This is a good question. It is fortunate that it demonstrates the reason why young people are scammed by loans step by step. Many people have no idea about the compound interest of exponential growth, thinking that the daily interest rate of 1.01 is a small number, but it is not. 1.01 per day is a terrifying number. 1.0001 per day is a relatively normal and reasonable value. The annual interest rate of 20% is called usury. For users who are trapped in usury, we have memorized an ancient article: borrow one year, pay it back in ten years, and pay it in a few lifetimes. Note that this article does not use exaggerated rhetoric. Because the interest rate of 20% is really not repayable for ten years, and the principal must be repaid more than six times in ten years. This is an extremely terrifying interest rate. And this extremely terrifying interest rate is only equivalent to a daily increase? 1.0005. In other words, a daily increase of 1.0005 = 5/10ths of a daily interest rate, which is extremely terrifying, a high interest rate at the usury level. Let’s look at the 10% annual interest rate, which is called stable profiteering. In other words, if your investment includes all profits and losses sideways, and the long-term average return can stably reach 10% per year, then it is a huge profit, and you are a Warren Buffett-level investor. Don’t be fooled by your temporary 40%, 100% income. This kind of income is often unsustainable. If you continue to trade stocks for five years or ten years, a certain high income will always be flattened by the subsequent sideways. In the long run, your The average return is still difficult to reach 10%. It is generally believed that you do not lose money in stocks, and you have already exceeded 90% of the stockholders. If you can achieve an average annual income of 10% in a long-term stability, then you are a stock god. But what is the daily income of the stock god level? It is 1.00026. In other words, a daily increase of 1.00026 = 2.6 ten-thousandths of a daily dividend, which is a high return at the stock god level. –So, how much daily interest is equivalent to a 5% annual income for a regular financial management level? Equivalent to 1.3 ten-thousandths of a daily interest rate. –Key point: The daily interest rate is 1.3 per ten thousandth, which is the normal financial management income, the daily interest rate is 2.6 ten thousandth, which is the stock god-level income, and the daily interest rate is 5 ten-thousandths, which is the usury-level interest rate. The subject teacher used: 1.01 = daily interest rate of 100%, which is 20 times higher than usury. This kind of terrifying growth is simply not something humans can do. Conclusion: There is nothing wrong with using index calculations. The problem is that the daily increase of 100% is really terrible. An increase of one in ten thousand is more realistic. In other words. In this formula, 1.01 is replaced with 1.0001, and 1.02 is replaced with 1.0002, which is a more reasonable value.


By zhiwo

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6 months ago

In fact, there is no problem, but 1% a day, the amount of improvement is too outrageous. In the real world, if something can maintain a daily increase of 1% for a long time, it will not take long to reach an astronomical number. Because he will double 40 times this year, 1,600 times in two years, and billions of times in 10 years. If any bank’s wealth management product claims to have a daily interest rate of 1%, then I can buy hundreds of China and the United States in ten years after putting in a penny. In fact, a steady increase of 5-10% a year in life is a big deal. This can basically be maintained at a doubling rate in ten years. After my country’s reform and opening up, the annual GDP growth rate has been around 6-8%, so the total economic output has roughly doubled over the past 40 years. This doesn’t sound very outrageous. It is not uncommon for risk investment products bought by banks to be basically stable at an annual interest rate of 8%. In fact, I think that people’s learning and growth are also at this speed. It is not too outrageous to double the level of study every ten years. So if the annual growth rate of a thing is 10%, what is its average daily growth rate? It is about 0.026%.

