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Before we dive into the really good stuff in this chapter and what is gonna be the majority of your test on this chapter, I just wanna talk about what the present value of money is actually talking about. So when we say, "Well, you gotta find the present value of a dollar," or, "You need to find the present value of this annuity," what in the world does that actually mean? Okay, so this is super fundamental if you're gonna even have a hope of understanding the rest of this chapter and trying to figure out how these problems actually work. So when someone says the present value of a dollar, that immediately tells you you're dealing with some time period.
We can say this is Year 0, and let's just call this Year 10. Let's make it extreme. Let's say that this is ten years. Now, if I say, which one is better, $1,000 today or $1,000 in ten years? I think most of us would agree $1,000 today is better. But what if I said, what's better, $1,000 today or $4,000 in ten years? Well, that starts to get a little bit trickier because mathematically it's hard to compare these two things because $1,000 today is way different than $4,000 in the future. You don't know which one of these is better because ten years is a long time.
Now, if you wanted to say which is better, $1,000 today or $4,000 today? Easy, $4,000. Which is better, $1,000 in ten years or $4,000 in ten years? Easy, $4,000. But the issue is you're trying to compare $1,000 today and $4,000 in ten years, and so you don't know how much this $1,000 could grow to. Could it grow to more than $4,000? If this $1,000, in ten years, could grow to $8,000, well, then we would say that $1,000 today is better than 4 in ten years. But what if this $1,000 in ten years could only grow to $3,000?
Well, then we would say that this $4,000 is better because it's more than $3,000. So the root of the issue is you cannot compare money from today with money from a year from now or even six months from now. And the reason is not inflation. We're not talking about will $4,000 buy me as many candy bars in ten years as $1,000 would buy me today. That's not really what we're talking about. Not in this chapter when we're dealing with businesses and investments and that sort of thing. What we're talking about is more this scenario. If I took $1,000 today and invested it wisely, how much would it grow to over ten years?
What would this final value be at the end of ten years? So we're not really talking about inflation as much as we are talking about rate of return or investment. And since we can't compare money in the present with money in the future, what we have to do is we have to either bring the present to the future or bring the future to the present. So what we do is this. We say which is better, $1,000 or $4,000? $1,000 today or $4,000 in ten years? Impossible to tell unless we bring this all the way back and say $4,000 in ten years is actually worth X amount today.
And then you can compare those just like you compare regular numbers. You just pick the biggest one. We could also say $1,000 today in ten years is gonna be worth some X number. And again, you can compare those two. So you have to get these into the same time period. You can't compare across time. It just unfortunately doesn't work. And the way that you do that, the way that you bring $1,000 forward or $4,000 backwards, is by using the present value or the future value of $1. So we can't compare these two unless we know, well, I can get a certain percentage return.
So when you know what percentage return you're able to get or what percentage return you require, you can calculate what $1,000 is gonna be in ten years, right? So let's bring that down to one year and say what's better, $1,000 now or $1,200 in one year?
So that's one year. This is Year 0. Is it better to get $1,000 or $1,200? And our percentage return that we require is 10%. So this tells me that the company is able to get 10% returns somewhere. Doesn't matter where. So the company is able to invest money now and get a 10% return in one year. So if they were to invest this $1,000 now, in one year they would have $1,100, right? 'Cause if you do $1,000 times 1.1, which is 110%, then after one year you get $1,100.
Okay, so we just brought this $1,000 into the future. Now let's bring this $1,200 into the past. If we say $1,200 divided by 110%, we're gonna get $1,091. 1,091. So if we bring this $1,200 into the past, we get $1,091. Now it's super easy to compare. This $1,200 is better. If we discounted it back at 10%, the present value of that $1,200 is $1,091. The future value of this $1,000, if we bring it forward, is $1,100.
So either way, if you wanna bring the $1,200 to the present or if you wanna take the $1,000 to the future, either way it's clear that this $1,200 is more money. So because our percentage return is 10%, the most we could make is this $1,100, and $1,200 is more. So it is better for us to take $1,200 in one year than it is to take $1,000 now. Simply because if we took $1,000 now, the best we would be able to do with it is $1,100, and $1,100 is worse than $1,200.
So that is what we're talking about when we talk about present value and future value of money. We're talking about what is your percentage return, and what would $1,000 be based on that percentage of return in a certain number of periods? And you have to bring the money to the same time period. I don't care if you bring it to the future or if you bring it to the present, but you can't compare across time periods. They have to be the same. So you can bring the $1,200 back or you can take the $1,000 forward. As long as you get them in the same time period, then it's just easy comparison which one's bigger.
We're gonna dive into way more depth than you probably want to on all of this stuff, but I want you to know right up front what this present value, future value stuff is all about, 'cause it doesn't often get explained what in the world it even is. It just gets explained how to do it. And if you don't know what it is, how to do it is quite hard to remember.