We are just doing future value of annuities and I'll show you now why this is such a cool thing. What I'm going to do is I'm going to do two examples, both for future value of an annuity and what's the other thing we do? Present value for an annuity. Remember, the amount of the annuity when you write could be called c, but when you go to a calculator or a spreadsheet, we'll call it PMT because that's what they call it, right? It makes sense? Okay. I would like you to stare at this problem and I know you have the ability to pause and so on, but I'll like to pause with you and what I'm going to do for every example, and if I don't, you should do this, is I'm going to read out the problem for you and we'll talk about it a little bit. Then I would really encourage you to try to do the problem. I'll do it with you but I would encourage you to think actively and be participating in it because I can't see whether you're doing it or not, but I hope you do. Okay. What will be the value of your portfolio? What is the portfolio? Portfolio, and there's lingo in finance. Portfolio means whatever your investment is, wherever you have put your money. The word portfolio is used generically because you'll see later, it's a hangover from the fact that life has risk and if life has risk and you do not like risk, which most people don't, you tend to not put all your eggs in one basket. The fact that you hold a basket of different things, it's called a portfolio, okay? I'll try to emphasize words which I take for granted because, I mean, if you're new to finance, which most of you probably are, you need to understand why certain language is used very commonly. At retirement if you deposit $10,000 every year in a pension fund. Now if you're really young, say you're 15 and taking this class, which I hope some of you are. Don't worry too much about retirement. Have some fun. You're in high school. You haven't even begun earning, hopefully, you just having fun. But this is something that you will do at some point, most people do. What I will recommend is just think of it as an intellectual problem, but actually it's a very real problem. What will be the value of your portfolio at retirement if you deposit $10,000 every year in a pension fund? What is a pension fund? Pension Fund is a place or account which hopefully has multiple assets, if you're risk averse. Multiple kinds of investments, a bond, a stock, and we'll talk about those. You put $10,000 every year. Why $10,000 fixed amount? Well, nothing is forcing you to put $10,000 every year. It can be $11,000 one year, $9,000 the other. But oddly enough to make life simple, perhaps many people tend to put away a certain amount of money every year for things they need in the future, so the notion of a pension fund is at some point I'm going to retire and I need some money. So you put away $10,000 every year. You plan to retire in about 40 years and expect to earn 8 percent on your portfolio. What have I given you? I have given you everything you need. I've given you PMT or C, which is $10,000. I have given you the number of years left for you to retire, 40, and I've given you an interest rate that you're likely to earn on your portfolio, which means where you put your money; a bank, whatever. We'll talk about that in a second. But let's just focus on this and try to do this problem. I hope you have been listening to me and I hope you have been paying attention because if you pay attention to a problem, it gets to be a little intense and I'll do the problems with you, and I have promised myself today I'll spend a lot of time just doing problems with you because that's how you learn. Another piece of advice, I have given you textbooks to read that you can go get and read. They can be secondhand, they can be whatever. The fundamental principles of finance have been known since we were in the cave. Just remember that what you're trying to do is focus on the fundamentals so read whatever you want if the video doesn't satisfy your curiosity. But the video is trying to be self-sufficient. Let's do this, let's now start doing the problem. What I'm going to do is I'm going to do two problems for future value, two problems for present value, but I'll take breaks with you. I'll let you know that maybe it's time to take some time off, get some coffee, go jog around the apartment building where you live or talk to your friend or watch a video on YouTube. Why not? Let's get started. I'm going to draw a timeline right here. You can use the box I gave you. I prefer this. How many years? Forty. Please remember, there's always one more point in time than the number of periods. If you remember that, or if you recognize that, you'll be okay. How many points in time? Forty-one, 0, 1 through 40. How many periods of time? Well, it takes two points of time to make a period, so they're one less, 1, 2. What we'll do to make our life simple is we'll assume that the first $10,000 is at the end of the year. Why did I do that? I could always start saving at this point, but I'm doing it simply so that I can use the formula and just directly use the calculator and do it and set up. We can change that, so don't worry. You can start a payment today and change it, it's just a minor difference. How much? Another thing that seems a little bit odd or manufactured in this formula is that you are saving at year 42. You may not be, or actually you may stop saving in between. But for convenience we are trying to understand the problem which is? Got 40 of these guys. The good news is, even though this formula is very complicated, you carry it forward by how much? One period, but there's no money. How much do you carry this forward by? Thirty-nine periods. How much do you carry this forward by? Thirty-eight. Which is the simplest piece of this? This guy. Why? Because I'm asking you what is the future value at this point in time. The future value of this point in time of this guy is just itself. That's what I mean, if you learn how to travel in time. Imagine you are at point number 40, the last PMT or C is $10,000, so at time 40 it's exactly 10. But when you look back, if you were to, you have to carry the past amounts you've invested as earning money, which is good news for you. It's earning how much? Eight percent. Let me tell you, that's not bad at all. We'll talk about that when we talk about risk and return in a second. Do you understand the nature of the beast? The beast is not easy. It's not easy. It's like doing 39 future values and adding them up. What I'm going to do is I'm going to now shift to using a calculator. If you notice I'm on the top panel and I'm going to use the formula of PMT. Remember, whatever you don't know, you type in here. PMT. The one thing you have to do before you do PMT, and not get excited like me, I'm Mr. Hyper, you have to put equal sign, otherwise you'll get all kinds of garbage. You open it up. What is the first number that shows up? The first number that shows up is the rate of return, and we know how much are we earning. We're earning 0.08. Again, emphasizing this. The only reason I'm using Excel right now is what? Simply, because the calculation is very difficult, but I've explained to you what's going on. You're doing 40 carry forwards, but actually only 39 because the first one is zero and the