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Hello. Welcome Back. I hope you have had the chance of now doing full problems at

Â your own pace. And today as I said, is going to be intense because we are trying

Â to pull in a lot of real world stuff. And I'm trying to tell you the meaning of

Â every bit of information to the extent I can. So, take your time and now let's use

Â this one simple example to show you the awesomeness of finance. I really mean it.

Â If you hang on to the next half hour or so and listen carefully, we'll be in good

Â shape. Okay. So what is a loan amortization table? First of all, I told

Â you last time that the, the loan example is a classic example of what a finance

Â instrument looks like or what finance is all about. So what I'm going to do here is

Â I'm going to take the same problem. How much did we borrow, a $100,000 so I'm

Â going to write $100,000 here. And the reason I'm writing $100,000 is because

Â that's the amount of money you started out with. I want you to recognize that the

Â amount here, tied to here is beginning balance. Why did I say that? Because

Â that's the amount of money you have walked away with or you owe the bank. At the

Â beginning of each year, year one so what point in time is this? It's time zero,

Â point and time zero. So, that's why the number of beginning it said so because

Â otherwise it's assumed things are happening at the end of the year, right?

Â So, please be very clear that if I draw a timeline, the $100,000 is at time zero and

Â who has paid you this? The bank so you have it now what do you have to do? Pay.

Â So, the first payment will occur when? At the end of the year. It won't occur here.

Â It will occur here and we know it's 6350. The good news is that this, for

Â convenience and very common in the real world, is what is called a fixed interest

Â rate loan. So, the interest rate was ten percent for convenience in CY but the good

Â news is. Right? So the yearly payment starting with this year is, I'll write 26K

Â for convenience. It's about 26,000, right? So what is an amortization table and why

Â am I doing it? Because it brings out the essenc e of what's happening during the

Â life of the loan and I think it's very important for you to time travel. If you

Â know how to time travel, you'll understand finance. So right now, you are here, and

Â let's begin time travel. At the end of the first year, what did we do? We pay 26,380.

Â Let's break it into two parts. The first part is the interest and we know the

Â interest is ten percent but remember the weakness of an interest rate if there is

Â any, it's not in Dollars. It's not in the form of evaluation that you're used to

Â dollars, yen and so on so how much will it be? I'm going to pause for a second. This

Â is not a difficult problem but people get stuck with it. It has to be ten percent of

Â what you borrowed and how much is that? Sorry, 10,000. Does that, is that clear?

Â This is very important. You owe interest on what you borrowed at the beginning of

Â the period and one year has passed and you owe 100,000 at the beginning so you owe

Â [inaudible]. So how much will you repay the loan? Remember, because the goal here

Â is not only to pay interest but to repay the loan so how much is left? Very simple,

Â if you are paying 26,380 and you're paying $10,000 interest, how much is the loan

Â repayment? Straight forward. Did this, subtract this, you're left with 16,380.

Â Now, you know why I took ten%. I took ten percent because I'm doing this problem to

Â do. I'm not using the calculator. In real life, that's why Excel is great. You can

Â do, instead of ten percent you can have .2, three, four, five whatever. So now,

Â the next step is a little bit important and the question is how much will you owe

Â the bank at the beginning of year two which is which point? Remember, beginning

Â of year two is .1, end of year two is .2. So at this point how much will you oh,

Â very simple, you owe 100.000. You paid the use of money ten%. You would love to

Â deduct it from how much you owe but the hand will come out of the bank and hit you

Â and say what the heck are you doing? This is for the use of money. On the other

Â hand, the bank would love for you to pay all 26,800 as interest. Of course, if you

Â are silly enou gh to do that the bank will try it, right? So it depends who's being

Â silly or stupid here. Okay so this is the amount you repay so what do you do? You

Â subtract this from this. And how much are you left with? Just to look, make sure I'm

Â getting the numbers, right. Everybody got it? So what has happened? I have lowered

Â the amount I owe because I paid 26 and only 10,000 was the interest, right? Now

Â at the end of the second year what do I do, I again pay 26K. Now what is going to

Â happen? Take a guess. Will the amount of interest go up relative to last year that

Â you pay or go down? Think about it. If the amount went up, you're going in the wrong

Â direction. The only way the amount would go up on interest is if you're actually

Â borrowed more rather than pay back some. And there's no good or bad here. It's

Â here, the assumption is that you're going to pay back the loan, right? So how much

Â will you pay in interest? Pretty straightforward, 8362. How did I do that?

