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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â how would we do this.

Â