We're gonna talk about asset values and interest rates.

And so anyway, as we start this, let's just talk about interest rates.

What those are.

I have heard a 1,000,000 people, possibly less than a 1,000,000 people.

I've heard many people talk about interest rates, and here's what they like to say.

And you should not write this down because I'm gonna tell you something's wrong.

Here's what they say.

Interest rate price of money?

No, the interest rate is the price of credit.

What's the difference?

Well, first of all, what do we mean by the price of something we mean what you have to give up in order to get it right.

And so if we were talking about the price of money, the price of money is what you have to give up more to get it.

And you can give up your labor service is you could give up goods and service is product.

And so if we talk about the price of money, the price of money is expressed in terms of the goods and service.

Is we give up or what?

What we give up in order to get.

That really doesn't sound right.

That didn't sound like the interest rate credit is alone.

And so the interest rate, her interest, That's what we pay to get alone.

And it could be borrowed money.

But you know what?

If you borrow something else, some other merchandise, not money, then you still have to pay for the use of that something.

And technically, that would be interest.

Also, back in the old days, before there was money and never is commodity monies and things like this are just commodities.

People would borrow commodities and pay interest for that loan.

And nowadays we might use the term rent or something like that you might go to Well, anyway, you want to go too far down that path.

But people paid for the use of various commodities.

So anyway, alone refers to credit, and the interest rate is the price of credit and were eventually in this unit going to get around and talk about what determines that price and gets one.

And there will be a lot of details that go into it.

But prices in markets get determined by two things.

What are they supply and demand And so we're gonna talk about supply and demand for credit and then that will determine the price of credit, the interest rate.

And so anyway, we'll eventually get around to that.

There's different ways of thinking about why I shouldn't say that.

The price of credits, what it is.

But it plays various roles in our economy.

One is this is it is an incentive two people to postpone spending.

Okay, For example, you goto work, you earn 1000 bucks.

You got 1000 bucks.

What you gonna do with it?

I couldn't just go out and spend it.

Well, if somebody comes along and says, Hey, if you'll loan me that money, I'll give you interest.

And what they're really saying about that is don't spend that money.

Let me spend Let me use it and then I'll pay you back later and you can spend right on dso when we get interest.

The way we get that interest is we don't spend everything we have on.

We postpone our spending until later, and so interest gives us an incentive to do that.

And also, let's just say you're in $1000 you spend $1000 and you want to spend more.

You want to spend $2000 you have to go out and borrow, and then you have to pay interest.

And so when you go out and pay interest, you're saying, Oh, man, that hurts.

Maybe I ought not to spend.

Maybe I oughta wait.

And again, we're back to this idea of postponement spending, okay?

And so anyway, this is an important role that is played by interest in our economy.

Let's kind of shift gears.

We're gonna talk about interest.

Ah, lot in this, uh, this unit of material.

But it's kind of shift gears and start talking about something else that will have interest blended into the discussion future value.

Okay.

And this starts off kind of simple, kind of slow.

Suppose that you have p dollars today?

All put little dollar sign up there, P.

And that could just be any number.

It could be $10 a $1,000,000 whatever you want.

But let's say you had P dollars today, and then you put that in a bank account or you invested in a bond or something like this, and you just let it sit there And now those dollars set there and then you come back one year hints one year from today and you say, Hey, how much?

Don't have not account well f dollars.

And by the way, you'll see this all in a few minutes anyway.

But I'm using P and f these air just, you know, symbols like the Exxon.

Why?

But I'm using the P because we're talking about the present amount of money okay today and then f ah, future amount of money.

And so I'm using letters here rather than the number because we're just using generalized notation.

Whatever we talk about.

If this were $10 the discussions the same as if it's a 1,000,000.

The specific numbers work out differently.

So anyway, we're just using these symbols to represent a certain number of dollars in the present.

A certain number of dollars in the future.

So how much is this and answer as well.

I would get back my p dollars.

Of course.

You know, in the future I would have the original amount.

Plus, I'd have interest, right if I put this money in a bank account and then I go back a year from now I would get back my p dollars, and I would also get back whatever the interest rate is.

I'll use this interest rate percent, and we'll put it in decimals.

So, like if it's 5% 0.5 but anyway, so if I go back a year from now, how much would be in my account in the future of my original P dollars pause interest multiplied by that original P dollars.

And so, if we let that be 5% and let's say P dollars are $100 today, then I go back at the end of a year.

I'd have my original $100 plus 5% 50.5 times the $100 equals 100 plus five equals $105 nearby with me on that.

That's kind of simple, right?

And by the way, I could factor a little bit here, and then it would look like this.