Â Pretty straightforward, again. The interest rate is ten%. I took the ten

Â percent and I didn't multiply it to the 100,000. I multiplied it to 83620, why?

Â Because I don't owe the bank 100,000. I owe the bank only 83,000 at the end of the

Â first year. The good news is my interest has dropped but the reflection of that

Â good news is that I'm paying back more. So, if I paid back 16,380 how much am I

Â paying back now? More or less? Answer is, if the interest amount has dropped the

Â repayment amount has to go up, assuming that I'm paying back the same amount 26K

Â or so every year. So the answer to that is 18018. For my, for the ease of saving time

Â I've just done these calculations ahead of time. And so how, how do I know that? I

Â know that eighteen + eight has to add up to 26 because is 26 is what I paid again

Â at end of year two. So at the end of the year two, what is happening? My interest

Â rate is going down, but my repayment rate is going up. And this is needed for you to

Â repay the loan, right? So here's your homework number one. Before you do

Â anything else, try to fill up this box and I will do i t quickly for you but the

Â principle is the same. How do I go from here to here? I subtract this from this so

Â let me write the number for you, 65603. How do I go from here to the interest

Â column ten percent of this? So 6560 and how do I get this column? I know that the

Â number has to increase because this drop and this amount is the same so 26 is the

Â same so I subtract 6500 from 26 I get 19820, okay? Same thing, let me just write

Â it out 75,783, this number drops to 4578. This number goes up to 21802. This number

Â becomes 23982. This number is 2398. And the last number is 23982. So, see what's

Â happening now. At the end of the year, how much did I owe? 23982 but I paid 26,380.

Â You see, I owed pay 23982 but I paid 2639, 380. Why did I pay more than I owed?

Â Because I owed 23982 at the beginning of the year and I have to pay interest on it

Â of 2398 so I have to pay 26380 to be able to pay back the loan. But, the good news

Â is when I am done in year five, how much do I owe the bank? Nothing. Again, I'm

Â saying it's good news, consistent with your plan to pay after five years. In

Â finance, the good news is, there's no good news, bad news. It depends on what your

Â objective is so for example, if you don't have money, you many times don't have

Â money coming in, people take interest rate only loans. That's okay because it is

Â dictated by the cash flow constraints you have. You pay less because you're only

Â paying interest. But most people want to pay off the loan, therefore this example

Â is very, very valid, okay? So please remember this, do this example one more

Â time, why am I going to emphasize this and where does the beauty of finance come in?

Â And now bear with me for a second. What are the first columns going? The year.

Â What are the second columns showing? Beginning balance. The early payment,

Â interest, and principal payment. Suppose I walked up to you, suppose I walked up to

Â you and asked you, hey you're taking a loan $100,000. You're just coming out of

Â the bank and I'm your buddy, and I know you know finance. I say how much did you

Â borrow ? I said $100,000. I say look, can you tell me how much will you pay the bank

Â every year for the next five years? Will you be able to do that? Sure. You have an

Â Excel spreadsheet with you, you're sitting in the car. You open it up and you do a

Â PMT calculation and you can come up with 26380, easy. So the good news is, once you

Â know how much you're borrowing, the yearly payment column at a fixed interest rate is

Â very straightforward but what is the most difficult part of this problem? The most

Â difficult part of this problem is the following answer to the following

Â question. If I were trying to figure out whether you really know finance and

Â awesomeness of it, I'll ask you the following question. How much will you owe

Â the bank? How much will you owe the bank at the beginning of year three? At the

Â beginning of year three, which is also the end of year two, right? So how much will

Â you owe the bank at the beginning of year three? How will you do that problem? So,

Â this is where if you did this problem this way, it'll take you ages to do. Because I

Â could ask you the question how much will you owe at the beginning of year four?

Â Look to get there, what will I have to do? If I were to say, how much do you owe the

Â bank at the beginning of the year four? I'll have to go through many roles of this

Â spreadsheet to be able to understand and this is where the beauty of finance comes

Â in. And I'm going to try to show you a timeline, which is very similar to this

Â one and I am going to call it. I'm going to call it, instead of amortization I'm

Â going to call it the power of the math. So let me start off with a simple question.

Â If I asked you, if I asked you to tell me how much do you owe the bank here?

Â Remember this is the beginning of each, first year. What point in time? Zero. Now,

Â it's a silly question to ask, but not quite. Why is it a silly question to ask?

