Learn the toughest concepts covered in your Macroeconomics class with step-by-step video tutorials and practice problems.

The Financial System

Time Value of Money Calculations



Future Value Calculations

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Alright now let's discuss the time value of money. So here's a quick pre test before we dive into time value of money pre test it's my money and I want it a now be 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 because 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 $1000 today or $1000 in five years? Think about that right? The $1,000 today you can invest in over those five years and it will be worth more than those $1000.05 years from now, right? Because of the interest. So there's two main concepts when we talk about 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 five years from now. It'll be worth that 1000 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 five years later I offered you $1000.05 years from now. Well what is that worth today? So we're taking a future sum of money $1000.05 years from now and removing interest to find out its value today. So we could take that $1000.05 years from now, remove interest for five years and say, okay, if I gave you this much today, you invested it for five years. It would have been worth $1000.05 years from now you follow. So we're taking some future money that five years in the future. We're saying, what is it worth today discounting it. So when you, when you deal with 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. Uh to to to kind of see how this works. So in this idea today you invest $100 at Clutch Bank at a 10% interest rate for three 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 0123 where zero is today. So zero is today, right? And those are periods into the future in this case years, right? But those could be months into the future. Uh days, weeks, whatever. Um 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 $100 today, right? Today, you're investing $100. So we would put $100 here and we're investing it for three years here. And what I like to do a lot of times, uh how we learn this is to put the interest rate here. So, we know what interests were gaining 10%. Right? So now we have a visualization of this this idea. We've invested $100 today at 10% for three 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 time value of money. Once you take a finance class, you're gonna learn all about this equation and all sorts of detail. Um But for now we're gonna deal with it on a simple level. They generally just kinda take it kind of easy when you deal with this in in a class like this. All right, So let's start here uh by defining the variables in the equation. So, we've got the time value of money equation where we've got F. V. Equals PV times one plus R. To the n. Cool. What do all those letters mean? So first we're gonna start with F. V. That is a future value. So if we want to know what something is worth in the future, we can use this equation. We can say okay the future value is equal to P. V. Which is the present value, what it's worth today plus the interest that it's gonna earn. So how do we find out the interest it's gonna earn? Well we're gonna have our which is the interest rate, right? And this is going to be the 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 one plus, let's say if it was 10% Is the interest rate or we would put 0.10 for our 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 and 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 gonna be worth in the future. So thinking about that equation, let's do this first practice problem right here the formula F. V. Equals PV times one plus R. To the end. 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 is worth in the future. So go back up to our definitions. What do you think this is compounding, discounting, rebounding, converting. It's definitely not one of the bottom two. 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

You invest $4,545 in Clutch Bank today earning a juicy 10% annual interest. What is the value of your investment in one year? What is the value of the investment after two years?

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Using a little bit of algebra, we can rearrange the time value of money formula:FV = PV x (1 + r)n

The formula FV = PV x (1 + r)n is best used for: 


You are saving up $12,000 for a luxurious European vacation two years from now. How much money would you need to invest today at Clutch Bank, earning their juicy 10% annual interest, to have enough for your vacation?

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You are saving up $12,000 for a luxurious European vacation two years from now. How much money would you need to invest today at Clutch Bank, earning their juicy 10% annual interest, to have enough for your vacation? How much would you need to invest today, if instead you could only earn 6% interest?

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