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So this problem says and if you're taking a break good for you. Let's do this

problem. This problem says, suppose you put 500 bucks in the bank. And the

interest rate is seven%. If you notice, what have I done til now? I've chosen

interest rate of ten%. Why did I do it? Because I can do the problem in my head,

and so can you. I'll take, have the luxury of doing it, the real world doesn't. In

fact, it has three decimals in it or something like that. Here, we'll make it a

little bit more interesting. Let's make it interesting, make the interest rate 70%.

However, the interest is not coming from the seven%. If I asked you, what is the

seven, what is seven percent of 500 bucks, I hope you can do the problem in your

head. And it, multiply the two and you get a good answer, whatever it is. It's 35.

Right? So, however, what's complicating things is how much will you have at the

end of ten years? So let's go back to basics. And I want, I'm going to force you

to do this. And the reason is if you don't, I'm going to do it. Whether you

want to do it or not is obviously your choice. I'm going to be very timeline

oriented, especially in the beginning of the class. So what's the time? This is

zero. Right? How many periods? Again for convenience ten years. What's the other

element you know in the problem? I know that I can put P here as 500. You can

think of it as B, B, B sharp. The question I'm now asking is what the heck is going

on here? Again please remember we have no risk. So I have gone from two years to ten

years and you know lot can happen, and lot has happened in the recent past. So I

don't mean to believe to what has happened, I just think that uncertainty

cuts both ways and we have seen lot of bad effects of crisis, but I'm going to ignore

all uncertainty for the time being so that we understand the effect of time. Now this

is not easy. It's very simple to understand conceptually because what would

you do. Just carry it forward one year of the time. And if we had all the time in

the world, and the only problem to solve, we cou ld do it and ten weeks would be

over. So, but we want to write the formula. I want to take one + r which is

the factor, which in this case is. And what do I want to do? How many times is

this happening? I know it's happening over ten years. So here is the problem. I'm

raising it to the power of ten. And remember every time you go forward the

factor is one + r so after this one here it will be times 1.07, 1.07^2, and so on.

This thing, by the way, if you can do it in your head, there's something seriously

wrong with you. You need to grow up and do more interesting things in life. But there

are people who can do this in their head, and I think there's something, you're

spending your time on the wrong thing. Just think through it. If you understood

what's going on, this is where you ask yourself, do I get a calculator? Or do I

get Excel? And what I'm going to do, is, you have notes on using either one. The

calculator has to be financial, but not in this problem necessarily, because you can

raise things to the power of ten and so on. But this is the kind of Algebra that

you have to be comfortable. Therefore, I'm throwing in the Algebra before actually

solving the problem. But to solve the problem, we'll do, have to what? We'll

have to go to Excel. And I'll show you very simple way of doing Excel. Okay. So.

Let's see. If you can see what I am doing there, I am going to the tab on top, the,

the, the space on top that says effects. And that is where the functions reside. So

if you haven't got the finance functions you can always get them from Excel, it's

not a big deal. But the thing I like you to know is this, it's very intuitive. So

what are the key elements you need to know to solve this problem. I mean the key

elements you need to know is, you are solving a future value problem. So the

first thing you do is you put in something that you don't know. You don't put in

something that you are, already know because the Excel will look back at and

will say, you already know the answer, why the heck are you asking me. So it's

feature value I don't know. And as soon as I press feature value, guess what pops up.

What pops up right there is the first thing you need to know, which is the rate.

And the rate is the interest rate. As I said, symbols are something are something

that you need to familiarize yourself with. And another thing about Excel, which

many calculators differ on, is in Excel, you have to rate, write the rate exactly

as it is. So it is .07. Many calculators would allow you to just write seven, but

in Excel if you write seven, that means you are assuming the interest rate as

humongous, right. So what's the next element it asks for? It says N P E R. The

N is the operative word, P E R stands for periods. So in this case I believe. We

have to type, ten, because there was interest rate is seven, the number of

years past is ten, and there is a button called, or there's a symbol called PMT.

