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Okay. The first example I'll do of a PV of annuity is just like a future value, I

Â will give you the annuity and I will ask you to calculate the PV. So, let's read

Â the problem very carefully. How much money, and just so that we are, I can

Â write on this. You see, I press a button here to be able to write all over, and

Â then go back and so I do local things that you can't see. Okay. Anyway, so, I love

Â technology and here's a person here sitting next to me. â‰«> [laugh]

Â >> Who is an awesome person and, I, without him I wouldn't be doing this,

Â honest. How much money do you need to put in the bank today so that you can spend

Â $10,000 every year for the next 25 years starting at the end of this year? So,

Â think about this. What kind of problem is this? This is a problem where you need

Â money today and you are thinking about using it and depleting it over time,

Â alright? So, suppose the interest rate is five percent and I think we've become very

Â real with interest rates. We've gone from eight to five now, yeah, that's what

Â [laugh] the real world looks like right now. So, what I'm going to do is I'm going

Â to draw a timeline. And I'm sorry, this is something I'll force you to do and another

Â use of Excel is it comes with a timeline with the ASL being zero and so on. Okay,

Â so 25, zero one, so remember more points in time by one than the number of periods,

Â right? So, what do I know here? I'm standing here. What do I know? I know that

Â I need $10,000, 25 times, alright? So, this to me is C, R, P, and T. So I know

Â PMT. But what do I do, want to figure out? Okay, I need to spend $10,000 but I need

Â to have it in my bank, because maybe I just want to retire or maybe over the next

Â 25 years I'm working, but I want $10,000 sets, set aside to, for some needs that I

Â am planning for me. Whatever the motivation, you've decided to do this, I

Â will have to figure out the, now if I did it the long way, what will I have to do?

Â $10,000 / (one + r), right? The story is not over. What do I have to do? $10,000 /

Â (one + r)^2? And how many times? 25 times. Now, if I had to do the same thing 25

Â times, life is easy. But again whose messing with my fun? Compounding. Because

Â every time I add another one, this two becomes a three, four, five, 25 times,

Â okay? So, what do I have to do? When in desperation for calculation, go to Excel.

Â Okay, so I'm going to do, I'm going to go to Excel. And the good news is, the

Â previous problem is already there. So, I do not want to do a PMT first, because I

Â already know PMT. But I want to do now, what? Pv, right? Interest rate is now, not

Â eight%, but it's five%. How many years left? I believe in, in, in our problem

Â that we were looking at, just let me just confirm what it is. We do have 25 years

Â left and so we are okay on that. What is the PMT? Well, I know might be empty. And

Â I'm going to remove that last element because it's not needed. So, lets say. So,

Â 140,939.45 cents. So, what is that tell me? I better have $140,939 in the bank to

Â satisfy the need of spending 10,000 in the future. So, let me go back to the problem

Â and tell you what's going on. So, I need in the bank 140, 939 now let me just for

Â convenience call it $141,000, alright. So, let me ask you this. If I put, spend

Â $10,000 every year and the interest rate zero, zero, right? How many times have I

Â spent 10,000, 25 times? Then it's 250,000, right? So, the number that I'm going to

Â put in the bank is nowhere close to 250, it's off by at least 110, approximately.

Â Why is that? Because when I put $141,000 in the bank, the world is helping me. The

Â ingenuity of the world is helping me, in the form of five percent rate of return,

Â right? So, the, the good news here is when you do PV in this case, you have to put

Â much less than what you need in the future, simply because, as the money is

Â being withdrawn. The remaining money is accruing in value because again, of the

Â positive interest rate. So, is this, this problem gives you a sense of how to do PV.

Â And remember, the PV is discounting. So, every $10,000 in the future is becoming

Â less so today. And the last $10,000 is being discounted by 25 years. So, w hat

Â happens is, you are not multiplying 10,000 by 25 to get this answer. Because of

Â compounding and a positive interest rate, you're getting an answer of $141,000

Â dollars. I would encourage you to do this in your own time. Try to, after we are

Â done with this class, see how much money are you left with at the end of 25 years

Â if you carry this money forward. And we'll do this in a context, and why I am

Â encouraging you to think like that is simply to confirm that this number is

Â right under the assumptions. One final comment before we move on to the next

Â problem. The interest rate is five percent here. So, if the world is the same as our

Â previous problem, it requires a strategy that is less risky than the eight percent

Â to follow. So, just wanted to bring that risk thing that's at the back of your mind

Â into the picture. Just to show you, you know the ten, you know the 25, and

Â basically you know the five. Of course, the five won't be five the more risk you

Â take, but that's true about anybody making an investment, right? So, please remember

Â that. This problem helps you a ton. What I'm going to do now is, if you want to

Â take a break, this is a natural time. But I'm going to, because we've become

Â familiar with doing these kinds of problems, I'm going to take the next

Â problem on right away. But as I said, I always take pauses for you to take

Â ownership. In spite of the fact that you can pause me anytime, I think it's good

Â for me to tell you what I think would be a good time for you to pause. Okay guys, now

Â I'm going to do a problem on which I will spend a lot of time. And why am I doing

Â this, spending a lot of time? You'll see this is a classic finance problem in the

Â real word sense. So, here goes the problem and please read with me. I'm going to try

Â to highlight things as I go along. You plan to attend a business school and you

Â will be forced to take out $100,000 in a loan at ten%. And the ten percent you'll

Â see is kind of artificial because I want to make my life a little easy here.

