The secret formula to getting wealthy

The secret formula is that there is no formula. So discard all your subscriptions to websites stating that they can make you rich in "just in 3 months" or get quick schemes. The real secret, and it's no secret at all, is that it takes discipline and self sacrifice. More specifically, it entails one to spend less than you earn and invest the residual. After many, many years, you can't help but be wealthy. Emphasis is on the time here that is involved. You must invest the money for long periods of time to allow the magic of compound interest to work. Let's illustrate a few points of how this works with an example.

Let's assume we invest $1, and this dollar earns 10% per annum. The only variable which changes here is the time period for which it is invested in.

1(1.1)^5 = 1.611          (1)
1(1.1)^10 = 2.594        (2)

1(1.1)^45 = 72.890      (3)
1.(1.1)^50 = 117.391   (4)


There are a few things to notice here apart from the aforementioned. Firstly, compound interest has little impact on the value of the dollar over a short period of time, as illustrated by (1). Secondly, as you increase the time period, from 5 to 10 years, i.e. the time period doubles, it's effect, as it is still a short time period, is minimal. For example, the percentage change in the value of the dollar from 5 to 10 years is only 61%.

Fast forward the same dollar, however, now it's invested for 45 years and we've turned it into roughly $73. A huge difference. Lastly, while the time period has changed by the same amount between (1) and (2), i.e. 5 years, the dollar has also grown by 61% but the nominal change is approximately $44.5. Which is much larger than the initial change of five years. One other thing related to this example, is that i used a difference of 5 years in both sets. This was intentional, as it illustrates that the first 5 years, i.e. from 5 to 10 years, represents a doubling of the time period. However, from the 45-50 year time period, it only represents an 11% change in time, but the result in relative terms, is both 61% (of the appreciation in the value of that dollar).

The key takeaway from this is that compounding works well, but only after long periods of time. This runs congruent with my initial reasoning that it takes many, many years for this process to work. Theoretically, this sounds easy but in practice this is a difficult task to adhere to.