I'll give you a minute to read this problem again and you'll recognize this problem. Reason I'm doing it is because it captured everything we did last time. But as you read it, you should see a difference. I'm throwing in something new into the problem so that you can think creatively to do this problem again. The problem again states that you're 30 years old, you believe you will save for the next 20 years until you're 50. This is exactly the same as last time. For 10 years following that, until you retire at age 60, you have an inability because of your expenses, college expenses, weddings, and so on to save and remember you're at 30, you're trying to figure your life out in the future. This is not difficult to do. This is all for your own thinking, not somebody else telling you what to do. I'm empowering you to think for yourself. Now, at 60, if you want to guarantee yourself $8,000 per month after that till you, "Are no more at 80." How much do you need to save for the next 20 years, starting at age 30? But the one wrinkle I've thrown in is I've made this from an annual to a monthly problem. I'm going to let that stay up there for a second. Since we've seen this problem before, I'm creating a new twist and we shouldn't be able to worry too much about the fact that there's months now. On the other hand, I think the problem becomes much richer, much more real world. Because it's compounding and you should always pause before you say that. Let's get started and since we are beginning this class, I'm going to just try to address this issue right away. First thing you always do is draw a timeline and I'm borrowing this timeline from last time. But notice I've done Something. If you are looking at this slide carefully, what you'll notice is, that I have made my life very simple by doing the first thing which is under my control is defining a period according to the nature of the beast. The problem here says, that I'll be saving monthly and the timeline converted to months solves a lot of my problems. The question now is, between years 30 and 50, there were 20 years but actually there are 240 months. Again, between years 60 and 80, there were 20 years there 240 months. The question is between 50 and 60 when I'm not able to save, but I'm not dis-saving, how many years are there? 10. But recognize that no longer can you work with years and therefore you have to convert that to a 120 months. That's basically the nature of the beast. Let's get started and do this problem a little bit faster than last time. What I'm going to do is, I'm going to show you months coming here. Why am I starting at this end? Why am I time traveling? Because remember, finance forces you to look forward and that's one of the best things about it. As I told you last time, don't look back, look forward because you're making decisions and then decide when you look forward, what is it that you're trying to solve? Here, you want how much per month? I believe my numbers now are 8,000 per month, you need for a long period of time. The PMT you'll put in solving this problem, is 8,000. We'll do it in a second. N is how much? N now is not 20 years, it's 240 months. Basically, this has to match this. If these two are not aligned you have a problem. Most importantly, you have to align this with the problem. If an annual interest rate is stated at eight percent, the monthly interest rate should be 0.08 divided by 12. If you were getting compounding on a quarterly basis, it would be different. Daily basis, it will be different. The question here is now, how do I solve this problem and what would they tell me? Because we've done this problem before, I'm going to recognize you remember that the first thing I'll try to do is PV of what I need and I'm going to put subscript here 60. You see the calculator Excel doesn't know where you are but you do. You know when you solve this problem, you are not at 0.30, you're at 0.60 in the future. You're already there in your mind and you're looking forward, you not looking back. Even though you are at 60 and it's yet to come 30 years from now, when you're solving this piece, you're looking forward, the same principle. Let's see, this is a tough one to do in your head. As I said, if you do it, there's something wrong with you. Let's presume you can't do it and let's use Excel to do it. What I'm going to do is, I'm going to toggle and go to Excel. Let's see. I had promised myself in this class that I wouldn't do lot of execution. But I'm not doing execution without hopefully, a need for doing it. Hopefully this is helpful to you without being hand-holding. Remember, what are we trying to solve for? We're trying to solve for a PV problem even last time remember, I screwed up. I thought I was solving a PMT problem, but I was actually solving a PV. The thing that you're solving for is the function and its PV. Remember in your head it's PV in year 6. Now, what is the interest rate? 0.08, but you got to pass. You do not have annual compounding, you have monthly compounding so you divide that by 12. How many periods do you have? 240, don't put 20 because if you put an interest rate of 0.08 divided by 12 and you put 20, your annual interest rate is almost non-existent, which by the way, matches with reality these days, but for the time being, let's do this problem. You have 240 PMT and then FV is what? We don't have a future value here, and, have you got all our numbers in there? 240, yes. The PMT is something I do know. The PMT comes before FV and I press 8,000. What do you get? You get $956,434 and I'm going to avoid the cents. Everybody recognize this. It's pretty straightforward and I'm going to leave it there and I'm going to toggle back to our presentation. This is art form, I'm going between different media without you even knowing, I hope you like that anyway. PV_60 we saw was, and I'm going to confirm this with my own notes, 956,434. I'm writing all these details simply because as I said, my philosophy is that I will not give you resources unless they are absolutely necessary for you to then sit back and consume. I want you to work through these problems yourself, so I'm giving you some minimal information. Now, the problem is, I cannot stay here. I got to match the tools I have to the problem I can do. Now clearly when you become proficient, you can do this in an Excel and do it all faster, and so on, but let's do it little bit logically. I want to