First, let's take a look at the formula: p=x[1+y (1+z) n]n, a formula that was sent out by Li Xiaolai, a few days ago, and says, "I've lived on this formula all my life."....... The back end with an ellipsis, can be said to be more meaningful. What's the magic of this formula? What does it mean?
首先我们来看一下这个公式：p=x[1+y(1+z)n]n 这个公式是前几天李笑来老师发出来的并说，我这辈子全靠这个公式活着......。后面以省略号结束，可以说是意犹未尽又意味深长。这个公式到底有什么魔力呢？它表示的又是什么意思呢？
We have always advocated long-term investment, so how long is this long term? Everyone's heart is not the same long. We illustrate and demonstrate through a table. You can also do it yourself, personally experience.
我们一直主张长期投资，那么这个长期到底有多长呢？每个人心中的长期也是不一样长。我们通过一个表格来说明，演示。大家也可以动手做一下，亲身体会下。
The first form is age, and we assume you're 33 now, and the second is the period of investment. We'll take 20 years as an example. The first line is annualized, with yields ranging from 10% to 35%. The principal is set at 1 in order to facilitate calculation and intuitive results.
第一张表格第一列是年龄，我们假设现在你33岁，第二列是投资年限，我们以20年为例。第一行是年化收益率从10%到35%。本金设为1是为了方便计算和结果直观。
In the following table, the formula in the C3 cell is: =C2* (1+C1); the C4 cell formula is =C3* (1+C1), followed by analogy. We can finish the manual (C column formula, and then hold down the C column drag the corresponding cell right automatic coverage formula, such as finished C3 cell formula and then press C3 to pull, D3, E3 until the H3 formula are out. It's not right if you do C3 and pull down
在以下表格中C3单元格里的公式是：=C2（1+C1）；C4单元格公式就是=C3(1+C1) 依次类推。（大家可以手动做完C列公式，然后按住C列对应的单元格向右拖动就自动覆盖公式了，比如做完C3单元格公式然后按住C3向右拉，D3,E3一直到H3公式都出来了。如果你做完C3往下拉，是不对的。）
As can be seen from the following formula, the difference is the biggest difference between the ability to invest. The same is 10 thousand of the principal, after 20 years of investment compound interest, annualized yield of 10%, eventually 67 thousand and 300, and if the annualized 35%, 20 years later, we can get 4 million 42 thousand and 700. According to 10% of the investment capacity, 19 years can get 6.12, but for 35% of investors, 7 can reach 8.17, the same result, shortened by 12 years. Yes. Can you make it 35% by 20? It's too hard。 Yes, that's the difference in the ability to invest.
从下面这个公式可以看出，差别最大的是投资能力的区别。同样是1万的本金，经过20年的投资复利，年化收益率10% 最终获得6.73万，而如果年化35% 20年后我们可以得到404.27万。按照10%的投资能力，19年可以得到6.12，但对于35%的投资者来说7就可以达到8.17 同样的结果，缩短了12年。是啊，保持20年年化35%可以实现吗？太难了。对，这就是投资能力的差别。
For the more powerful people, the longer the shorter. In other words, the weaker you are, the longer your longer.
In this table, we also see the compound interest formula f=y (1+z) ^n f=, future value y=, investment amount, z= annualized yield, n= investment cycle
对能力越强的人来说，长期越短。换句话说就是，你越弱，你的长期越长。
在这个表格里我们也看到了复利公式 f=y(1+z) ^n f=未来期值 y=投资金额 z=年化收益率 n=投资周期
Now let's look at the formula p=x[1+y (1+z) n]n, and we can split it into 2 parts. Is p=x[1+f]^n a compound interest formula with a compound interest formula in it?. Here at f we can be seen as the rate of return on investment, can also be understood as investment ability, through the daily learning progress, our investment capacity is strong, the daily growth rate of return on investment to achieve interest. That is to say, compound interest in the annual yield, through persistent learning, can achieve compound interest. Do you think the year 35% is over? Far from it, many people earn more than 35% by their own studies. So they realized their wealth freedom in the short run. Bitcoin, for example, has achieved several decades of growth in just 3 or 4 years. This makes long term investments fairly short-term, because the yield in the formula is greatly improved.
现在我们再来看公式 p=x[1+y(1+z)n]n 我们可以把它拆分成2部分 p=x[1+f]^n 是不是复利公式里面套着一个复利公式。在这里f我们可以看做投资收益率，也可以理解为投资能力，通过每天的学习，进步，我们的投资能力逐年变强，每天的成长使得投资收益率也实现了复利。也就说复利里面的年化收益率通过坚持不断的学习是可以实现复利的。你以为年化35%就到头了吗？远远没有，很多人通过自己的学习，收益率远远超过了35%。所以他们短期实现了财富自由。比如比特币，短短3，4年的时间实现了几十倍的增长。这使得长期投资变得相当的短期，就是因为公式里面的收益率大大提高的原因。
There are many factors that affect the long-term. For example, for people who can use the right strategy, it's much shorter; it's shorter for those who have the ability to make money outside of the investment
影响长期的因素还有很多。比如：对能使用正确策略的人来说，长期更短；对有能力在投资之外赚钱的人来说，长期更短
The two conclusions are mainly about the amount of investment. We can see from the above table that the size of the initial investment is another important factor to determine the final income. Those who have the ability to make money outside the market can not spend the money they make in the short run, and they can also add money to their investment accounts. Nature greatly increases the speed of compound interest.
这两个结论主要是对投资金额来说的，我们从上表可以看出，起始投资金额的大小是决定最后收益的另一个重要因素。有能力在场外赚钱的人可以短期可以不动用投资所得的钱，而且还能源源不断的往投资账户添钱。自然大大增加复利的速度。
No wonder compound interest has become the eighth wonder of the world. Do you doubt the result of compound interest above?. Yes, I see the result. I doubt it too. Can you really harvest so much for 20 years? What's the hard part? Is to insist on re investment, and constantly learning, so that their investment ability is more and more strong, shorten the investment time, 20 years target, may be 10 years will be achieved. Even for 5 years. So one day without study, without thinking, is actually behind.
The above content is Lao Li learning laughter, the teacher got column experience.
怪不得，复利被成为世界第八大奇迹。你是不是怀疑上面的复利的结果。是的，看到结果我也很怀疑，坚持20年真的可以收获这么多吗？难的是什么？是坚持复投，而且不断的学习，使得自己的投资能力越来越强，缩短投资时间，20年的目标，可能10年就会实现。甚至5年。所以一天不学习，不思考，实际上都是在落后。
以上内容是老李学习笑来老师得到专栏后的心得体会。