Hello, welcome back. I hope you have had a chance of not doing for problems, at your own pace. And today as I said is going to be intense, because we're trying to pull in a lot of real world stuff. And I'm trying toe tell you the meaning of every bit of information to the extent I can. So take your time and now let's use this one simple example to show you the awesomeness of finance. I really minute, if you hang on to the next half hour or so and listen carefully, will be in good shape. Okay, so what is a loan amortization table? First of all, I told you last time that, the loan example is a classic example of what our finance instruments looks like or what finances all about. So what I'm going to do here is I'm going to take the same problem. How much did we borrow? $100,000 so I'm going to write, $100,000 here and the reason I'm writing $100,000 is because that's the amount of money you started off with. I want you to recognize that the amount here, the title here is beginning balance. Why did I say that? Because that's the amount of money you have worked with or you owned the bank at the beginning of which year? Year 1, so what point in time is this? It's time 0, point in time 0, so that's why we're never beginning, it said so because otherwise it's assumed things are happening at the end of the year, right? So please be very clear that if I draw a timeline, $100,000 is at time 0 and who has paid you this? The bank, so you have it now what do you have to do? Pay so the first payment will occur when at the end of the year, it won't occur here it will occur here. And we know it's 26,380, the good news is that this convenience and very common in the real world, is what is called a fixed interest rate law. So the interest rate was 10% for convenience, we'll see why, but the good news is. Right, so the early payment, starting with this year, is I'll right 26k for convenience. Is about 26,000, right? So what is a normalization table, and what am I doing it? Because it brings out the essence of what's happening during the life of the loan, and I think it's very important for you to time travel. [LAUGH] You know how to try and travel, you'll understand finance. So right now you are here and let's begin time travel at the end of the first year. What did we do? We pay 26 380. Let's break it into two parts. The first part is the interest, and we know the interest is 10 percent. But remember the weakness, often interest rate. If there is any, it's not in dollars. It's not in the form of valuation that you used to dollars, Yemen and so on. So how much will it be? I'm going to pause for a second. This is not a difficult problem, but people get stuck with it. It has to be 10 percent of what you borrowed, and how much is that? 10,000, is that clear? This is very important. You owe interest on what you borrowed at the beginning of the period, and one year has passed and you owe100,000 at the beginning. So you're attentive. So how much will you repay the loan? Remember? Because the goal here is not only to pay interest, but repay the loan. So how much is left? Very simple. If you're paying 26 380 and you're paying $10, 000 interest. How much is the loan repayment Straightforward. Take this. Subtract this. You're left with 16,380 now you know why I took 10%? I took 10% because I'm doing this problem with you. I'm not using a calculator in real life. That's why Excel is great. You can do instead of 10 percent, you can have 0.2345 whatever. So now the next step is a little bit important. And the question is, how much really owe the bank at the beginning of year two which is which point? Remember, beginning of year two is 0.1 end of year two is 0.2. So at this point, how much will you owe, very simple. You own 100,000. You paid the use of money 10%. You would love to deduct it from how much you owe. But the hand will come out of the bank and hit you and say, What the heck are you doing? This is for the use of money. On the other hand, the bank would love for you to pay all 26 8000 has interest off course. If you're silly enough to do that, the bank will try. Right? So it depends whose being silly or stupid here. Okay, so this is the amount you repay. So what do you do? You subtract this from this. And how much are you left with? Just to look. Make sure I'm getting the numbers right. Everybody got it. So what has happened? I have lowered the amount I owe because I paid 26 and only 10,000 was the interest. Right now, at the end of the second day, what do I do? I again pay 26k. Now what is going to happen? Take a guess. Will the amount off interest go up relative to last year that you pay or go down? Think about it. If the amount went up, you're going in the wrong direction. The only way the amount would go up on interest is, if you are actually borrowed more rather than pay back some and there's no good or bad. Here is here. Assumption is that you're going to pay back the loan. Right? So how much will you pay in interest? Pretty straightforward. 