6 months ago

After seeing this picture quoted by the subject, my inner feelings are really mixed, and it’s hard to say a word. Because when I was still studying, I saw a lot of masters and soul chicken soup masters in the airport talking about this on the Internet. At the end of their passionate speech, there are usually two PPTs, one of which is the seventh steamed bun and the law of the lotus pond on the twenty-eighth day, and the other is the one quoted by the subject. The seventh law of steamed buns is that a person eats seven steamed buns before he is full, and complains why others don’t give him the seventh one at the beginning, so that he doesn’t have to eat the first six. Most people use this law to warn everyone about the importance of accumulation and be patient. Before you eat the seventh steamed bun, you will still feel hungry after eating several steamed buns, just like you have done a lot of things and paid. Efforts still do not see the same effect. The law of the lotus pond on the 28th day means that the daily growth rate of the lotus in a lotus pond is double that of the previous day, and the whole lotus pond will grow in 30 days. Then on the 28th day, you will find that the lotus on the lotus pond The lotus area only accounts for a quarter of the lotus pond. This is also telling you the importance of persistence. Don’t give up the night before success. Similarly, some people like to quote the mining diagram below. There is nothing wrong with these laws themselves. Whether it is linear growth or exponential growth, they all illustrate the importance of persistence. Without persistence, there will be no results of these growth. The biggest problem with these laws or chicken soup is that there is no direction. Because they are actually telling you, don’t worry about so much, you will be done. When you ask him what you should do, they will still tell you, it’s all done! This simple and crude concept is only suitable for brick-moving work and the second stage of learning. What is brick-moving work? That is, you have passed the adjustment period and mastered the basic essentials of moving bricks. No other skills are needed. At this time, if you move 100 bricks, you can earn ten times more wages than if you move 10 bricks. What is the second stage of learning? That is, you have mastered the basic concepts and laws, and have been able to solve a certain type of problem, and the rest is the problem of proficiency. In the same minute, you can calculate forty four arithmetic problems, and others can only calculate ten. Road, then you can win the four-arithmetic contest in a limited time. The world we face is often complex and non-linear. Many problems are intertwined with a combination of multiple non-linear problems, which cannot provide you with a runway where you can move forward as long as you have momentum. Many people who are new to the workplace will have a strong sense of powerlessness after encountering several setbacks in the workplace, a strong feeling that there is nowhere to be effective. It was because they were blocked by some temporarily insurmountable high walls. For a while, they couldn’t open the door, turn over, or go around. What they need at this time is to find another track, or go to Find the key that can open the door lock in this high wall. And during the time they are blocked, they will find that the people who were left behind are slowly catching up, and they have not been able to pass this high wall, seeing the lead is slowly exhausted. , The mentality of many people collapsed. At this time, what they need is definitely not the so-called persistence, let alone the power of time, but new vision and ideas that can help them cross the wall. And this process of self-upgrading and completing a spiritual escape cannot be done simply by doing it. Just like the two sentences I often quoted before: the problem cannot be solved by the way of thinking that caused this problem. Crazy is doing the same thing repeatedly, but expecting different results. At this time, if you don’t care about the three-seven-ones, and try to work hard in the lower levels with the thought of doing nothing, the final result must be to spin around in front of the high wall.

6 months ago

When the teacher calculates 1377, you can completely ask the teacher, the college entrance examination does not have a score of XXX (different from province), how should this 1377 be honored? Seriously, it seems that we should use the hierarchical multinomial distribution model to assume that there are a subdivision knowledge points in the college entrance examination. It is assumed that after learning to subdivide the knowledge points, you naturally learn the connections between the knowledge points (the connection can be regarded as another kind of detail). Divide knowledge points), and then the college entrance examination question is to examine the combination of subdivided knowledge points. After you learn all subdivided knowledge points, you have a certain probability (for example, 95%) that you have a correct answer and 5% carelessness. …This model should be correct, but it’s too complicated to get accurate answers (mainly because I’m too lazy to write programs to simulate…). You might as well use the Dirichlet process model to learn every day, and p/(p+a) according to the teaching progress Probability to review one of the p knowledge points that have been discovered (if you think that 1 per day is slow, you can change it to 1 every 45 minutes/1 every 15 minutes, here only one per day), with a/( The probability of p+a) introduces a new knowledge point, and for the new knowledge point explained by the teacher every day, students have a probability of q to learn. After a period of stressful high school life is over, students will have an exam with 100 questions. For each question, the teacher will use a known knowledge point with the probability of p/(p+a). College entrance examination questions, and use a new knowledge point with the probability of a/(p+a) (in the syllabus but the teacher did not mention it), and then the simplest setting of various simulation tests: we use “one year” and ” “End of term” as standard

