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Albert Einstein said that

compound interest may be

one of the most powerful forces

in the universe, true story.

Let's kind of look at why this is so

important in a little section I like

to call, the Time Value of Money.

What will $500 placed in an account

earning 3% interest be worth in five

years or in ten years for that matter?

How does that work?

Well in five years it's

going to be about $580, and

in ten years it's going to be about $672.

How do we get to those numbers, though?

Because that's not a straight forward

application of just x percent per

year times the number of years.

It's a little more complicated than that.

And that's what we're going to refer

to as the magic of compound interest.

Now why is that so much more?

Compound interest refers to the idea

that we put money somewhere and

the money is going to earn money, right?

So our interest earns interest, and

then that interest earns interest.

And you can see where this goes,

right, it become a very big effect.

In fact, mathematically we're going to

see that this is an exponential function.

The relationship then

between present value and

future value of a one time payment

is what we've just been exploring.

So, money today, right,

times 1 plus a growth rate,

which is going to be a decimal form,

raised to the power, right?

The number of years, and then that's

going to be equal to our money tomorrow.

So, that's what we

want to think about then.

That's that basic math function, that

we call the Future Value of a lump sum.

Now, this can work backwards too.

Say, I want to have $1,000 in five years,

and I can earn 5% on that money.

How much do I have to put in today?

So think of this as a goal

we're trying to reach, and

we need to operationalize that goal.

We need to figure out how

much I have to put in,

how much of that money I

have to defer to the future.

How do we get there?

Same math, right?

$783.53, now how did we get there?

We'll take a look, right, $1,000 divided

by 1.05, which was our interest rate,

right, 1 plus the interest rate

raised to the power of five,

because we said this was going to

be when we want to have that money.

So, the formula for that is the future

value divided by 1 plus the percent,

raised to the number of years.

Same equation, just manipulated

with a little bit of algebra.

So this works forwards and backwards

when we think of future values and

present values of one time dollar amounts.

So we have two key concepts that

we're introducing right now then.

The first is when we go forward.

When we take money today and

have it grow towards the future,

we refer to that as compounding, right?

So, in the first example we

started the presentation with,

we had compounding interest.

When we started with the future and

wanted to come back to the present,

that's discounting, right?

So, and either way we're talking

about this multiplier or

exponential effect of compound interest,

whether it's compounding to the future,

discounting back to today.

We're going to use those

terms a lot in this course.

So just want to make sure we're

very comfortable with them.

So, when something earns interest,

the interest earns interest.

This increases the value exponentially.

The fact that the interest was

earned means that it needs to

be factored into saying, what would that

have taken today to get to that point.

So right, again, in either case

compound interest may be

one of the most powerful forces

in the universe, true story.

Let's kind of look at why this is so

important in a little section I like

to call, the Time Value of Money.

What will $500 placed in an account

earning 3% interest be worth in five

years or in ten years for that matter?

How does that work?

Well in five years it's

going to be about $580, and

in ten years it's going to be about $672.

How do we get to those numbers, though?

Because that's not a straight forward

application of just x percent per

year times the number of years.

It's a little more complicated than that.

And that's what we're going to refer

to as the magic of compound interest.

Now why is that so much more?

Compound interest refers to the idea

that we put money somewhere and

the money is going to earn money, right?

So our interest earns interest, and

then that interest earns interest.

And you can see where this goes,

right, it become a very big effect.

In fact, mathematically we're going to

see that this is an exponential function.

The relationship then

between present value and

future value of a one time payment

is what we've just been exploring.

So, money today, right,

times 1 plus a growth rate,

which is going to be a decimal form,

raised to the power, right?

The number of years, and then that's

going to be equal to our money tomorrow.

So, that's what we

want to think about then.

That's that basic math function, that

we call the Future Value of a lump sum.

Now, this can work backwards too.

Say, I want to have $1,000 in five years,

and I can earn 5% on that money.

How much do I have to put in today?

So think of this as a goal

we're trying to reach, and

we need to operationalize that goal.

We need to figure out how

much I have to put in,

how much of that money I

have to defer to the future.

How do we get there?

Same math, right?

$783.53, now how did we get there?

We'll take a look, right, $1,000 divided

by 1.05, which was our interest rate,

right, 1 plus the interest rate

raised to the power of five,

because we said this was going to

be when we want to have that money.

So, the formula for that is the future

value divided by 1 plus the percent,

raised to the number of years.

Same equation, just manipulated

with a little bit of algebra.

So this works forwards and backwards

when we think of future values and

present values of one time dollar amounts.

So we have two key concepts that

we're introducing right now then.

The first is when we go forward.

When we take money today and

have it grow towards the future,

we refer to that as compounding, right?

So, in the first example we

started the presentation with,

we had compounding interest.

When we started with the future and

wanted to come back to the present,

that's discounting, right?

So, and either way we're talking

about this multiplier or

exponential effect of compound interest,

whether it's compounding to the future,

discounting back to today.

We're going to use those

terms a lot in this course.

So just want to make sure we're

very comfortable with them.

So, when something earns interest,

the interest earns interest.

This increases the value exponentially.

The fact that the interest was

earned means that it needs to

be factored into saying, what would that

have taken today to get to that point.

So right, again, in either case

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