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# Be Patient

This step here is likely the single most important, if boring, step of all.

We briefly touched on the grains of rice on the chess board. Legend has it that when the inventor of the game of chess showed the king her creation, the king was so impressed that he offered the inventor whatever she wanted. Clearly an expert on compounding, she asked for just one grain of rice for the first square on the board, two for the second, four for the third and so on, doubling at every subsequent square. The king, unused to the concepts of compounding and exponential growth, readily agreed. If you do the calculations, then by the time you arrive at the last, i.e. the 64th square, you will need not mere millions or billions or trillions or quadrillions but over 18 quintillion grains. A quintillion is a thousand quadrillion. In other words, an altogether too large number to comprehend.

The point of the story is to illustrate how hard it is for us to wrap our heads around compounding and exponential growth. Our brains can understand linear growth: twice the effort, twice the result. Four times the effort, four times the result. Two people can paint a wall twice as fast. And so on.

Here's another such illustration of exponential growth but in reverse. Say there's a large lake and there's small patch of algae on its surface. The algae multiplies rapidly such that after 29 days, half the lake is covered in algae. How much longer do you think before the other half is also covered in algae? Not another 29 days - but rather just ONE more day. Algae - like life - comes at you fast! Here's a second question: At what point was this lake LESS than 2% covered in algae? Again the answer is not on Day 3 or 4 but actually on Day 24 when it is only about 1.5% covered. A mere 6 days later - boom!

While it is likely an apocryphal story, Albert Einstein is rumored to have said that "Compound Interest is the eighth wonder of the world". Whether he said it or not, it is truly an awesome force.

Hopefully by now you are convinced - even if you are reeling a bit - by the power of compounding. And the best way to benefit from compounding as an investor is by being patient. Even if the stock market has a great year, unless you actually need the money for an emergency, don't sell. Let it compound. Time is your friend here.

How does the stock market actually do - over the long term? Let's look at a great proxy for this: the S&P 500. This composite index has a rich history: it was birthed in 1926 with 90 of the largest stocks of the day. In 1957 it was expanded to the current 500 of the nation's most valuable stocks by market capitalization. The average annual return since the mid 1920s has been 9.8%. Remember that this period includes World War II, various wars in between, lots of market crashes and recoveries - and COVID-19. And since 1957 the annual average return has been 10.1%. That is, an investment of \$1000 becomes about \$1100 after a year (on average). Nice, but hardly enough to get your heart pounding.

At this point it's probably important to remind ourselves that there are two other thieves of wealth: taxes and inflation. In reality, that 9 or 10% average annual return is actually closer to 7% once adjusted for inflation. To figure out how long it takes for your money to double, there's a handy rule called the "Rule of 72". Just divide 72 by the average annual return to get appromixately how long it will take for your money to double. 72/7 is about 10 which is how long it takes for money to really double: a decade.

A 20 year old with \$1000 in the stock market will be worth \$2000 (inflation adjusted) by the time she's 30. By 40, she'll be worth \$4000 and so on. By age 65 (the nominal age of retirement) her \$1000 will have grown to be worth about \$23,000. 23X - wihout her need to add a single penny to her original \$1000.

If, instead, to her initial \$1000 investment, she added just \$100 each month, then by age 65 she would have over \$400,000! And that's \$400K in inflation adjusted dollars. And no, that's not a typo. You can plug in the numbers and see for yourself at this compound interest calculator at the government website: investor.gov

I am being conservative here. Lots of websites take the full 10% without any adjustments such that your money doubles in 72 divided by 10 or in about 7 years. If we use 10% vs 7% in the calculator above, she would be worth well over a million dollars by age 65. And she gets to be a millionare quite modestly: by starting with \$1000 and adding \$100 each month. And by being very patient. (At 10% a year, the same \$400K number would be reached in her mid 50s.)

Say that our 20 year old, let's call her Jane, has a twin. Let's call him Jack. Jane invests \$1000 at age 20 and adds \$100 every month. Jack on the other hand, only sees the light at age 30. He decides to double what Jane is doing and starts with \$2000 as an initial investment and adds \$200 each month. Would it be enough to catch up with Jane? No - on their 65th birthday, Jane will still have \$17K more than Jack. If Jack started at age 40 and puts in \$4000 to start and \$400 each month, can he catch up? Nope - he will still have over \$50K less than Jane.

That is the real benefit of starting early and being patient. You allow compounding the time it needs to work its awesome math. After some point, the more money you have (invested) the more money you'll make. It's like an unstoppable force. Most people don't realize this but Warren Buffet made almost half his wealth in the last 8-10 years of his life. Fully 99% of his current net worth was earned after he turned 50.. As of 2023, Buffet is 93 years old. If, as we all hope, he gets to be a hundred years old (like his partner, Charlie Munger), Buffet will be worth nearly double what he is already worth today. Stay in the game. Be patient.

Most college kids don't realize that it is entirely possible to start with a \$1000 investment in a passive index fund, add \$100 a month to it, and have hundreds of thousands - or even a million dollars - by retirement age. And this is doable without having to invest tens of thousands of dollars in one go to start with or have to be lucky enough to pick the Apples and Teslas of tomorrow. It's even nicer that you don't need to spend hours each day devouring market trends and government data or investor journals or companies' SEC filings. Or take all sorts of crazy risks that could either result in millions or wipe you out. Just get started today and keep going. Enjoy your life and let compounding do its thing.

We've mentioned retirement a few times. Here are some thoughts on creating a nest egg as part of a plan for retirement.