6 months ago

According to the understanding of “1.01 365 times”, the model believes that the individual’s original knowledge level score is 1, and through regular learning every day, the knowledge level increases by 0.01 times the original, thus reaching 1.01 times the day before. We can take two numbers to get a feel: On the 364th day, the individual’s knowledge level is 1.01^364≈37.41, and on the 365th day, the individual’s knowledge level is 1.01^365≈37.78, which means that the increment on the last day is 0.37 The total knowledge level of the individual on the first day is 1. In fact, don’t underestimate this 1. If the teacher wants to use this exponential formula to tell students the impact of learning efficiency on learning results, there is a prerequisite first, that is, students must be able to understand the exponential function , And the exponential function is the learning content of the students in the first semester of high school. Therefore, teachers are facing at least freshman and above students. A high school student who has received 9 years of compulsory education, his total knowledge is only 1,365 days later, can his one day of study increase his knowledge by 0.37? This 0.37 exceeds 1/3 of the previous 9 years of study. Is this possible? In fact, the exponential change of total knowledge is unreasonable. It has been suggested that as the amount of knowledge increases, because you are more familiar with the knowledge in the field, the speed of learning knowledge will become faster and faster. However, there are many factors that affect knowledge acquisition. For example, with the deepening of learning, the difficulty of knowledge increases, which will reduce the speed of knowledge acquisition. For example, as the more knowledge is mastered, the possibility of individual repetitive learning will become Bigger, after reading a book before, it was full of gains, now after reading a book, most of it is nonsense to you. Diminishing marginal benefits are equally effective for knowledge learning. Therefore, we cannot accurately judge the changing law of individual long-term knowledge learning efficiency, but if we only consider high school career learning, this problem becomes relatively simple. Since high school knowledge belongs to the elementary-intermediate level in the entire knowledge structure, the difficulty is generally moderate, and the total difficulty rises gradually over time. This avoids drastic changes in learning efficiency due to changes in knowledge reserves when learning introductory knowledge, and also avoids the marginal effect caused by in-depth learning of domain knowledge. Therefore, in the three years of high school learning, we In order to simplify the model, the influence of the total amount of knowledge on the rate of change of the total amount of knowledge can be directly excluded. Then considering the limited learning time of individuals, after regular learning under the mandatory requirements of the school (teacher), the daily increase in knowledge should be considered to be basically fixed. So how much change does this regular study bring to students?

6 months ago

Suppose a person’s personal comprehensive knowledge level score is L. Assuming that the amount of knowledge acquired every day is fixed, then the personal knowledge level score is increased by a fixed value k every day. According to this simplest model, the relationship of the individual’s level score over time (t days) is: a+tk. As mentioned before, students are at least one grade high, so I might as well assume that the student is a high school, and its initial level is 1 student after 9 years of compulsory study before high school, assuming the influence of winter and summer vacations aside (because winter and summer vacations can also study), a total of The number of learning days is 9*365=32853285 days of learning brings a learning level of 1, but of course we cannot simply think that the daily learning increment is only 1/3285, because as we grow older, our intelligence gradually develops. The high school stage reached its peak, so our learning increment is gradually increasing. Considering the unclear curve model of intellectual development, we might as well assume that our intelligence grows linearly before high school, and our level of intelligence in the first grade of elementary school is almost 0 compared to our first grade, so our learning efficiency in high school is the same over the years. The average efficiency is about twice, so the daily increment reaches 2/3285, then L=1+2t/3285. According to this simple model, after 365 days, L=1.22, after 3 years, L=1.67

6 months ago

Suddenly I thought of a more interesting adaptation: 1 day of work and 1 day of rest 1.01 * 0.99 = 0.9999 <1. The same day, the effect of rest is always greater than the effect of work. In the long run, it will be regressive:) Let’s look at the effect of working for 5 days and rest for 2 days. 1.01 ^ 5 * 0.99 ^ 2 = 1.030095, yes, it is approximately equal to the effect of working for 3 days. If you do it for 3 days a week, how can you not fall behind? ! If you change the 955 work system of civil servants to the 996 work system of the program, try it. First, the 8 hours a day was extended to 12 hours, and the work progress changed from 1.01 to 1.015. Then the rest was still 0.99, so 1.015 ^ 6 * 0.99 = 1.082509> 1.01 ^ 7 in a week. Look, it is more than 7 days without rest. Keep on working hard~~

