hit the gym, so to speak. And maybe the actual gym? 😉

### Keep Going

Stick with it—whatever “it” is. As long as you do not let your pace of learning diminish with time (age) you will have massive gains in a short period of time—after a long period of time.

-Blair

**In the original version of this post I mistakenly had $1 turning into a mere $1 million in 30 days and not the correct $1 billion. *

***Yes, walking is good for you but it’s not exercise. It is its own category of thing—called “walking”—in between “fresh air” and “exercise.” No need to email me your thanks for clearing this up. I’m here to help. 😉*