8, 362 how did I do that? Pretty straightforward again. The interest rate is 10%. I took the 10% and I didn't multiply it to 100,000. I multiplied it to 83 620. Why? Because I don't owe the bank 100,000. I owe the bank only 83, 000 at the end of the first year. The good news is my interest has dropped. Yep. But the reflection of that good news is that I'm paying back more. So if I paid back 16, 380 how much am I paying back now? More or less answers. If the interest amount has dropped, the repayment amount has to go up. Assuming that I'm paying back the same amount 26 k or so every year. So the answer to that is 18 or 180 for my for the ease off saving time. I've just done these calculations ahead of time. And so how do I know that I know that 18 plus 8 has to add up to 26, because 26 is what I paid again, at the end of the year 2. So at the end of the year 2, what is happening? My interest rate is going down, but my repayment rate is going up, and this is needed for you to replay the loan, right? So here's your homework number one. Before you do anything else, try to fill up this box, and I will do it quickly for you. But the principle is the same, how do I go from here-to-here, I subtract this from this. So let me write the number for you, 65,603. How do I go from here to the interest column, 10% of this, so 6,560. And how do I get this column, I know that the number has to increase because this dropped and this amount is the same. So 26 is the same, so I subtract 6,500 from 26, I get 19,820, okay? Same thing, let me just write it out, 75,783. This number dropped to 4,578, this number goes up to 21,802. This number becomes 23,982. This number is 2,398, and the last number is 23,982. So let's see what's happening now. At the end of the year, how much did I owe, 23,982, but I paid 26,380. You see, I owed 23,982, but I paid 26,380. Why did I pay more than I owed? Because I owed 23,982 at the beginning of the year, and had to pay interest on it of 2,398. So I have to pay 26,380 to be able to pay back the loan. But the good news is, when I'm done in year 5, how much do I owe the bank, nothing. Again, I'm saying it's good news, consistent with your plan to pay off the five years. In finance, the good news is, there's no good news, bad news, it depends on what your objective is. So for example, if you don't have money, you many times don't have money coming in, people take interest rate-only loans. That's okay, because if it's dictated by the cash flow constraints you have, you pay less, because you're only paying interest. But most people want to pay off the loan, therefore this example is very, very valid, okay? So please remember this, do this example one more time. Why am I going to emphasize this, and where does the beauty of finance come in? And now bear with me for a second. What is the first column showing, the year. What is the second column showing, beginning balance, the yearly payment, interest, and principal payment. Suppose I walked up to you, suppose I walked up to you and asked you, hey, you're taking a loan, $100,000. You're just coming out of the bank, and I'm your buddy, well, and I know you know finance. I say, how much do you borrow, you say, $100,000. I say, look, can you tell me how much will you pay the bank every year, for the next five years, will you be able to do that? Sure, you have an Excel spreadsheet with you, you're sitting in the car. You open it up, and you do a PMT calculation, and you come up with 26,380, easy. So the good news is, once you know how much you're borrowing, the yearly payment column, if at a fixed interest rate, is very straightforward. But what is the most difficult part of this problem? The most difficult part of this problem is the answer to the following question. If I were trying to figure out whether you really know finance and the awesomeness of it, I'll ask you the following question. How much will you owe the bank, how much will you owe the bank at the beginning of year 3? At the beginning of year 3, which is also the end of year 2, right? So how much will you owe the bank at the beginning of year 3, how will you do that problem? So this is where, if you did this problem this way, it'll take you ages to do. Because I could ask you the question, how much will you owe at the beginning of year 4? Look, to get there, what will I have to do? If I were to say, how much do you owe the bank at the beginning of year 4, I'll have to go through many rows of this spreadsheet to be able to understand. And this is where the beauty of finance comes in. And I'm going to try to show you a timeline which is very similar to this one, and I'm going to call it, I'm going to call it, instead of amortization, I'm going to call it the power of finance. So let me start off with a simple question. If I asked you to tell me, how much do you owe the bank here? Remember, this is the beginning of each year, first year, what point in time, 0. Now, it's a silly question to ask, but not quite. Why is it a silly question to ask, because you already know how much you've borrowed, which is what, $100,000. But let me ask you this, as soon as you walk out of the bank, this is something that the bank will tell you, believe me, it will, that you need to pay how many