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Time Value of Money Equation:Future Value

Brian Krogol
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Alright so let's go into the time value of money equation. This is pretty much the core of time value of money and the core of your finance class once you get there. But we're gonna use it in pretty simple fashion throughout this course. Okay so the time value of money equation we're gonna have F. V. This is our first variable and FV. Is future value. So future value. This is some future amount of money, right? So we're talking about our example above the $100 is what the present value is, what it's worth today and the $110 a year later. Well that was the future value of that $100 today. So future value is the value of money some point in the future. Okay at some point in the future compare that to present value right? PV. Is present value and that's the value of a sum of money right now. So if I told you I'm gonna give you 100 give you $1000 right now, guess what the present value of that $1000 I'm about to hand to you is it's $1000 right? The present value is what it's worth today. But future value is what that $1000 might be worth at some future point in time when we consider interest. So talking about interest is our next variable that are right here. So notice we have future value equals the present value what it's worth today times one plus r which is the interest rate. And when we talk about the interest rate here we're talking about the market interest rate, we're gonna go into more detail about market interest rate versus the stated interest rate or coupon interest rate. And that's when we deal with the bonds payable. So you just want to note whenever you're using your time value of money equation, you always use your market interest rate when you plug into this equation. OK. And you want to make a note that the market interest rate, you're gonna express it as a decimal, right? So if I told you the market interest rate is 10%. Well, You want to put that in a 0.10, right? And it's always gonna be this one plus the rate. So it would be 1.10 that goes into that parentheses there. Right. So market interest rate. Well, that's the interest rate on the market, right? The common interest rate. That could be found generally the competitive rate on the market. Okay, So that's our market interest rate. And finally we have N notice N here is an exponent. So we're having exponent here. And generally in this class, you're not gonna be compounding for 20 years or something because most of the time you can only use a very simple calculator that doesn't do exponents. So for the most part they'll maybe do three years, four years, maybe five years if they really want to push it. But you'll you'll be able to use this exponent for N. And N. Is our number of periods. Okay. The number of periods which is usually years. So above in our example that we were talking about investing at the clutch bank for for three years. Well three would be our exponent here for N. Right? So if we're trying to find the future value up here, the future value of our investment of $100 so notice that $100 that would have been our present value times one plus the interest rate of 10%. So one plus 10.10. And we would raise it to the third power, right? That would be our end for three years. And that would tell us the future value. So what is it going to be worth in three years? What would be 100 times 1.10 to the third power? Let's go ahead and do that real quick just to solidify that example here. So 1.1 and let's say we don't have an exponent, right? We don't have an exponent button. Well we would do 1.1 times 1.1 times 1.1. So you do it three times right? 1.1 times 1.1 times 1.1. And then we multiply that by the 100 in present value. And we're gonna get a value of $133.10. So the $100 today? Uh compounded for three years at 10% interest will be worth $133.10 3 years from now. Cool. And that's because it earned interest of 10% each year. So the future value of the $100 today is 100 and $33.10 three years from now. Cool. So this is a very important equation here. Future value equals present value times one plus R. To the N. Power. Okay. This is your time value of money equation. Cool. Let's go ahead and do some practice problems before we continue on with this topic.