6 months ago

I also discussed this issue with my students some time ago. I said: “I saw this slogan last time in a classroom invigilating an exam. There were also classmates in our class at that time. Have you noticed these students?” The classmates said, “I didn’t pay attention.”… I said, ” It’s okay to pay attention now. Think about it and discuss it. Do you agree with the content of this slogan? Why?” The students began to discuss. Although they do not like to discuss some teaching issues, they are often very interested in such sudden gossip. Finally, a classmate stood up and said, “This is an exponential growth. It uses multiplication. Multiplying it all the way will be an astronomical number. It’s impossible. In real life, not many people can do it even with addition every day.” I said: “Yes, that’s why you always find it difficult to stick to it. Because a lot of chicken soup tells you that if you stick to it, make progress every day, you will succeed in the end. But in fact, our realistic model may persist for three days. Slacking for five days; or persisting for five days, it is not as effective as slackening to learn some time ago.” Many times, when a classmate made up his mind to persevere every day, the first difficulty he encountered was “persistence.” “If you can’t go on,” the second hurdle is “persistent, but the results have regressed.” When the chicken soup tells him that he can succeed if he persists, he will suspect that he may not be this material, and his achievements may be a mysterious thing, and he can only do whatever he wants in his life. So the chicken soup is counterproductive. Although some students persisted all the way, they were very painful. Because what he felt was an improvement at the additive level, but Jitang told him that he should have made an exponential improvement. Just like Zhihu telling you, 985 walks all over the floor, and your annual salary is less than one million, you are not worthy of being a Zhihuer. In this way, the chicken soup brings anxiety instead. Other students will become procrastinated. Because he has counted with his fingers (if multiplication can also be counted with his fingers), even if he started working hard three months before the college entrance examination and improved by 1.01 times the day before, he could eventually achieve a good result. This is the so-called “I am not doing well now because I have not formally exerted my strength; when I take the shot, I will naturally succeed.” I said to my classmates: “In real life, many slogans and chicken soup cannot stand scrutiny. Relying on chicken blood to maintain state is actually an act of lowering their IQ. Really powerful people will face the existence of learning. It’s difficult to understand the reality, be prepared to walk with it all the way, and have no trouble, no regrets.” The classmates were silent for a while, and then a classmate tentatively asked me: “Teacher, you are giving us again Have you poured chicken soup?”

6 months ago

When I was in the second grade of elementary school, I especially didn’t like to listen to classes, because the things I talked about in class were too mentally retarded, so I just let it go. What are you doing? have a bee in one’s bonnet. What are you thinking about? I was just thinking, I jumped up and down the stairs every day. If there is a step that increases by one millimeter every day, I jump another millimeter every day, then when I graduate, I will definitely be able to jump into the sky and blow up planes with grenades! Look, I know the marginal effect when I was 8 years old. So many respondents are still talking about hard work and accumulation. Think about it, if hard work is useful, they will not even understand the marginal effect?

