Simple Future Value – An Example

So what I'm going to do now is as I promised use examples to show you why that insight that a dollar today is worth more than a dollar tomorrow works. And we'll use the terminology we just introduced. FV, PV and so on. So let's do an example, and please stare at the screen. And I'm using PowerPoint, make your notes, this is very simple but let's do it together. Suppose a bank pays a 10% interest rate per year. And you are given a choice of two plans. The first plan is I give you $1,000 today. The second plan is, I'll give you $1,000 one year from now. Okay. So remember what the two choices are.

A is, I give you 1,000 at point zero. B is what? I give you 1,000 one year from now at point one. Let me again, I know I'm going to be painfully slow about this. So the question is which one would you prefer? And, in our example let's draw the time line. A is 0 1. A is 1,000 here.

B is where? If you draw the timeline for B.

For B, you're getting $1,000 here.

So it's a very simple example, but it is really powerful. Why? Because most people say a thousand versus thousand, who cares? The point is the key thing difference between them is, and I say this often in the class, never forget the passage of time. Because time has passed, and we have assumed what? That the interest rate is positive, that the time value of money is positive, because typically that's what we see in the real world. Again, complex issue, more complex than most people believe, but let's assume that's the case. It turns out that you will prefer plan A or B? Think about it and we'll do it together. But, I'm going to do it using the concept of future value.

You can do it using future value or you can do it present value. And we'll do it future value. So, think about it as I said. You can pause right now, but because it's so simple, I'm going to keep going. So what was the interest rate? 10% and what was the comparison between A and B? The key difference was the timing. So again let's see what happens. To make them comparable I'm going to carry this to the future. Remember, future value is here, present value is here. So I could either do present value comparables or do future value comparables. I think future values are actually easier to think about because you're thinking about real world investment, right.

So how much will this become? People say it'll become $1000

Plus you'll get something in addition to that which will depend on what? Two things, how much time has passed which is one period and how much interest rate are you making. Our interest rate was 10%. I'm using round numbers so that we are easy to talk about right? In real life the numbers will change but the concept won't. So what is 10% of 1000.

It turns out to be $100. So the total of plan A is $1100, which is greater than plan B, think. Look at my sign, greater than sign. I'm writing sideways. So, which one will you prefer? You will prefer A. Using the concept of future value. Let's take a little break, think about it, it's very simple but I'll do this, I'll take breaks and we come back and formalize this concept