bring it back here. Why do I want to do that? The reason is, I do know how to calculate a PMT, which I'm trying to calculate. What is my saving monthly? If I know its future value at this point, but if there's a gap, it's a problem, so why not take the problem to something you know how to do rather than just wait there and expect some magic to occur, and it's not a big deal. It helps your thinking. Now, what do we do? Let's go back and try to understand what's going on and do Excel again. What I'm going to do now is I'm going to, as I said before, toggle back to Excel. Now, the good news is I already have a number up there, 956, so let me take equals PV. Why did I do PV? Because now I'm bringing something at year 60 to 50 to match what I want, so let's do it. You have to be little careful because I think as I said, if you're not careful, you'll put in the wrong numbers. Now, 0.08 divided by 12 again. Please remember not eight percent, but 12th of that. How many periods? Well, between 50 and 60, there are 10 years, but 120 months. We've got those two numbers and now we need to figure out what do I put in next? Remember the next item here is PMT, that's how it's been set up in Excel. But I don't have a PMT. This time I don't, I put a zero there, but I do have a future value, and the future value is sitting in which cell? We just solved the problem I've retained that cell A1. Look what happens. I think this happened last time too, just because you're doing it monthly, it doesn't mean this won't happen. The value has dropped drastically, in fact to less than half. What's the reason for it? 120 months have passed and the monthly interest rate is non-trivial. Let me just toggle back to the PowerPoint. Where am I? I am now at this point, and I have a number that I can deal with, I think it's 430,896. What does this number mean? Let's just pause for a second. It was more than twice here. What does this number mean? In English. This is the amount of money I should have in my bank at age 50, to support what? To support all my post-retirement 8,000 a month expenses. That's one way of thinking about it. Now, however, I don't have that money, so I need to act today, starting end of next month to start saving, but what kind of problem is it? It's a PMT problem. How much money do I save a month? Whose future value? I already know. Make sense? Let's do it. Just one more step, and then after that, I will take a break. Because I want you to think about this a little bit, and see what's going on. Let's go to Excel. Now if you look at the two numbers on top, the first number is, it's showing negative simply because I'm putting a positive number as a payment. Now, 430 needs to be in the bank at which time? At time age 50, that is 956, it grows into if it stays in the bank or in a portfolio. Let's do the PMT problem. Because now we're solving for PMT. How many periods do you need? First is, you need 20 periods, but you also need a rate of return before that, 0.08 divided by 12, everybody got that? How many periods do I save for? Twenty years, which is 240 months. Fair enough? Got it. Now, the next number. Again, you have to just be paying attention because as to what Excel offers and in which sequence, and don't try to memorize it because you've got junk in your head doesn't help. Next item is PV, and we know we don't know the PV. We could do the PV, but we don't know it. What is the future value and where is it sitting? It's not sitting in cell A1, it's sitting in cell A2. Remember what's sitting in cell A1 is the future value at year 60, and you want it at year 50. Let me see what I did. You see I can guess when I'm doing something not quite right. You have A2, 240, you see I told you you should put zero there, and somehow I put a zero and disappeared. But I have intuition. Once you start doing this number, a number will jump out at you and say, "That doesn't make sense." Saving $3,000 a month just doesn't make sense today to get $8,000 in the future, look how much are you saving? Your saving about $732. Just to recap everything, let me go back one more time, and show you what you've done. Basically, what you've done is, we have solved a problem where we started off wanting 8,000 a month 240 times, we figured out it's present value at this stage. Then we said, how much do you need to save every month to solve this problem? Look, I'm not going to enter the items here, we already did this. What I'm going to enter is, what did we get over here? We got $732. I wanted you to think a little bit about it. Look at the poverty of time and compounding. I have to save only $700 a month plus 730. But in return for that, I'm able to enjoy $8,000 a month. The thing that has changed is time between the two. Why is it that I can save so little, and enjoy so much in the future? One, because time has passed, two, because of the interest rate. I repeat again, an interest rate of eight percent a year, which is 8 percent divided by 12 a month, is a very high number, first point. Second point, yes, you are working hard hopefully, to get the saving possible of $700 plus. But remember who's giving you the benefit? The world is investing your money in good ideas hopefully, and we'll see what good ideas are later today, that's the topic of today's class. You are able to enjoy what the world has to offer through the ability to invest in other things. That other thing we call what's portfolio. But remember that portfolio grows over time, simply because of two things. More months, more the growth, higher the interest rate, higher the growth. The two together is the profound effect of compounding, which even Einstein said he couldn't file them. Turns out, that's why you need Excel and other things to calculate these numbers. I hope this put everything together one more time, and the small twist of going from a year to a month, helped. Do one last thing, answer the following question, if compounding is monthly, and the stated interest rate is eight percent annually, what really is the annual interest rate? I can give you the directional answer, it has to be more because of pause, compounding. I would take your time to solve that problem, and we are not going to do it, you have a formula, you have information, do it for yourself, and it'll help you understand. The only difference is you're going from month to a year, instead of a year to many years. Again, just messing around with the timeline.