Compound interest is something we all know about, but not something we fully grasp. Sure, most people in the developed world in 2017 know what compound interest is and what that it's a pretty powerful thing, but few know exactly how powerful it is. There's a rumor that Einstein said something to the effect of "compound interest is the greatest force in the universe." If that's true, he was a smart man.
So, how can we approach a better understanding of compound interest? There seem to be two possible approaches here:
It seems that both are important, bu that the examples always are better in getting the ball rolling. Some examples are so astonishing that students of finance and financial theory are in awe both at the power of compound interest nad the previous disrespect for it. Here is one such example for your entertainment and pleasure. Let's imagine 3 scenarios:
So, we've got 3 scenarios here, with each person separated by two main differences:
So, we know what's different, but what is the same? We have a few things that are the same for the people in all 3 scenarios:
So, we now have what we need  we have 3 babies born on the same day in the same hospital to different families. Let's take a look at how things turn out for them over the course of their lives. We first notice that the baby in the Ideal scenario starts accumulating wealth  although not very much. In the first year, $1200 is saved. By Year 10, however, almost $20,00 has been accumulated thanks to the 10% growth. Another 10 years goes by and by Year 20 the Ideal baby has accumulated almost $69,000  a very significant sum especially given the fact that the parents have only saved/invested $24,000 over the course of those 20 years. Now, let's move to Year 25  the Optimistic baby is now and adult and is joining the pack here. Unlike the Ideal adult who now has a lot of cash at Year 25 (about $118,000), the Optimistic baby has nothing. However, the Optimistic baby is saving 10x what the Ideal baby is saving  that's $1200 a year vs. $12,000 a year! So, let's observe these two over time. At Year 30, the Ideal adult has roughly double the amount the Optimistic adult has (that's about $197,000 vs. $93,000). This might seem not astounding unless you realize that the Ideal adult has only saved/invested $36,000 over the course of his or her life while the Optimistic baby has already (over the course of just 5 years) invested $60,000. Continuing through to Year 50, where the Typical adult finally joins us, we see an interesting situation  the Ideal and Optimistic adults have roughly caught up with each other. Each has about $1.3 million, BUT the astounding part is only revealed when we think about how much each has saved/invested over the course of their lives:
Now, we've got everyone in the game  the Ideal, the Optimistic, and the Typical adults. Let's follow through until 65  they have 15 more years to save and growth their wealth. Catching up with all of them at 65, what do we see? We see a few interesting things, but first, let's start with the numbers:
BUT, let's again sit in awe of the power of compounding by taking a look at how much each saved/invested:
So, we see that they're all very wealthy, but they've achieved their wealth in very different ways. While the Ideal person barely saved anything throughout their life, the Typical person saved a ton. Digging deeper, we can see that the Ideal person actually saved less in their entire 65 years than the Typical person saved in one single year. This is truly astounding and provides excellent evidence at the amazing power of compounding. We can see that time matters a lot. In fact, this example clearly shows that in many cases, time matters more than money. The one who started first finished ahead of everyone and barely had to save anything. The Idel person could have earned $40,000 their entire lives with no raises at all but would still have more money at 65 than the Typical person who had to earn enough from 50 to 65 to be able to put away $120,000 per year (that's very hard considering that savings comes after expenses and aftertax for the most part). The Typical person would probably have to earn at least $400,000 per year to be able to reasonably save that much money  even at that level of income saving $120,000 per year would feel like an incredible sacrifice. Take a look at the table below for a rundown of all the numbers. You'll see the age of our group on the left along with the savings rates and rates of returns at the top. 
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