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| Image taken from Wikipedia, thus the labeling in a foreign language... |
Charlie Munger famously said "the first $100,000 is a [naughty word that starts with B]." With apologies to Mr. Benford for conflating his name in an unfavorable way, there's a perfectly good mathematical reason why things work this way: Benford's Law.
Benford's Law basically states that if you take a large group of numbers spanning several orders of magnitude, the probably that any number will begin with a one is close to 33%. If this seems counterintuitive, here is a video explaining it in more detail. It's nine minutes long, which is an eternity in internet time, but I found it fascinating.
Near the end of the video, the guy mentions stocks as an example of Benford's Law. Let me instead use your net worth. Every time you add another digit onto your net worth, you'll be stuck near that number for a while. Think of it in terms of doubling your money. Imagine that it takes five years (I wish) to double your money. You start with $10,000. To get that first $100,000, it will take you something like seventeen years. Then to get your next $100,000 it would only take five years. Then less and less as your money picks up momentum. However, to go from $100,000 to $1,000,000 would take seventeen years again.
So what do we do with this information? Well, first, start saving and investing early, so you have many years of compounding ahead of you. Second, don't get discouraged with small efforts. Money attracts more money. As your investments get larger and larger, they'll earn more and more money on their own without any work from you. "Now ye may suppose that this is foolishness in me; but behold I say unto you, that by small and simple things are great things brought to pass; and small means in many instances doth confound the wise."1
Just remember, there's mathematical proof that the first $100,000 is, in fact, a Benford.
1 Alma 37:6↩
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