For now, ignore it. And the reason I'm asking you to ignore it is it doesn't

enter our problem. That's the next element we'll get into next week. And PMT stands,

basically for something called payment. So what when does do payments happen say for

on a loan? They happen regularly. Right now we're just looking at $one transferred

travel, time travel over time. So I will put a zero there, because if you don't put

a zero, it won't know what's going on. And then I put PV, and I know PV. It's I who

put money in the bank, so I better know how much it is. Alright, so I put it in

there and then I press return. Now what you will notice is it, it's showing up in

red. You are noticing $983 and some cents. By the way I'm not interested in cents

here, right. So I'm not even interested in the answers so much. I'm interested in

your understanding why I use Excel and the reason I used Excel is because the human

mind cannot calculate something raised to power ten very easily. And in fact,

there's a, there's a whole video created and researched on this, that human are

very good with linear stuff. And humans are not very good with non-line ar stuff.

So, that's why maybe, sometimes finance looks like a challenge. But if you break

it up into bite-size pieces, and recognize why you're using Excel, Excel doesn't

control you. You control Excel. Right? I, I hope that's pretty obvious. So if you've

seen Matrix, it's a very different world and we are not there yet. So don't let

Matrix enter your mind thinking that Excel is solving your problems, one day it will

but not for now at least. So what is 983? $983 is the value of $500. How much, how

many years from now? Ten. But there has to be another element, in answering this

problem, and that is the interest rate. So the interest rate is seven%, and the world

remains the same for the next ten years. And I get the seven percent a year,

assuming no risk right now. I'll get 983 bucks in the bank. But clearly, if the

interest rate was lower, I would have less. If the interest rate was higher, I

would have more. The real core dynamic is the interaction between time and the

interest rate. So the interest rate is a pretty year number, in this case seven

percent but the real cool interaction, which we call compounding, is between the

seven percent interest and the number of years, ten. And the more years that

happen, and we'll see a problem soon, the more the dynamic becomes very powerful. So

here, you've almost doubled your money in ten years at an interest of seven that

wouldn't happen at a lower would happen faster at a higher rate. So I hope this is

clear to you. Now one last comment, and I said I am not going to spent too much time

on Excel, but I have to kind of satisfy your curiosity. Why is the number in red?

Why is it negative? Now think about it this is actually a pretty cool thing. So

Excel has been set up to make you realize. That if you put enough 500 plus today it

has to be negative in the future. So think about it. Who's getting the 500 bucks

today? You're giving it up. But who's getting it? The bank is getting it. And

what will they have to do ten years from now? If they're getting it? Remember I put

500 positive in the PD. They'll have to give up 983. So the lesson from Excel is

pretty cool, and that is, you can't get something for nothing. There is no such

thing as a free lunch. So if the bank, if you give 500 and are willing to give

another 983 to the bank, then your the sucker. Not the bank. And banks would be

pretty happy. In fact, probably will feel like doing business with you and you go

out of business and the bank will be in business forever. So, just wanted to give

you a sense of that. I'm going to come back to this in a second because I want

to, you to recognize that doing that doing these problems on Excel, is simply because

you can calculate things faster. So, let me do some examples. By the way, and I

want to emphasis one thing, a lot of these examples that I am using in this class. I

don't even remember how I thought of them. I mean, lot of my colleagues at Michigan

have helped me become a good teacher if I'm a good teacher at all. Lot of the

things we talk about. Lot of the examples we use, lot of the notes we use. We use

with each other. And, to be honest when you read literature out there. Lot of

these numbers have real world meaning. So let's go to the next problem. And show you

the power of compounding. What are the future values of investing 100 bucks at

ten%, versus five%for 100 years. Why am I doing this? I am, I'm doing this simply to

give you a, actually the real world context. So which kind of person, and I

promise I won't talk about risk but I, I'm by implication talking about it because if

there is no risk how many interest rates would there be? One, and it would be the

same. Because risk, largely, is responsible for different interest rates.

But for the time being, let's assume, for whatever reason, you have two

opportunities, five percent or ten%. In the real world, what would this mirror?

The five percent is kind of closer to a bond, where the difference between a bond

and a stock is it's less risky. The ten percent is kind of closer to what the U.

S. Stock market say, has given. It's given more over the last, say, 80 years. So I'm

just anchoring them in kind of real world problems, but keeping the interest rate

simple, so it's not 4.265, you know? For the sake of time. And you can do more real

world problems in your personal investing. But here's, here's a cool question.

Suppose a grandfather, a great-grandfather, had invested 100 bucks,

hundred years ago in the stock market versus a bond. That's the kind of context.

