Let's have a look now, at the present value calculation.

So our formula for growth, our model for growth is that at time Pt in the future.

We're going to have the principle P0, times theta to the power t.

Now, that tells us how the future depends on the present value.

What we would like to do now, is make P0 the subject of the formula.

If we do that, we can restate this equation as P0 equals Pt,

times theta to the power minus t.

That's what happens if you go through and make P0 the subject of the formula.

And now this formula tells you how you can take a value in the future, Pt.

And discount it back to today's value.

How much is that worth now?

By multiplying through by theta to the power minus t.

Remember, theta is the constant proportional growth factor.

So, using this formula, we can see that $1500 in ten years time

in a 4% interest rate environment is going to be worth,

in today's money 1500 times 1 plus 0.04, that's 1.04,

that's the multiplier, if you've got 4% interest.

So that's our theta, and

now to the power of -10, because we're discounting it back, 10 time periods.

So that's how much it's worth in today's money.

If we work that out, again you can do that on your calculator or using a spreadsheet,

you're going to see that this equals $1,013, just a little bit over.

Now, $1,013 is worth more than $1,000 which was your alternative,

to get $1,000 today.

So a typical person, or a rational person would prefer the second

investment of $1500 received in ten years time,

because it's present value is greater than the $1000, the other option on offer.

And so, the great thing out of this simple, this straightforward

quantitative model for growth, the proportionate model for growth.

And it gives us a really simple discounting formula, and

discounting is one of the activities that businesses go through,

as they think about quantitative modeling.

because we'll often think about a value in the future and

make comparisons between objects at different points in time.

And we need to create a time baseline to do those comparisons, and

that's what the discounting is going to allow you to do.

To take a future value and bring it back to a current value, so

we can create a common baseline, typically to compare investments and do valuations.

So let me tell you of a couple places,

where you can see this idea of present value being used.