Â Because you already know how much you've borrowed. Which is what, $100,000 but let

Â me ask you this, as soon as you walk out of the bank. This is something that the

Â bank will tell you, believe me it will, that you need to pay how many times? Five

Â times, right? Right? So you walk into the bank, you know the yearly payment and I

Â ask you the following apparently silly question, how much do you owe the bank the

Â moment you walk out of it? You know what many people will say? Many people will

Â multiply 26380 by five and you have just. Destroyed me if the answer is that. You

Â might as well take a big knife and stick it in my stomach. And the reason is, you

Â cannot add a multiplier over time because of compounding and the positive interest

Â rate, right? Because if you do, how much do you owe? You owe 20,000 five times if

Â interest rate was zero so your answer is not a good one. So here is what you do,

Â you make 26380, five times of PMT, right? And what do you make m? Five. Yes, because

Â you owe five of these. What is the only other number you need to do? R, which is

Â what ten%. If you do this problem, what button do you need to or what execution in

Â Excel or a calculator do you need to do? Well, to figure this out, you have to

Â figure out Pv. Please do it. I wish your answer will work out to be 100,000, right?

Â We know that. Why am I emphasizing this? Because the awesomeness of finance comes

Â from the following simple principle number one. All value is determined by standing

Â at a point in time and looking forward. You can do value in many different ways.

Â You can do it a time - five and bring it forward, or do it in the future but the

Â best way to think about decision making is, you're standing at zero and you're

Â looking forward. So when you're standing at zero and looking forward, how many

Â payments of 26385? Each one separated by one year, the first one starting in which

Â year? End of the first year and when you do the Pv of it, you better come up with a

Â 100,000. And this is .one of the most profound Nobel Prize winning points,

Â please keep it in mind we'll come back to it later which is the following. You

Â cannot make money by borrowing and lending, right? If the present value of

Â 26,380 was different than 100,000, somebody's made a fool of. So suppose the

Â bank gives you more than $100,000, the bank is being an idiot and let me assure

Â you that won't happen. If you walk off with the less, somebody's shafting you. So

Â the question here is, how does the bank then make money? Well. They makes money by

Â charging you little bit more on the borrowing lending rates difference. They

Â have to feed the family too, right. They work for you. They create the market but

Â that's the friction I was talking about but value cannot be created by borrowing

Â and lending other wise you and I would be home and creating value. Yes, it grows

Â over time but the present value is still the same as the money I put it, right?

Â That's the very fundamental point in finance. Value is created not by

Â exchanging money which is this, borrowing and lending. Values creating by coming up

Â with a new idea for creating value for society, right? So that's what I'm trying

Â to say. So let me ask you this, how much will owe the bank at beginning of year

Â two? What would you have to do? You would have to calculate the interest rate, you

Â would have to calculate the principal payment, and then you subtract it from

Â this. Answer is very straight forward. And this is where I love the math. Just change

Â one number, make this four. So change the five to four and do the Pv, what will you

Â come up with? Please do it. You'll come up with 63280. So what have I done? Instead

Â of sticking with time zero I've time traveled to period one. If I'm at period

Â one, I've already paid this up. How many more left? Four left. So m is four and

Â interest rate is ten percent and how many am I paying? 26,380. So 83,620 is very

Â easy to do if you recognize that. So how would you do the next column? It's 65,

Â 603. How will you do it? You just make m three so you see what I'm saying? What I'm

Â saying is the simplest thing in finance is don't get hung up on the past. Get hung,

Â whenever you are asked about value of anything, whether you owe it or you're

Â getting the value, look to the future and the problem becomes trivial. Why? Because

Â if you know all these values, th ese are just ten percent of this. So this is just

Â ten percent of this row and then this is just these two added together is this. So

Â if I add these two, I get this. So I can do this in a second as opposed to doing it

Â over an amortization table. So one more time. If I were to ask you to do this

Â problem all over again, what would you do? You wouldn't use any prop, you only Excel

Â to solve the problem. So if I asked you, how much do you owe in a particular year

Â to the bank which is a very good question to ask. You will just do what? You will

Â time travel, right? You remember my tricks? Jumps across two buildings. First

Â time is not successful but that's life but then manages to jump across, right? And if

Â you haven`t seen Matrix, see Matrix. It`s much more interesting than this problem.

Â So, time travel to year, whatever forward, look forward how many payments are left

Â just to the PV. Okay? I hope you like this because this is, if you remember this,

Â this is finance. Compounding plus this is mostly what finance is all about. So, it`s

Â a mindset, you always look forward, okay?

Â