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

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

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

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

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

technology and here's a person here sitting next to me. ≫> [laugh]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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