Alright. Now, let's discuss the time value of money. So here's a quick pretest before we dive into the time value of money. Pretest, it's my money and I want it, a, now, b, some other time. Now, right? It's my money and I want it now. Why is this so important? This is the key to the time value of money. Is that money is worth more today than it is at some point in the future, right? If I offered you a dollar today or a dollar tomorrow, a dollar today has more value. Why? Well, you can invest that dollar and it'll be worth more tomorrow. Imagine if I offered you $1,000 today or $1,000 in 5 years. Think about that, right? The $1,000 today, you can invest it over those 5 years and it'll be worth more than those $1,000 5 years from now, right? Because of the interest. So there are 2 main concepts when we talk about the time value of money and it all has to do with this idea of interest.
So the first one is what we call compounding and you've probably heard of compounding before when we talk about compound interest, where you earn compound interest being interest on interest, that's exactly what we're talking about here. That's taking current money and earning interest as time passes into the future. So the money today, the $1,000 I offered you today, what will it be worth 5 years from now? It'll be worth that 1,000 plus all the interest that it earned, right?
Now the other idea is discounting and this is the opposite of compounding. This is where we're taking future money, money at some future date such as the 5 years later I offered you a $1,000 5 years from now. Well, what is that worth today? So we're taking a future sum of money, the $1,000 5 years from now and removing interest to find out its value today. So, we could take that $1,000 5 years from now, remove interest for 5 years and say, okay, if I gave you this much today, you invested it for 5 years, it would have been worth $1,000 5 years from now. You follow? So we're taking some future money that 5 years in the future. We're saying what is it worth today, discounting it.
So when you deal with the time value of money, a very helpful tool is the use of a timeline. So it helps you visualize the cash flows. Let's draw a timeline here, to kind of see how this works. So in this idea, today you invest $100 at Clutch Bank at a 10% interest rate for 3 years. So we would draw a timeline that looks like this. We would put our years on top. This is generally how we do it. 0-1-2-3 where 0 is today. So 0 is today, right? And those are periods into the future. In this case, years, right? But those could be months into the future, days, weeks, whatever, into the future. So there we go. Now, what we wanna do is we wanna put our cash flows on the bottom.
So our cash flows are gonna be underneath and what we're saying is we're investing a $100 today, right? Today, you're investing a $100 so we would put a $100 here and we're investing it for 3 years here and what I like to do, a lot of times, how we learn this is to put the interest rate here, so we know what interest we're gaining 10%, right? So now, we have a visualization of this idea. We've invested $100 today at 10% for 3 years, well, we could go ahead and find out what that money would be worth into the future, right? How we would calculate what it's worth in the future and we're gonna do that using this equation.
This is the fundamental equation here of the time value of money. Once you take a finance class, you're gonna learn all about this equation in all sorts of detail, but for now, we're gonna deal with it on a simple level. They generally just kinda take it easy when you deal with this in a class like this. All right? So let's start here by defining the variables in the equation. So we've got the time value of money equation where we've got FV=PV⋅(1+r)n. Cool?
What do all those letters mean? So, first, we're gonna start with FV that is a future value. So, if we want to know what something's worth in the future, we can use this equation. We could say, okay, the future value is equal to PV which is the present value, what it's worth today plus the interest that it's going to earn. So how do we find out the interest it's going to earn? Well, we're going to have R which is the interest rate and this is going to be the market interest rate. When we talk about what we're gonna use in this case, we use the market interest rate or the available interest rate on the market and we express it as a decimal, right? We're gonna put 1 plus let's say if it was 10%, is the interest rate? Well, we would put 0.10 for r. Okay? And this is gonna have to be given to you in the question. They're gonna have to tell you what the interest rate is. Cool? And finally, we have n, the exponent here. N and that's the number of periods, okay? And that's generally gonna be years, but sometimes it could be weeks, it could be days, whatever. The number of periods and this is generally the amount of time this is generally years and it's the amount of time that's passing between the present value where we're starting and the future value. What we're trying to figure out what it's going to be worth in the future.
So thinking about that equation, let's do this first practice problem right here. The formula FV=PV⋅(1+r)n, what's that best used for? Compounding, discounting, rebounding, converting, which one do you think it is here? Look what we're solving for, right? We've got future value by itself. So we want to know what something's worth in the future. So go back up to our definitions, what do you think this is? Compounding, discounting, rebounding, converting? Well, it's definitely not one of the bottom 2. I just made those up. Remember, when we talk about Time Value money, it's compounding or discounting. If we're going into the future, we are compounding. We're compounding into the future. We're taking present money today and we're seeing what it's worth in the future.
So this formula helps us find out what a future value is of some present amount of money. Cool? Let's pause real quick and let's do another practice problem. You guys try and apply this formula in the practice problem. Let's check.