How much money would you have today? Clearly you cannot have, you cannot do

this problem easily. Right? In your head. So but I'm going back to the problem we

just had and I'm going to just modify it. So how much was the interest rate

possible? So let's start off with. Instead of seven percent the new problem has

either five or ten, so let's start with five. What is N? It's very obvious that n

was ten in my previous problem, but now it's 100. And zero is PMT again, but how

much, amount of money am I putting in? In the previous problem, I put in 100, 500

and now I'm putting in 100, right? So, if my fingers are going all over the place

and I punch the wrong number. We'll all deal with it, right? I mean I'm, I'm

teaching you one on one, I feel like you are listening. Believe it or not, I feel

like I can see you. But anyway, before you think I'm really strange let's move on.

Okay, so you have about $13,000, plus a little bit. If, what do you do. If your

grand great granddad, had put 100 bucks in kind of a bond, and it had grown to, and

of course this is your units of government long term bond, and the government is

still there, and so on. So remember this number, 13,150, but the question asked

you, how much could it be? At ten percent and if you asked a lay person on the

street, was probably smarter than me, but if you just ask them because they haven't

done finance. So suppose I change the interest rate from five to ten. What do

you think would happen? And I think what that person will think is, think linearly.

They'll try to say, oh, okay. Maybe it'll double. So remember what was answer the

first time. About 13,000. So, I think I got this, everything right here, 100

years, 100 bucks, that hasn't changed. Look at the answer. And the answer is

about 1.3 or $1.4 million. So what does that tell you that it's a mind bogglingly

dramatic change. And the culprit there is what? Simple, who's the culprit,

compounding? Or who's the beneficiary, compounding? So I want you to just think

about this for a second. And I'll go back to the problem and show it to you, so that

you feel comfortable with the question I have asked you. What are the future values

of investing 110 percent versus five%? So what did we see? 30,000, 1.3 million if

I'm, you know, reading it right. Huge difference. So what's going on? Let me ask

you this suppose there was no compounding. Right? Suppose there was no compounding,

which is what? Interest will be treated like it's different. Interest cannot earn

interest. The only thing that can earn interest is the original 100 bucks. Let me

ask you, with five%, how much will you have after 100 years? And you should be

able to answer that question, very easily. And the reason is very simple. Simple

interest rate is adjective. It's linear. We are very good at it. So let's take,

will the 100 bucks still be there? Sure. But every year how much will I be getting?

Five percent of 100 bucks is five bucks. After 100 years of five bucks how much is

it? 500. So you see how simple it is, that you have 500 bucks, five bucks at a time

for 100 years, plus the original 600, which was our answer. Our answer was

13,000. Alright? So what's the, where's the difference coming from? Compounding,

you see? [laugh]. It's very, very unbelievable. You know, you can't

visualize this stuff. But let's go to the more diff, more, the second problem. So

now I intrigue, increase the interest from five to ten%. How much am I getting every

year, on the 100 bucks? Well, twice as much. I was getting five bucks first, now

I'm getting ten bucks. What is ten bucks times 100, 100 a year. Thousand, so how

much do I have? I have a hundred bucks plus another thousand bucks. Sounds pretty

reasonable? But what was the answer at ten %, more than a million dollar? So you see

what's happening, two things are happening. Compounding is very tough to

understand but it's real. It's been happening. People have made money with

risk of, obviously. However. What's even more complicated is that comp, the

comparison with compounding between five and ten becomes a total nightmare. It's

very different, difficult to comprehend. Because it just blows in your face. If you

want to, if you want think about a really cool example. Actually provided in I teach

executives with a couple of my colleagues. And this is borrowed from their example.

And it's a real world scenario. So, read this for a second. Peter Minuit, if I'm

saying that right, by the way I don't speak French, so if I've screwed up his

name pardon me, everybody screws up my name, so no big deal. Peter Minuit bought

the Manhattan Island from native Americans for 24 bucks in 1626, right. Suppose the

native Americans decided, had decided not to. It's just had decided to sell the

land. And then taken the money of 24 bucks. And put it as a "financial

investment". At about six%. Whey am I choosing six%? Because it's not neither

too high. It's neither too low. Though, you don't know what interest rates will be

like in the future. Given what's happening now. But lets stick with six%. I Think

just as an example. How much would the native Americans have, in the bank today.

So this is your problem to solve, and it is not an easy one. So let's try and see

how would we do this.