Simple Future Value – A Formalization

We are talking about comparing things over time. And the first thing we need to understand is because time has value, you cannot compare time zero with time money directly.

Even in very sophisticated circles we approximate this all the time. That means we are violating the assumption that time has value. And this is not an assumption that's theoretical. It's actually very practical. So let's talk about the concept of future value, right? We used future values to show that plan a was better than plan b. So what is future value? Turns out, future value has two components. The first component is the initial payment. How much was it? The initial payment and writing again was $1,000. But at which point did you receive that, at .0. But future values being measured at which point, .1. So this initial payment can stay $1,000. And nothing changes, it's only if interest rates are zero.

But then to this initial amount for plan A, to compare it to plan B, which is already $1,000, but in which period? Period 2. So it doesn't have to be taken forward, right? You take plan A forward. The initial payment was 1,000 plus accumulated interest and we calculated it. Well, how much was that? 100 bucks. I'm not going to write out why 100. Because it's 10% of 1000. How is 10% chosen? As I said, I'm choosing round numbers so that we can move on and do numbers in our head. In real life, it'll be determined by what I said was competitive markets, and not by one person squeezing you. This happens, unfortunately, and that's why the field of microfinance emerged.

Sorry I take detours, but it is important to understand that competitive markets are crucial to having rates that are reasonable, right? So accumulated interest, 100, so the total becomes what? 1,100. Let's keep going with the formality of it a little bit. So let's write out the formula. So the future value, if you look the formula is right there, I will give you a sheet with formulas. But if you look it up, the future value has two components, many times people call it the amount or the principle. This was $1,000. And this was 10% of, and this sign by the way, the star is multiplication. This is multiplied by 1,000. How much did we get when we multiplied 10% by 1000?

We got 100 bucks. But you can write it as this. Notice, there's something common to the initial amount and the interest which is the initial amount, which we call P. So it turns out to be 1+r per taking multiplied by P because if you expand it, it becomes P + rP. Now this little guy is behind every finance textbook. It's called future Value factor. Writing again future,

Value, Factor.

And what do you think it is? It's simply the value of one buck, one dollar. How many periods from now? One period from now. So if you know the future value factor, and it's the value of one buck in the future, what do I need to figure out if it's $1,000 future value? I just multiply it by 1000. So this future value factor is an important thing which was printed behind text books, still is. Because we didn't used to have calculators, and it was very difficult to calculate very complex problems. Remember we are in a one period world, so the problem's extremely simple. I hope this is helpful to you.

When we come back in the next short clip, I'll show you how powerful future value can be and we will talk a little bit about it, okay?