Alright, so we're going to discuss one of the more difficult topics for this course; it's the time value of money. Okay? So, the time value of money, this is how some amount of money today is going to be worth a different amount in the future, okay? And we use this mostly when we deal with bonds payable. So the liability, bonds payable, well, we're going to use the time value of money when we're pricing these bonds. Alright? Let's go ahead and dive right into the ideas of the time value of money. So I got a quick pretest for you to set your mind in the right direction. So it's my money and I want it blank. Now or some other time? It's my money and I want it now, right? It's my money and I want it now. So think about it, if I offered you $1,000 today or a $1,000 5 years from now, which one would you take? The $1,000 today, right? You want that money today, and you can start spending it now or you could invest it, and it'll be worth more money in the future. So that's the main idea here. This is the big takeaway of the time value of money, is that a dollar today is worth more than a dollar tomorrow, right? That same dollar could have earned some interest and have been worth more in the future.

So when we talk about the time value of money, we're going to talk about 2 main concepts and they're opposites of each other. The first one, you might have heard of before, is compounding. So you might have heard of compounding interest, right? You might have talked about compounding interest at some point in a math class. And you're compounding interest into the future. Right? You're going to have some current amount of money. So you're going to take some current amount of money, say the $1,000 that I offered you today, and you're going to earn interest. Right? You're going to take that money and you're going to earn interest as time passes into the future. So you're compounding into the future. Right? So you can imagine that there's going to be an opposite to compounding and that's going to be discounting. So we're going to use this term discounting when we're taking some future sum of money. So now, that $1,000 that I offered you 5 years from now. Well, if we were to take out the interest that would have occurred over the 5 years, it would have been worth some lower amount of money today. Right? So what we're taking is some future sum of money and removing the interest that occurs over time to find its value today.

So think back to that offer I made you, right? I offered you either $1,000 today or $1,000 5 years from now. So that wasn't so enticing, right? You want the $1,000 today, but what if I offered you $1,000 today or maybe $1,500 5 years from now. Maybe now you'd weigh your options. What could how much could I earn on that $1,000 or what is it worth to me to have that $1,000 right now compared to the interest that I would earn or what it would be worth 5 years from now, right? So now you have a little more options to weigh, and that's because of the time value of money. And it all comes down to that interest. So we talk about the time value of money, it becomes very useful to use timelines. I'm sure you've used timelines before in a math class, but it's very useful to see visualize these cash flows on a timeline so you see them all in one place. Okay? So let's go ahead and do an example and build a timeline here.

Today you invest $100 at Clutch Bank at a 10% interest rate for 3 years. So, what we're doing is we're going to take that $100 and we're investing it for 3 years, and it'll be worth some amount of money in the future. We're compounding the $100 today into some future sum of money. So let's go ahead and draw a timeline, so we can visualize what's happening here. So this is how we usually do a timeline. We're going to draw something like this and then we're going to draw the different years here. So we're dealing with 3 years, so we always start today. Today is going to be 0 and I like to put my years above the graph. So these are the years right here. And we always talk about right now as 0, okay? When we deal with this concept, we deal with it as 0.

And before I go on here, I want to make a point that the time value of money in this class, we usually keep it pretty basic. You're going to go into a lot of detail with the time value of money when you take a finance class. In finance, you're going to buy a financial calculator and you're going to do all sorts of complicated time value of money, equations and transactions. For this point, we keep it generally pretty simple and we mostly use it for valuing bonds payable, that liability bonds payable. Alright. So let's go ahead and finish up our timeline. So we had year 0 here, which is right now year 0. Then year 1, 1 year from now, 2 years from now, and 3 years from now. Pretty simple, right? And then, underneath the timeline, you write your cash flows. So in this one, it's pretty simple; we only had one cash flow of $100 and the thing is, once you start doing bonds payable and once you get into higher-level courses and doing more difficult transactions, you're going to have multiple cash flows at different points in time. So the timeline helps you a lot to visualize and see where all these different cash flows are happening. Okay? So that $100 is what you invest today and then we like to put our interest rate right here. So the interest rate was 10% in this case. So you can imagine, you would earn 10% and we're not going to do the calculations here, and you would get in 1 year. Well, we could do this first one, right? You have a $100 and you earn 10%. So it would be worth, say, $110 a year from now, right? Because if you took it and in 1 year, it'd be worth $110 and then you keep compounding, right? There's another 10% and keep going in the future, 10% And you keep earning interest, right? And that's the whole thing. When we're compounding, we're earning interest on the interest. Because in the 2nd year, you're earning interest on the $110, not just the $100. So you're getting a little extra interest, so you can imagine it's going to keep growing over time like that.