"Compound interest is the eighth wonder of the world. He who understands it, earns it...He who doesn't...pays it."
I'd like to play a game. Answer the following question as quickly as you can.
In a lake, there is a patch of lily pads. Each day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?*
Here's another question:
Imagine I convince you to give me $0.01 on the first day of December and you double it every day until the end of the month (for example, on the second day of the month you give me $0.02, and $0.04 on the third). How much would you owe me on New Year's Eve?
Many people get the first question wrong. The answer is 47 days. The second question is hard to get our heads around. On New Year's Eve, you would owe me over $10 million (go ahead - get a calculator...I'll wait).
It's hard to comprehend compounding, or exponential growth. In the beginning, like in the penny game, it's quite boring and it doesn't seem like anything is happening. But later on, if we stick with it, it spirals out of control.
This doesn't just happen with money. It happens with our skills and self-improvement, too.
*This example is from Thinking Fast and Slow.
Compound interest is the basis of what's called the time value of money. The idea is that a dollar today is worth more than a dollar tomorrow (or at any other point in the future). Therefore, in order to exchange money in between different time periods (i.e. borrowing or lending), there needs to be an incentive. This incentive is called interest. The time value of money is the relationship between the value of money today, the value of money in the future, and the interest rate that connects the present and the future.
The "compound" part of compound interest means that when you make (or pay) interest in one period, that interest gets added to the original amount. Then, in the next period, you make (or pay) interest on your original amount AND on the interest from the last period.
It's very powerful, and in fact, is the foundation of modern finance. It's also the reason you benefit a lot more by starting today. Starting today means you get to the exciting part of the curve faster, and you get to spend more time there.
Positive Feedback Loops
Imagine something happens that causes something else to happen - A causes B. Further, imagine that B also causes A. If A happens then B happens, but then A happens again, making B happen again. And on and on it goes. This is called a positive feedback loop. Imagine a young athlete who is a little better than his or her peers. That skill leads to getting more coaching and training, which leads to more skill, which leads to more coaching and training, and so on. Or think of a stampede. A few cattle start running, which causes some panic in the herd, which causes more cattle to start running, which causes more panic.
Think of it like balancing on a teeter-totter. The further you get away from the center, the faster you will fall.