6 months ago

Inconsistent, 1% improvement every day is not in line with reality. Let’s not say. Let’s take an example. Let’s take an example. Suppose Xiao Ming studied for an hour on New Year’s Day and worked hard by 1% every day. At the beginning, Xiao Ming had to study for about 1 hour a day. In March, Xiao Ming’s daily study time only exceeded 2 hours, which sounds wonderful, right? By the end of April, Xiao Ming now has to study 3 hours a day. Now it seems that this is just a story of the scumbag gradually trying to surpass the scholastic master, isn’t it? In mid-May, Xiao Ming now has to study 4 hours a day. Although Xiao Ming is still an inexperienced bastard compared to his classmates studying in school, Xiao Ming, who has been full of chicken soup, is convinced that he can become the number one student leader in the school by relying on 1% of the profit. At the beginning of June, Xiao Ming had to study for 5 hours a day. At this time, Xiao Ming was still leisurely like a kindergarten kid, eating, sleeping, playing, playing and eating. But what he didn’t know was that there were not many good days for him. At the end of June, Xiao Ming had to study 6 hours a day, barely catching up with classmates’ time to make up classes every weekend. At this time, Xiao Ming was still eating, sleeping, playing, playing and eating. In mid-July, Xiao Ming’s daily study time was 7 hours, gradually catching up with the study time of elementary school students. At the end of July, Xiao Ming implemented an eight-hour work system every day, ah, no, a study system, no weekends, no overtime, no statutory holidays, and Xiao Ming, who could not ask for leave, felt the benefits of traditional weekends. At the beginning of August, Xiao Ming had to study for 9 hours a day. For Xiao Ming, a scumbag, this kind of life is not as good as death. In mid-August, Xiao Ming felt the power of the exponential explosion. He now studies 10 hours a day without any form of holiday. Xiao Ming studied the labor law in private, but Xiao Ming discovered that learning is not within the jurisdiction of the labor law. At the end of August, Xiao Ming studied 11 hours a day, catching up with or even surpassing the class time of his classmates. Taking into account various factors, Xiao Ming has actually become a model representative of hard work. At the beginning of September, Xiao Ming officially started his life in 997 instead of 996 surpassing 996. Tiredness made Xiao Ming almost die suddenly. But the worse is still to come. In mid-September, he has to study 13 hours a day. In late September, Xiao Ming had to study for 14 hours a day, and at the end of the month it reached 15 hours. Xiao Ming now starts to take some drops every night to avoid sudden death. During the October Golden Week, when students deal with the exercise books, make-up classes and vacation homework every day, Xiao Ming spends 2/3 of his time on studying every day. If it were not for medical staff to be on call 24 hours a day, Xiao Ming would have passed away long ago. Up. In mid-October, Xiao Ming’s study time reached 17 hours/day! The high-intensity study greatly consumed Xiao Ming’s energy and physical strength, and Xiao Ming successfully lost weight in just 3 days. In less than 6 days, Xiao Ming’s study time reached 18 hours of high performance. The programmers of Zhongwei, Rice, Yali and Gudi were ashamed. Putting their heads into their crotch one after another. But what’s more frightening is that in just five days, Xiao Ming’s daily study time reached 19 hours. At this time, Xiao Ming’s daily nutritional intake mainly relies on various pills and suspenders. In order to reduce sleep time, Xiao Ming is dark and thick. All her hair had been killed on the beams of the house, and the walls of the neighbor’s house and Xiao Ming’s house had been turned into ruins for the purpose of digging and stealing light. At the end of October, Xiao Ming studied 20 hours a day, and now doctors all over the world have concentrated on Xiao Ming’s home to study how Xiao Ming is still alive. According to a scientist present at the time, who can explain where Xiao Ming’s tenacious vitality comes from will win the Nobel Prize in Medicine and Biology. At the beginning of November, Xiao Ming studied 21 hours a day. In addition, he had 5 CTs and 10 blood tests every day. The criminals publicly claimed to have obtained Xiao Ming’s blood sample and developed an elixir based on this. Five days later, when Xiao Ming studied 22 hours a day, he reached an astonishing 23 hours after five days! Now physicists from all over the world have joined in. They are waiting for the moment when Xiao Ming studies more than 24 hours a day. Finally, Kung Fu is effortless. On the 321st day of this year, that is, November 18th, Xiao Ming awakened his stand-in. He used [World]’s time stop ability to study for more than 24 hours a day! Physicists built various instruments and equipment around Xiao Ming’s home to explore the source of Xiao Ming’s time ability. Three days later, the original 007 learning system can no longer help Xiaoming. When [World]’s stop-stop ability can no longer meet Xiao Ming’s needs, Xiao Ming has awakened [Platinum Star]’s stop-stop ability to go further! However, 25 hours a day only lasted four days, and then Xiao Ming studied 26 hours a day. For this reason, he awakened [Men’s Domain] again! Now Xiao Ming can go back in time! After only 4 days, Xiao Ming had to find someone to start a substitute for him in order to cope with the 27-hour work schedule. Three days later, 28 hours a day! Four days later, 29 hours a day! In order to cope with 30 hours of study, Xiao Ming awakened again [Baizhe Shichen]! Now Xiao Ming can be used for 2 days in one day! After that, Xiao Ming’s study time reached 31 hours after four days, after 3 days, 32 hours, 3 days, 33 hours, 3 days, 34 hours, 3 days, 35 hours! 3 days, 36 hours! 2 days! 37 hours! With the end of the year, when the New Year’s bell rang, Xiao Ming died of overwork and fell. Xiao Ming’s life is a legendary life. According to inadequate statistics, about tens of thousands of people have completed doctoral dissertations with Xiao Ming as the research object. Hundreds of thousands have obtained special medicines due to medical experiments on Xiao Ming. The system building was covered by dark clouds because of Xiao Ming! The Nobel Prize was officially renamed the Xiao Ming Prize to commemorate Xiao Ming’s contribution to providing research objects to the winners in the next few decades. The 321st day of each year is called Xiao Ming’s Singularity to commemorate Xiao Ming’s efforts to rebuild physics. The great cause of the building, and the people who put forward the 1.01 theory are called prophets by countless people. The 1.01 religion has become the fourth largest religion in the world, with believers all over the world. After this, every year there will be a new 1.01 teaching believer to become a new Xiao Ming, and physicists use the opposite 0.99 teaching to break through the Planck time limit, and the world gradually becomes very different. But what does this have to do with Xiao Ming?

6 months ago

How thick is a piece of paper, folded in half 50 times? 150 million kilometers, equivalent to the distance between the earth and the sun. Why didn’t people go to heaven with a piece of paper 2000 years ago? Suppose you have 1 million and an annual income of 20%. In 50 years, you will have 9.1 billion. How come there are not a few stock gods? Therefore, exponential growth does have a very powerful magical power, and it is also a big trick that is often used to make chicken soup. However, it is very difficult to actually do it. The exponential growth of the natural world will almost all become linear growth when reaching a certain stage, and there will even be retrogression and repetition. The author is an independent investor ¥ psychological consultant. He is concerned about financial investment and self-upgrading. Welcome to search the public account “Times” on WeChat for more cash benefits and dry goods.

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