My f dollars, How much I would have in the future equals p times one plus I not taking that dollar sign out of their just cause we don't need that forever.

Okay, Pretty straight forward.

Right.

Well, what if I go back in two years.

We've got a simple case there.

I went back one year from now.

What if I go back in two years?

I put down P dollars today and then I leave it there and then I get F dollars and I wait two years.

Well, then, here's how much is there.

It's my original P dollars.

And then for the first year, I got interest on that P dollars.

And then in the second year, I got interest on that P dollars again, Is that it?

Anybody can hear me out there.

Perhaps there's a glass wall here.

Is that it?

Interest on the interest.

So here's what happened.

Here's what would happen.

I put my dollar in my money there, toe work, and it stays there and it works for one year.

And here's when.

I would have $105 right?

But I don't collect it.

I just let it stay there.

And so in the second year, I should get interest not only on my original $100 but here's another five bucks.

And so here's the interest on the original $100 for year two year one, but also in year two up.

What year to here?

I get interest on the first years interest, right?

And this I, times P.

That was the $5.

And so now it's just interest on interest.

How much is 5% of $5?

Pardon me.

50 cents.

25 cents.

Right.

So that's not a lot.

Is it?

That extra 25 cents.

And so what would we have?

We would have $100 plus 5% of the hundreds.

$5 5% of 100.

This $5 and 5% of $55 is 25 cents.

And so then what would you have?

$110.25.

Except we don't have to keep doing it this way.

What I could do is do a little bit of factory, just as I did before.

And here's what I get P.

Times one plus race a little bit here.

Plus I p i p huh?

To I Okay, and then here's a P.

And in I square.

Well, that's a nice expression.

Now this is back where you remember in fourth grade in your sand.

Why do I have to do that learned to factor things because this can be simplified to p times.

I mean, the P isn't being simplified, but this thing right here is one plus I to the second power squared.

I don't know if you did that, but that's what I said.

Fourth grade.

Why do I have to be able to factor?

I'll never use that again.

No, just for the rest of my life.

Well, let's go back over here after one year, I put a one up there, but that was a woman up there, Pete.

Times one plus I to the first power after two years P times to the second power.

Well, guess what?

I could just write a more general formula.

And here's what it looks like if equals p my original amount of my office.

How much I get back in the future, By the way, I'm gonna put a little footnote that are, ah, sub script down here.

I'll say t t as in some point in the future sometime period.

Okay.

Equals my original amount of money.

Times one plus I.

This is the interest rate in decimals raised to the T power.

However many years I have to wait.

Now hear T is a sub script with the F and it's just telling us tea time.

How many years do I have to wait to get my money back?

And then this tea, Though it has a mathematical value, we are raising this one, plus I to a power.

And so if I put that money there and I wait 30 years, then this would be $100 times 1.5 There's my interest.

And then if I wait 30 years 30 is my ex opponent, okay.

However long you wait, that's how much will be there in that account.

I'm not gonna do this calculation.

I started it, but I want to do something else, not only get sidetracked here.

So this is our general formula.

The 1st 2 years, one year, two years, I kind of expanded that to kind of show you what a person would do.

We could have come back here and said, I wait three years and and add another I pee and then another interest on this interested in another years, we could do that, but this is just the general statement right here.

So if you invest some money in the present.

This is today how much you invest.

One is just one is the loneliest.

Number one is just the number one.

The eye is the interest rate that were earning or the rate of return we're earning in decimals.

Right?

And so then and T is how long that money is working for us.

Okay.

And so there's how much would show up in that account later on.

Now we did this.

I want to come back and talk about it just a little bit more moment ago.

This is 25 cents.

Remember, this is interest on interest.

What do you call that?

Compound interest?

Interest on interest is compound interest.

What?

We call this interest on the principal amount simple interested?

And so here's what we had.

We had $10.

This is with the two year investment.

We had $10 in simple interest.

We had 25 cents and compound interest.

And, you know, you could just I mean, a person could say Gosh, 25 cents.

Who cares?

Almost.

Who cares?

But here's the deal.

Compound interest matters not so much in two years and not so much and three.

But over the long term, it matters a lot.

I just mentioned 30 years.

Let's talk about 30 years for just a second.

Let's say that we just said, Well, compound interest is so small.

Let's ignore it and just leave it out of the story.

Let's say all we got with simple interested interest on our original $100.

How much would be there in 30 years?

Well, we'd have our original $100 right?

And then we'd have $5 an interest a year.

Simple interest on our principal.

Our original amount times 30 years.

So that would be $150 100 plus 152 150 bucks.

And so if we leave the compound interest off makes it a lot simpler, doesn't.