Â Hopefully, you don't need to pay ten%, you need to pay much less. But th e $100,000

Â is an fact of life. It costs about that much for two years worth of tuition. And I

Â teach at the business school and clearly, I benefit from the value provided by

Â business school education in people's willingness to pay, but I want to

Â emphasize, this is not a small number. And remember, when you come to school, you're

Â also giving up an opportunity of working. So, when you do your calculations to go to

Â school, it's not a minor thing. And being in education, a part of me really believes

Â that things like this class I am knowing is should be a large part of the future.Of

Â course, it brings up the questions, how do people survive if everything is for free

Â and so on. But I think, I personally feel, this hundred thousand numbers is a bit too

Â high, even if I benefit personally from it. Anyway, you want to figure out your

Â yearly payments given that you will have five years to pay back the loan, right?

Â So, what do I know? We call this guy n, we call this guy what, PV, FV, PMT? Well, we

Â call it PV. Why? Because when I walk out with the bank, from the bank with $100,000

Â of loan, I have the money, today. But what do I have to do? In this case, pay a hefty

Â ten%. But I emphasize again, the good news is, the interest rate is not that high,

Â and should not be that high. Let me throw in the word should there too. Because

Â simply because it's just too high, from any standard. Anyway, so at ten percent

Â simply because you will see later it will help us with the calculations. So, the

Â first question to ask ourselves is let's draw the timeline and in this case there's

Â five, zero, one, two ,three, four. Now, I'm going to ask you, is this a real world

Â problem? And if you tell me no. I'd, I'll think they'd choose with you, not with me,

Â right? This is a real world problem, the only thing that will change is the

Â numbers, right? So, the quick question to you is, who decides $100,000? $100,000 a

Â year, who decides it? Well, all of us collectively. The fee is determined by the

Â school or the university, wherever you are going and the amount you need to borrow

Â depends on your ability to finance the education, right? So, you'll borrow, let

Â say that you're going to borrow a 100,000, which is two years worth of tuition and,

Â of course, you need to spend the money on yourself too, let's keep that aside for a

Â minute. Who decides the ten%? This is a very interesting question and goes back to

Â my emphasis on markets. If it is one person in the whole market deciding the

Â interest rate, that person is called a monopolist. And if, in finance, or

Â borrowing and lending money, there is one person you know who will get screwed, us,

Â the customers or the people borrowing money. So, that's why competitive markets

Â are important. Competitive markets are important so that the consumer benefits.

Â Not the producer, necessarily. And by the way, all of us are the same people. It's

Â not us versus them. I'm just emphasizing that markets are for people. Markets are

Â not for one person or a few of us, right? That's the beauty of markets. Anyway, so

Â the ten%, hopefully, is coming out of competition. Why? Because if there are

Â three banks, you'll always go to the lowest interest rate, right? So,

Â competition among banks on the internet, hopefully is getting better to help you

Â get a reasonable interest rate. So, R per period is ten%. And how did you decide

Â five years? Well it's again, an interaction between you and the bank. And

Â interest rates will vary depending on the periodicity or the length of the, sorry,

Â the majority of the loan and so on. So, let's keep that issue right now in the

Â risk category, right? So, you have five years to pay it back and the question I'm

Â asking is what? How much will you pay every year, per year, right? So, lets do

Â this problem. And to do this problem, I have to go to Excel. And I'm going to now

Â try to do things a little quickly on Excel. So, lets do it without screwing

Â things up, obviously. So, what was our problem now? I know my PV and I'm going to

Â calculate what? Pmt, right? This is a number I should know and the bank should

Â tell me. So, the interest rate is how much? Interes t rate is10%. And how many

Â years? Not 25, five. And the next number is PV, fortunately, if I see it right,

Â yup. And you got to keep your eye on the ball. And how much did I borrow? 100,000,

Â right? So, huge number, so the answer to this question is 26,380. And I think what

Â this is telling you is, and I'm, I kind of rounded things off again without decimals

Â there. It's telling you that I, or you, whoever is borrowing the money will get

Â $100,000 today, but will have to pay $26,000 plus 380, five times. So, just

Â pause there. This looks like a huge number. Now, the number, don't get fixated

Â on the number. If you were borrowing 10,000 it will be less. If you were

Â borrowing 50,000 it would be less. If you are borrowing one million, the payment

Â will be more. But there is a one to one relationship between what you are

Â borrowing and what you have to pay. So now, let me ask you this question, suppose

Â the interest rate was zero, suppose you could go to the bank and just get $100,000

Â and not pay any interest. How much would you pay every year? Pretty simple, take

Â $100,000 and divide by five. In this case, you're paying 26, 380 more every period,

Â every year. And for simplicity we've kept the year as a fixed quantity not a month.

Â We'll get to that in a second. S, o what I'm going to do now is I'm going to take

Â the 26, 380 and do this. What should be the present value of this? With n, five, r

Â of ten%. What should be the PV? If you can answer that question, you know how to mess

Â with Excel, actually know how to do something profound. If you do this

Â exercise, which I encourage you to do. It has to be a $100,000, right? Because the,

Â you're just going back and forth with the same problem. Okay? So, $26,380 is the

Â amount of money that you'll have to pay every year on a loan. What I'm going to do

Â next and I'm going to take a break now. And I think you need to take a break, is

Â you know how to do this problem. I'm going to now use this problems to show you how

Â great and awesome finance is. And after that, I will do a couple of other problems

Â a nd get you completely internalized with the class today. As I promised, the class

Â is intense because I'm doing problems. I'm bringing in the real world. If I were just

Â doing the formulas, you'd be much happier because time would just be passing by

Â quickly but the learning I believe won't be the same, okay? So, lets take break,

Â we'll come back and deal with this issue in a second.

Â