last one is just itself, so that's why I said. You put a comma, and what's the next one? Forty, number of periods. Actually, let me just backtrack a little bit. The thing that we want to figure out is FV, so put in FV and now I want rate 0.08. You see what I was doing, we'll do next time. Number of periods is 40 and in this case, I know my PMT. My PMT is $10,000. What is PV? Don't worry about it, it's not in there. Just hit. What do you get? You get a lot of money, basically. You get $2.59 million, is 2,590,565. What does this tell you? This tells you that if you invest $10,000 in a bank, 40 times, the future value of that will end up being $2.59 million. What I'm going to do, I'm going to try to talk you through the problem again just so that we are working together. What did I do? I calculated future value. In order to calculate future value as something that I don't know, I have to use the future value function in the calculator or in the spreadsheet. Out popped, I gave this information $10,000 was PMT, 40 was m, but most importantly, eight percent was r. I gave all this information to Excel or a calculator, whatever you choose to be using, simply because it's a very complicated calculation. Conceptually, it's not that difficult and we got 2.59 mill. I'm going to just use it approximately because I'm not going to calculate or write all the digits and so on. What has happened here? Let me just walk you through this problem. First of all, remember yesterday, whenever I asked you what is the answer to a finance question or anybody asks you, what should you say? Compounding. But you always have to pause because you want to look smart. You take a pause and you say compounding. Let me ask you the following question. Suppose there was no interest rate, or in other words, how much of the 10,000 are you throwing in? Suppose interest is zero, this problem is very simple to do. Why? Because you do 40 times 10,000, you have $400,000. The interest rate time value of money is zero. You will have a lot of money in your bank account, but how much will it be? Four hundred thousand. How much do you have if the interest rate is eight percent? 2.59 million. Huge difference in magnitude and who's the culprit? Compounding. In this case, the culprit is helping you. But in the case of if you are paying it, it hurts. We'll do a loan later. Here it's helping you. Let's talk through this problem a little bit and so that you understand how empowered actually you are and finance will make you feel liberated in this simple problem. Here you go. Let me ask you, who decided the 10,000? Think about it. Who should decide 10,000 every year? You or your financial advisor? Who? I hope the answer is you. So 10,000, I know it's not easy to figure it out. But I would encourage you to think about what your needs are in the future so that you can figure out how much you need to put away. We'll do a problem, quite the reverse in a second. You put away $10,000. Who decides that? You decide that. Second question. What is the other number in this problem? It's 40. How many years to retirement? I know you can say that your job may have a retirement age or so on, so forth, but I challenge you on that. Hopefully, you have much more control on when you retire. Than you think you do. By that I mean you should keep learning in life so that you always have the opportunity to do something. We're talking about a money problem but it could be about anything. Let's take the extreme case scenario. You're doing a regular job and you know 40 years from now you're going to retire. My point there is you have more control on there but sometimes people don't. People have jobs where they are dependent on the employer on how many years they work. But it's a given. You won't go to a financial advisor and say," In how many years do I retire." The person will give you an answer but they'll charge you a lot of money for giving the answer. The 40 is also information that you should know. Ten thousand is the information you should know. Now the 8 percent. I'm going to violate the assumption that I said make at the back of your mind but to be fair, I never said assume it's not there. I said, I know it's there, keep it at the back of your mind but for convenience sake, we'll ignore it and that is risk. Let me ask you this. Who determines the 8 percent? If you can answer that you have arrived and the answer is simply nobody. If anybody knew what the interest rate was in the future for the next 40 years or something, they would be omnipresent, they would know the future. We are all wanting to be like that but I think the beauty of life is nobody knows. In fact, one of the most profound developments in finance in recent years, I should recent say last 40-50 years, which gets challenged because it's a good idea. Bad ideas don't get challenged, good ideas get challenged. The notion there is that nobody in a good market should be able to tell the future because everything we know is already in the marketplace. That's why I said competitive markets at the beginning are extremely important to what do we do. Quick question. Who determines the 8 percent? The answer is you. This is where I have to bring in risk a little bit. Why? Because 8 percent, let me tell you, if you get over the next 40 years, may the force be with you, because it's going to be easy. You have to take risk to get high rates of return and with risk comes volatility, so the 8 percent the higher it is, the more likely it is that you are jumping all over the place, like the stock market. So if you want to be safer, what will you have to do? You will have to lower the interest rate to say 4 percent. Put it in a bond issued by the government in the long run and you'll be safer. But what will happen to the $2.59 million? Do this exercise for yourself. Lets, after this class is over, use 4 percent instead of 8 percent and what will you see? A dramatic drop in the amount of money you have at the end. Why am I emphasizing so much in one little problem? Because that's what finance's beauty is. If you understand these problems inside out and you know how to use the Excel spreadsheet to calculate the answers you have arrived. If you use 4 percent what happens? You get rid of your nervousness about risk but what happens to the amount of money you have? It'll drop dramatically. We know that, we know the power of compounding. It helps when interest rate goes up, it hurts when it goes down. Having said that, if the interest rate is 4 percent you're going to suffer. What can you say about the 8 percent 4 percent choice? Neither one is good or bad. What's important is you have control over the 4 and the 8 in the following sense, not that you can predict it but if you choose to put 4 percent in your calculations, it has to be matched by your investment strategy. If you're thinking you're going to earn 8 percent and put it in the bank, especially today and if these low interest rates go on, you're dreaming. You'll have closer to $400,000 if the bank is still there after 40 years. Think like that everything is under your control and the beauty of markets is, for most of us, we do not need to second guess what the interest rates are. All we need to do is match our preferences of risk with our investment strategy and then not worry about it too much.