Hello. Welcome Back. I hope you have had the chance of now doing full 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, the loan example is a classic example of what a finance

instrument looks like or what 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, a $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 out with. I want you to recognize that the

amount here, tied to 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 zero,

point and time zero. So, that's why the number of 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, the $100,000 is at time zero 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 6350. 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 was ten percent for convenience in CY 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, right? So what is an amortization table and why

am I doing it? Because it brings out the essenc e 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 pay 26,380.

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

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

any, it's not in Dollars. It's not in the form of evaluation 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 ten percent of

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

[inaudible]. 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. Did this, subtract this, you're left with 16,380.

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

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

do, instead of ten percent you can have .2, three, four, five 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 two which is which point? Remember, beginning

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

very simple, you owe 100.000. You paid the use of money ten%. 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 26,800 as interest. Of course, if you

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

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

here, the 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 ten%. I took the ten

percent and I didn't multiply it to the 100,000. I multiplied it to 83620, 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 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 18018. For my, for the ease of saving time

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

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

at 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 i t 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, 65603. How do I go from here to the interest

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

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

same so I subtract 6500 from 26 I get 19820, 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 26,380.

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

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

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

is when I am 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 after 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 it is

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 are the first columns going? The year.

What are the second columns showing? Beginning balance. The early 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, and I know you know finance. I say how much did you

borrow ? I 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, you're sitting in the car. You open it up and you do a

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

know how much you're borrowing, the yearly payment column 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 answer to the following

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

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 owe at the beginning of year four?

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 the year four? I'll have to go through many roles 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 am going to call it. I'm going to call it, instead of amortization I'm

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

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

Remember this is the beginning of each, 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 into 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 26380 by five 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 a multiplier over time because of compounding and the 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 your answer is not a good one. So here is what you do,

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

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

what ten%. 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 - five and bring it forward, or do it in the future 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 26385? 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 a

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 with the less, somebody's shafting you. So

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

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

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

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

and lending other wise 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 the very fundamental point in finance. Value is created not by

exchanging money which is this, borrowing 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 owe the bank at 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 straight forward. And this is where I love the math. Just change

one number, make this four. So change the five to four 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 with time zero I've time traveled to period one. If I'm at period

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

interest rate is ten percent 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? You just make m 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 hung,

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 trivial. Why? Because

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

ten percent 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 wouldn't use any prop, you 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? 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 to the PV. Okay? I hope you like this because this is, if you remember this,

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

a mindset, you always look forward, okay?