Hello, welcome back. I hope you have had the chance of now doing four problems at your own pace. And today, as I said, is going to be intense because we are trying to pull in a lot of real world stuff. And I'm trying to 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 mean it, if you hang on to the next half hour or so, and listen carefully, we'll 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 a finance instrument looks like, or what a finance is 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 right here, the title here is Beginning Balance. Why did I say that? Because that's the amount of money you have walked away with or you owe the bank at the beginning of each year, year one. So what point in time is this? It's time 0, point in time 0. So that's why whenever beginning, it's said so, because otherwise, it's assumed things are happening at the end of the yard. So please be very clear that if I draw a timeline, the $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'll occur here. And we know it's 26,380. The good news is that this for convenience, and very common in the real world, is what is called a fixed interest rate loan. So the interest rate will stay 8% forconvenience, and you'll see why. But the good news is Right? So the yearly payment starting with this year is, I'll write 26K for convenience It's about 26,000. So what is an amortization table and why 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. If you know how to time 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 paid 26,380, let's break it into two parts. The first part is the interest, and we know the interest is 10%. But remember, the weakness of an interest rate, if there is any, it's not in dollars. It's not in the form of valuation that you're used to, dollars, yen 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% 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 owe 100,000 at the beginning. So you owe 10K. So how much will you repay the loan? Remember because the goal here is not only to pay interest but to repay the loan. So how much is left? Very simple. If you are paying $26,380 and you're paying $10,000 interest, how much is the loan repayment? Straight forward. 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%, you can have 1, 2, 3, 4, 5, whatever. So now the next step is a little bit important and the question is, how much will you owe the bank at the beginning of year 2? Which is which point? Remember, beginning of year 2 is .1, end of year 2 is .2. So at this point, how much will you owe? Very simple. You owe 100,000. You paid the use of money 10%. You would love to deduct it from how much you owe, but a 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 26,800 as interest. Of course, if you're silly enough to do that, the bank will try. So it depends who's being silly or stupid here. 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 year, what do I do? I again pay 26K. Now, what is going to happen, take a guess. Will the amount of 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 had actually borrowed more, rather than paid back some. And there's no good or bad here, is your assumption is that you're going to pay back the loan, right? So, how much will you pay in interest? Pretty straightforward. 8362. How did I do that? Pretty straightforward, again. The interest rate is 10%. I took the 10%. And I didn't multiply to the 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, yeah. 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? Answer is if the interest amount has dropped the repayment amount has to go up, assuming that I'm paying back the same amount 26K or so every year. So the answer to that is 18,018. For the ease of saving time, I've just done this calculations ahead of time. And so how do I know that? I know that 18 + Eight has to add up to 26. Because 26 is what I paid again, that end of year two. So at the end of the year two what is happening? My interest rate is going down but my repayment rate is going up and this is needed for you to repay 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 6560, 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 drops to 4578. This number goes up to 21802, this number becomes 23982. This number is 2398, and the last number is 23982. So, see what's happening now. At the end of the year, how much did I owe? 23982. But, I paid 26380, you see I owe 23982, but I paid 26380. Why did I pay more than I owed? Because I owed 23,982 at the beginning of the year and I have 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 five, 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, you 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 early payment, interest and principle payment. Suppose I walked up to you and asked you, hey you have taken a loan, $100,000, you're just coming out of the bank, and I'm you're buddy. And I know you know finance, I say, how much did you borrow? He said, $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, it's sitting in the car, you open it up, you do a PMT calculation, and you can come up with $23,680, 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 following concept, or 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 three? At the beginning of year three, which is also the end of year two, right? So how much will you owe the bank at the beginning of year three? 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 earn at the beginning of year four? Look to get there, what will I have to do? If I were to say how much will you owe the bank at the beginning of year four? 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, instead of amortization, I'm going to call it the power of finance. So let me start off with a simple question. If I ask you to tell me, how much do you owe the bank here? Remember, this is the beginning of which year? First year. What point in time? Zero. 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 in a positive interest rate. Because if you do, how much do you owe? You 20,000 five times if interest rates were 0. So your answer's not a good one. So here's what you do. You make 26,380 five times per PMT, right? And what do you make n? 5. Yes? Because you owe five 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 the 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 workout 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 at time minus 5 and bring it forward, or do it in the future. But the best way to think about decision-making is you're standing at 0 and you're looking forward. So when you're standing at 0 and you're looking forward, how payments of 26.380? 5. Each one separated by one year, the first one starting in which year? End of the first year. And when you do the PV of 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 26,380 was different than 100,000, somebody's made a fool of. So suppose the bank gives you more than $100,000. The bank is being an idiot, and let me assure you, that won't happen. If you walk off the less, somebody's shafting you. So the question here is how does the bank then make money? Well, they make money by charging you a little bit more on the borrowing lending rates difference. They have to feed the family too, right. They work 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 in, right? That's a very fundamental point in finance, value is created not be exchanging money, which is this, borrowing and lending. Value's 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 two? 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. Answer is very straightforward, and this is why I love finance. 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 63280. So what have I done? Instead of sticking the time 0 I've time traveled to period 1. If I'm at period 1, I've already paid this up. How many more left? Four left. So n is 4 and interest rate is 10%, and how many am I paying, $26,380. So $83,620 is very easy to do if you recognize that. So how would you do the next column? It's $65,603. How will you do it? We'll just make n 3. 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. Whenever you are asked about value of anything, whether you owe it or you're getting the value, look to the future and the problem becomes trivia. Why? Because if you know all these value, these are just 10% of this. So this is just 10% of this row, 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 prompt, 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 one. You will time travel, right, you remember my tricks, jumps across two buildings, first time is not successful but that's life. But then manages to jump across, right? And if you haven't seen Matrix, see Matrix it's much more interesting than this problem. So time travel to year whatever forward, look forward how many payments are left, just do the PV, okay? I hope you like this because if you remember this, this is finance. Compounding plus this, is most of what finance is all about. So it's a mindset. You always look forward, okay?