We start with present value, what does that mean? Well, let's imagine we start with some kind of cashflow in the future. I might receive a thousand from the bank.

How far into the future though? Well, that's going to be denoted by N of the number of years. Let's say I'm going to receive 1000 in three years time. I'm now thinking if I'm going to receive some cash in the future, that probably means there's been some interest that I've earned along the way. Interest is denoted by I or sometimes R.

What I'd like to do is take that future amount of a thousand and strip out the three years of interest to work out how much I should have invested today to get that thousand. What I'm trying to do is to calculate the present value. There's a really simple equation to calculate that present value. The equation says your present value equals the future value times by 1 over 1 plus R, where R is your interest rate. So you can use I or R to show the interest rate, and we put that whole bracket to the power N, which is the number of years. Now, as I said earlier, the interest rate can be denoted by one of two things, I or R. And you may have seen it in both or either, depending on your previous studies.

It really depends where you're looking. Sometimes if you're looking on a computer, it can be R, but often when you look on a financial calculator, it can be I, we are going to use these terms interchangeably. Let's do a quick example. We've got a question. How much should be invested now at 8% to get 100 in 10 years time? Well, we need to fill in our diagram. We'll start off with the future value. The future value is 100.

Next, how many years is it going to be invested for? N that's going to be 10.

What's the interest rate I or R? Well, that's 8% In this example.

Now we have all our bits of information. We can drop them into the equation. So to get our present value, we start off with a hundred, the future value, and we times it by one over 1 plus I or R. That's 8% to the power N or 10 out pops. The present value and the present value is 46.3.

We're now going to go the other way. We're going to start with the present value and trying to get to a future value. So let's put our diagram together. I might be investing an amount today, maybe 10. I then have to ask myself, how long is it going to be invested for? And that will be N the number of years. Next, I need to ask myself what the interest rate or rate of return will be that's shown by I and sometimes R. If we can put those all together, this will get us our future value and now need an equation to get the future value. And that's a rearrangement of the previous equation. We looked at the present value equation. So here's our equation. The future value equals the present value times by 1 plus R to the power N.

And notice what's really different here is that previously we had a one over and so we were making the number smaller and now we don't have that 1 over. And so we're making the number bigger. This counts for the difference in terminology that you'll sometimes see where one is called discounting, making smaller, and the other is called compounding making bigger.

Now remember, I and R can be used interchangeably depending on where you're doing it, maybe on a computer versus a financial calculator.

So now let's go through a quick example. If we read the question, it says 100 is invested now at 8%. How much will it be worth in 10 years time? Let's take the bits of information from that question and put them into our diagram. Firstly, we've got the present value and the present value is a hundred. We then need to decide what value N is going to be. We're told it's going to be invested for 10 years.

What's the rate of return we're getting? What's the interest? Well, I or R in this case is 8%.

Now let's put all that information into the equation. The equation for future value starts off by saying 100 times one plus R. So that's one plus 8% in brackets all to the power N, which in this case is 10.

And this gets us our future value, which in this case is around 216. And just one more time, remember, I and R can be used interchangeably and you might see them on different places. For example, if you use a computer or a calculator.

In this pair of workouts, we're gonna explore the ideas of present value and future value.

You can see workout one is asking us for the present value I.e.value today of the below cashflow. And you can see the stacks up against workout two, which is asking for the opposite future value. And so workout one we could call discounting and workout two, we could call compounding. And this is kind of language you might see referring to these operations elsewhere.

Now let's start with workout one. The amount is 100 and this is a cashflow, and that cashflow is going to get received in 10 years. And we could call this N.

Then we've got the discount rate, and this is our rate of interest or our discount factor. You might see this called R or I, and we'll use those terms interchangeably. So we're being asked to put together the present value here. And what we do is we remember our equation and the equation goes cashflow times 1 over, and then careful with brackets one plus R to the power N.

And you know you are discounting properly and your brackets are good if you end up with a smaller number than the cash flow. And this makes sense because we're discounting the present value of that a hundred is lower than it seems, and that's because I could invest 38.6 in a bank account today at 10 percent and expect to receive a hundred in 10 years time.

Now that kind of logic is exactly what's being asked for in workout too. It's asking for the future value. And now instead of saying amount, it says investment amount. And that means that this is something we we're going to be perhaps putting in a bank account or other financial instrument today.

And we're being asked what would happen in 12 years time if the interest rate were 8%, where would that 900 end up? We are being asked for the fair value. And so again, remembering our equation, we take the cash flow and we multiply it, and then we remember our bracket and we say 1 plus R or I to the power N, and then we hit enter. And you can see again we're onto a good thing because we are compounding. So that number got bigger. We could expect to get 2,266 from our investment if we waited 12 years at 8%.