### Although they have little to do with each other the analogy is easy to understand

Let’s imagine there is only one tree in the middle of the meadow and it is capable of producing two seeds. If we add those two new trees growing from the seeds to the original tree, the next generation will have up to three trees. Now imagine that the two new trees are also capable of producing two seeds each. In this case, we will have six new trees in the next generation and that makes for a total of 9 trees.  If we follow this progression the subsequent generations would have the following number of trees:

1,3,9,27,81,243,729

By the time we reach the seventh generation (or 6 generations after the original tree) we would have no less than 729 trees. The meadow is no longer a meadow as probably it will have turned into a forest.

Compound interest works in a very similar way. Sometimes, we refer to the “magic” of the compound interest due to its multiplicative effect. The compound interest progressive effect is the same that occurs in our previous example about the trees as new trees are able to produce more seeds. Similarly, when we invest a certain amount, once it accumulates returns, the new returns are capable of producing new financial benefits.

The compound interest formula related to the trees would be:

Initial tree x (1 + ability to produce seeds) ^ generations

So in our example:

1 x (1 + 200%) ^ 6 = 729 or a forest full of trees:

We had one initial tree. This is 200% as 2 seeds / 1 = 200%. This percentage raised by the power of 6 (6 generations after the first) will give the number of trees in the seventh generation. If we keep in mind this idea the formula in terms of investments would be:

Initial Capital x (1 + i) ^ n In this case, “i” would be the interest rate (in the former example the ability to generate seeds), or the investment returns, and “n” means the years we maintain this investment (in the example it would be the same as the prior generations).

In the example about the trees we’ve used very unlikely investment returns just to make a clear and illustrative simile. If we take the S&P 500 average performance, which historically is about 9% (a more likely number) and 10.000 €, after 7 years it would become:

10.000€ x (1+9%)^7= 18.280 €

The “magic of compounding” means that even though we invest a small amount of money, the compound interest gives us the chance, with an average return over time, to build-up a reasonable amount of money at our disposal for our retirement.

In this case, the forest’s counterpart (source of life), could be an alternative retirement plan (source of future security). One only needs to do the same calculations but for a longer period by considering more years. For example, in 20 years we would accumulate up to over 56,000 € and in 35 years more than 204,000 €.  Remember that we are always taking into account that we are willing to assume S&P 500 associated volatility and that 9% is the average of our returns.

This is the long-term investors reward.

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