Compound interest is a miracle maker. It accelerates your financial journey in a way that most people wouldn't expect to be possible. You'll need to a few things, though, in order to benefit of it. First, you have to keep doing what you are doing and follow your million dollar plan. Second, you'll need to give it time to work its wonders. It is more than worth the effort and wait though, especially as its impact just keeps getting better when time goes on.
Compound interest means simply adding the interest or capital gains to the principal and then getting the similar interest or capital gains also on the increased part of the principal. Or, as Wikipedia defines it, "Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest."
Accordingly, if you start with $10,000 and earn 10% interest on it, your first year interest is $1,000, second year interest is $1,100 (10% on $11,000), third year interest is $1,210 (10% of $12,100), and so on. While the growth remains slow at the beginning, it later accelerates quickly: your 11th year interest in this previous case would be nearly $2,600 - more than a quarter of the original $10,000 principal - and the 15th year interest is almost $3,800. And if you've kept this going for 20 years, the interest in the 21st year would be over $6,700 - thus more than two thirds of the entire original principle. Thus in 25 years original humble $10,000 would have grown more than 10-fold to $108,347. And if you then gave it yet another 5 years, it would grow by another $66,000 into about $174,500.
Below is an example of compound interest vs. simple interest, with $100 starting principle and 8% annual growth rate. As you notice "acceleration" just keeps getting better when the time goes on. Raise the growth rate or lengthen the period of time, and it looks even more impressive.
Compound interest needs time in order to start having a significant impact. That's why it's better for your to start early if you can, and stay the course. Of course, the higher the interest rate, the earlier and more impressive the acceleration. Growing the capital - i.e. investing - with an unusually high rate of return tends to be hard to sustain though. If you assume to be able to keep growing at high interest rates - say over 20% a year - you either have a rare ability - great for you! - or may be setting yourself up for a disappointment. The nice thing is that compound interest works at lower rates of return, too, even if the results are a bit slower to come and somewhat more modest in magnitude.
Besides time you also need sustained effort: you must keep doing what your are doing and not slow down or touch the compounded principal. Otherwise your magic will dampen or disappear. The temptation to snatch a piece - "just a tiny bit, no-one will notice" - of the principal may be big, especially when quite some time has already passed and the initial investment has multiplied. However, if you take away any part of the principal, this will set you back a bit right away - or a lot if you took a bigger piece. Similarly, if you let the growth rate decrease, the impact of the compounding takes bigger hit than what would seem obvious from the difference in the interest or growth rates.
Here is an example of how big the negative impact is if you snatch a way a small piece of your pie early on and slower your rate of compounding just a little. After growing your $10,000 for the first 10 years at 10% annual pace into $25,937, if you take away just $3,000 and then keep growing the remaining $22,937 at 8% rate for the next 20 years, you'll have only $106,900 - rather than $174,500 - at the end of the 30th year. What a huge difference for such small reductions in the principle and growth rate!
If you found a way to invest that initially yields high rates of returns, great for you! Just be aware, though that it tends to be hard to sustain unusually high growth rates. The high returns you can get on smaller amounts of capital are not always available for larger amounts. Then again, this is to a great extent up to you - if you accept the challenge and keep finding great opportunities that sustain or improve your capital growth rates, you will be magnificently rewarded over time through compound interest.
Besides time and sustained effort, the size of the initial principal also matters a lot for compund interest. If you start with, say, $30,000 instead of the $10,000 of the example above, the 10% growth rate will get you to $523,500, a lot more than the not-too-bad $174,500 resulting from $10,000 original principal. This is why you should try to maximize the principal early on, as you'll then be greatly rewarded when time goes by.
Warren Buffett is a living testimony to the miracle of compound interest - in this case with a sustained high growth rate over an amazingly long period of time. Compound interest - along with his frugal ways and unique investment skills - has made him one of the world's richest people. Even if you didn't start as early as he did - around the age of 10 or so - and even if you wouldn't be able to sustain the same rates of returns - an average of over 20% in the past 45 years - that's OK: he is a multidecabillionaire, while we are only shooting for the level of (multideca)millionaires here.
You need to achieve less than one thousandth of what Warren did and yet you can be a multidecamillionaire and financially free! Just don't forget to get started early enough and maintain reasonable rate of return, so that compound interest will have enough time and power to boost your finances to the stratosphere!