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 7%. If you'll notice, what I've done until now, I've chosen interest rate of 10%. Why did I do it? Because I can do the problem in my head and so can you. I'll have the luxury of doing it, the real word 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 7%. However, the interest rate is not coming from the 7%. If I asked you what is 7% of 500 bucks, I hope you can do the problem in your head. And multiply the two and you will 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'm going to force you to do this. And the reason 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 0, right? How many periods? Again for convenience. 10 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 P, PV, short. So the question now asking is what the heck is going on here? Again, please remember we have no risk. So I've gone from two years to ten years, and you know a lot can happen, and a lot has happened in the recent past. So I don't mean to belittle what has happened, I just think that uncertainty cuts both ways. And we have seen a 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 will you do? Just carry it forward one year at a time. And if we had all the time in the world and the only problem to solve, we could do it and ten weeks would be over. But we want to write the formula out. I want to take 1 + R which is the factor, which in this case is. And what do I want to do? How many times does this happen? I know it's happening over ten years. So here's the problem, I'm raising it to the power of ten. And remember that every time you go forward, the factor is 1 + R. So after this one here, it will be times 1.07, 1.07 squared 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 you're spending you're 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 with, therefore I'm throwing in the algebra before actually solving the problem. But to solve the problem we'll have to do what? We'll have to go to Excel. And I'll show you a very simple way of doing Excel. Okay, so let's see. If you can see what I'm doing there, I'm going to the tab on top, the space on top that says fx. 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'd 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 think the key elements you need to know is you're 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 already know because the Excel will look back at you and say. You all ready know the answer. Why the heck are you asking me? So its future value I don't know. And as soon as I press future 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 you need to familiarize yourself with. Another thing about Excel, which many calculators differ on, is in Excel you write the rate exactly as it is. So it is 0.07. Many calculators would allow you to just write seven. But in Excel if you write seven, that means you're assuming the interest rate is humongous, right. So what's the next element it asks for? It says nper. The n is the operative word, per stands for periods. So in this case, I believe we have to type 10 because there was interest rate of 7, the number of years passed is 10. And then there's a symbol called 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 when do payments happen say for on a loan? They happen regularly. Right now we are just looking at $1 transfer, time travel over time. So I 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 has put the money in the bank, so I better know how much it is, right. So I put in there and then I press Return. Now what you'll notice is it's showing up in red. You're noticing $983 and some cents. By the way, I'm not interested in cents here, right. So I'm not even interested in the answer so much. I'm just understanding why I used Excel. And the reason I used Excel is because the human mind cannot calculate something raised to power of ten very easily. And in fact, there's a whole video created and research done on this that humans are very good with linear stuff. And humans are not very good with nonlinear 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 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 dollars, 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 7% and the world remains sane for the next ten years. And I get the 7% a year. Assuming no risk right now. I'll get $983 bucks in the bank. But clearly if the interest rate were 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 per year number. In this case 7%. But the real cool interaction, which we call compounding, is between the 7% 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 rate of 7. That won't happen at the lower. It would happen faster at a higher rate. So I hope this is clear to you. Now, one last comment. And I said I'm not going to spend 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 they will have to do 10 years from now, if they are getting it? Remember, I put 500 positive in the pv. 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's no such thing as a free lunch. So if the bank, you give $500 and are willing to give another $983 to the bank then you are a sucker, not the bank. And bank will be pretty happy. In fact, probably will feel like doing business with you and you'll 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 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 emphasize one thing. A lot of these examples that I am using in this class, I don't even remember how 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. A lot of the things we talk about, a lot of the examples we use, a lot of the notes we use, we use with each other. And to be honest, when you read literature out there, a lot of these numbers have real world meaning. So let's go to the next problem. And show you the power of compounding. What the future values of investing 100 bucks at 10% versus 5% for 100 years? Why am I doing this? I'm doing this simply to give you, actually, a real world context. So which kind of percent and I promise I won't talk about risk but I am by implication talking about it. Because if there's no risk how many interest rates there be? One and it will be the same. Because risk logically is responsible for the interest rates. But to the time being let's assume, for whatever reason, you have two opportunities, 5% or 10%. In the real world, what would this mirror? The 5% is kind of closer to a bond, where the difference between a bond and a stock is, it's less risky. The 10% is kind of closer to what the US 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 that it's not 4.265. It'd just take up time. And you can do more real world problems in your personal investing. But here's a cool question, suppose your grandfather or great grandfather had invested 100 bucks, 100 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 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 7%, 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 money am I putting in? In the previous problem, I put in $500, and now I'm putting in $100. So if my fingers are going all over the place, and I punch the wrong number, we'll all deal with it, right? I'm teaching you one on one. I feel like you're listening there. 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. What do you do? If your great granddad had put 100 bucks in kind of a bond. And it had grown to, and of course, this is your, it's a 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 10%? And if you asked a lay person on the street, who's 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, okay, maybe it'll double. So remember what was the 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 that culprit there is what? Simple, who is 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 $100 at 10% versus 5%? So what did we see? $13,000, $1.3 million, if I’m 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 means 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 5%, 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 additive. 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? 5% of 100 bucks is 5 bucks. After 100 years of $5, how much is it? $500. So you see how simple it is? That you have 500 bucks, 5 bucks at a time for 100 years plus the original $600. Which what was our answer? Our answer was $13,000, all right. So where's the difference coming from? Compounding, you see? [LAUGH] It's really, really unbelievable. You know, you can't visualize this stuff. But let's go to the more difficult, the second problem. So now I increase the interest from 5 to 10%. How much am I getting every year? On the 100 bucks? Well, twice as much. I was getting 5 bucks first, now I'm getting 10 bucks. What is 10 bucks times 100 year? $1,000, so how much do I have? I have 100 bucks plus another 1,000 bucks. Sounds pretty reasonable, but what was the answer at 10%? More than a million dollars. 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, obviously. However, what's even more complicated is that comparison with compounding between five and ten becomes a total nightmare. It's very difficult to comprehend because it just blows in your face. But if you want to think about a really cool example actually provided an IT executive with a couple of my colleagues, 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 have 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 had decided not to. Sorry, had decided sell the land and then taken the money of 24 bucks and put it as in, quote unquote, financial investment at about 6%. Why am I choosing 6%? Because it's neither too high, it's neither too low, though we don't know what interest rates are like in the future, given what's happening now. But let's stick with 6% 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's not an easy one. So let's try and see how would we do this.