times, five times, right, right? So you walk out of the bank, you know the yearly payment, and I ask you the following apparently silly question. How much do you owe the bank the moment you walk out of it? You know what many people will say> Many people will multiply 26,380 by 5, and you have just destroyed me, if the answer is that. You might as well take a big knife and stick it in my stomach. And the reason is, you cannot add or multiply over time, because of compounding and a positive interest rate, right? Because if you do, how much do you owe? You owe 20,000 five times, if interest rate was zero. So you answer is not a good one, so here is what you do. You make 26,380 5 times a PMT, right? And what do you make n, 5, yes, because you owe 5 of these. What is the only other number you need to do, r, which is what, 10%. If you do this problem, what button do you need to, or what execution in Excel or a calculator do you need to do? Well, to figure this out, you have to figure out PV. Please do it, I wish your answer will work out to be 100,000, right, we know that. Why am I emphasizing this? because the awesomeness of finance comes from the following simple principle. Number one all value is determined by standing at a point in time and looking forward, you can do value in many different ways. You can do it a time minus five and bring it forward or do it in the future and me. But the best way to think about decision making is you're standing at zero and you're looking forward. So when you're standing at zero and looking forward, how many payments of 26 3 85 each one separated by one year, the first one starting in which year end of the first year. And when you do the PV off it, you better come up with 100,000. And this is one of the most profound Nobel prize winning points. Please keep it in mind. We'll come back to it later, which is the following. You cannot make money by borrowing and lending, right. If the present value of 26 3 80 was different than 100 0, somebody's been a fool off. So suppose the bank gives you more than $100 thousand. The bank is being immediate and let me assure you that won't happen if you walk off, the less somebody shafting you. So the question here is, how does the bank then make money? Well, that makes money by charging you a little bit more on the borrowing lending rates difference. They have to feed the family too, right? They worked for you. They created the market. But that's the friction I was talking about. But value cannot be created by borrowing and lending. Otherwise, you and I would be home and creating value. Yes, it grows over time, but the present value is still the same as the money. I put it right. That's a very fundamental point in finance values created not by exchanging money, which is this borrrowing and lending values creating by coming up with a new idea for creating value for society. Right, So that's what I'm trying to say. So let me ask you this. How much will you owe the bank at the beginning of year to what would you have to do? You would have to calculate the interest rate. You would have to calculate the principal payment and then you subtract it from this answers very straightforward. And this is where I love that. Just change one number. Make this 4 so change the 5 to 4 and do the PV. What will you come up with? Please do it. You'll come up with 63 to it. So what have I done? Instead of sticking with times zero I've times traveled to period one. If I'm a period one, I've already paid this up. How many more left? Four left. So? And this for an interest rate is 10%. And how many am I paying? 26 3 80. So 83 6 20 is very easy to do if you recognize that. So how would you do the next column? It's 65 6 or three. How will you do it? You just make end three. So you see what I'm saying? What I'm saying is, the simplest thing in finance is don't get hung up on the past. Get whenever you are asked about value off anything whether you owe it or you're getting the value. Look to the future and the problem becomes trivial. Why? because if you know all these values, these are just 10% of this. So this is just 10% of this role. And then this is just these two added together is this so if I add these two, I get this so I can do this in a second, as opposed to doing it over an amortization table. So one more time. If I were to ask you to do this problem all over again, what would you do? You won't use any prop, the only excel to solve the problem. So if I asked you how much do you owe in a particular year to the bank? Which is a very good question to ask. You will just do what you will. Time travel, right? Do you remember matrix jumps across two buildings? First time is not successful. That's life, but then manages to jump across, right? And if you haven't seen metrics in metrics, it's much more interesting than this problem. So time travel to your whatever forward. Look forward how many payments are left just to the baby. Okay, I hope you like this because this is if you remember this. This is finance compounding plus, this is most of what finances all about. So it's a mindset. You always look forward. Okay,
