WEBVTT

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Well now you've learned what I
think is quite possibly one of

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the most useful concepts in
life, and you might already be

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familiar with it, but if you're
not this will hopefully keep

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you from one day filing
for bankruptcy.

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So anyway, I will talk about
interest, and then simple

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versus compound interest.

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So what's interest?

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We all have heard of it.

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Interest rates, or interest
on your mortgage, or how

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much interest do I owe
on my credit card.

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So interest-- I don't know what
the actual formal definition,

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maybe I should look it up
on Wikipedia-- but it's

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essentially rent on money.

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So it's money that you pay
in order to keep money

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for some period of time.

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That's probably not the most
obvious definition, but

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let me put it this way.

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Let's say that I want to
borrow $100 from you.

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So this is now.

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And let's say that this
is one year from now.

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One year.

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And this is you,
and this is me.

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So now you give me $100.

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And then I have the $100
and a year goes by,

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and I have $100 here.

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And if I were to just give you
that $100 back, you would

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have collected no rent.

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You would have just
got your money back.

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You would have
collected no interest.

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But if you said, Sal I'm
willing to give you $100 now if

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you give me $110 a year later.

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So in this situation, how
much did I pay you to keep

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that $100 for a year?

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Well I'm paying you
$10 more, right?

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I'm returning the $100, and
I'm returning another $10.

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And so this extra $10 that I'm
returning to you is essentially

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the fee that I paid to be able
to keep that money and do

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whatever I wanted with that
money, and maybe save

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it, maybe invest it, do
whatever for a year.

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And that $10 is
essentially the interest.

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And a way that it's often
calculated is a percentage

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of the original amount
that I borrowed.

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And the original amount that I
borrowed in fancy banker or

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finance terminology is
just called principal.

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So in this case the rent on the
money or the interest was $10.

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And if I wanted to do it as a
percentage, I would say 10 over

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the principal-- over 100--
which is equal to 10%.

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So you might have said, hey Sal
I'm willing to lend you $100 if

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you pay me 10% interest on it.

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So 10% of $100 was $10, so
after a year I pay you

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$100, plus the 10%.

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And likewise.

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So for any amount of money, say
you're willing to lend me any

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amount of money for
a 10% interest.

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Well then if you were to lend
me $1,000, then the interest

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would be 10% of that,
which would be $100.

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So then after a year I would
owe you $1,000 plus 10% times

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$1,000, and that's
equal to $1,100.

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All right, I just added
a zero to everything.

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In this case $100 would
be the interest, but

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it would still be 10%.

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So let me now make a
distinction between simple

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interest and compound interest.

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So we just did a fairly simple
example where you lent money

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for me for a year at
10% percent, right?

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So let's say that someone were
to say that my interest rate

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that they charge-- or the
interest rate they charge to

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other people-- is-- well 10% is
a good number-- 10% per year.

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And let's say the principal
that I'm going to borrow

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from this person is $100.

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So my question to you-- and
maybe you want to pause it

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after I pose it-- is how
much do I owe in 10 years?

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How much do I owe in 10 years?

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So there's really two ways
of thinking about it.

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You could say, OK in years at
times zero-- like if I just

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borrowed the money, I just
paid it back immediately,

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it'd be $100, right?

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I'm not going to do that,
I'm going to keep it

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for at least a year.

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So after a year, just based on
the example that we just did, I

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could add 10% of that amount to
the $100, and I would

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then owe $110.

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And then after two years, I
could add another 10% of the

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original principal, right?

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So every year I'm
just adding $10.

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So in this case it would be
$120, and in year three,

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I would owe $130.

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Essentially my rent per year to
borrow this $100 is $10, right?

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Because I'm always taking
10% of the original amount.

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And after 10 years-- because
each year I would have had to

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pay an extra $10 in interest--
after 10 years I

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would owe $200.

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Right?

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And that $200 is equal to $100
of principal, plus $100 of

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interest, because I paid
$10 a year of interest.

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And this notion which I just
did here, this is actually

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called simple interest.

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Which is essentially you take
the original amount you

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borrowed, the interest rate,
the amount, the fee that you

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pay every year is the interest
rate times that original

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amount, and you just
incrementally pay

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that every year.

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But if you think about it,
you're actually paying a

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smaller and smaller percentage
of what you owe going

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into that year.

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And maybe when I show
you compound interest

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that will make sense.

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So this is one way to interpret
10% interest a year.

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Another way to interpret it is,
OK, so in year zero it's $100

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that you're borrowing, or if
they handed the money, you say

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oh no, no, I don't want it and
you just paid it back,

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you'd owe $100.

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After a year, you would
essentially pay the

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$100 plus 10% of $100,
right, which is $110.

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So that's $100,
plus 10% of $100.

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Let me switch colors,
because it's monotonous.

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Right, but I think this
make sense to you.

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And this is where simple
and compound interest

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starts to diverge.

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In the last situation we
just kept adding 10%

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of the original $100.

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In compound interest now,
we don't take 10% of

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the original amount.

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We now take 10% of this amount.

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So now we're going
to take $110.

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You can almost view it
as our new principal.

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This is how much we offer
a year, and then we

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would reborrow it.

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So now we're going to owe
$110 plus 10% times 110.

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You could actually undistribute
the 110 out, and that's

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equal to 110 times 110.

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Actually 110 times 1.1.

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And actually I could
rewrite it this way too.

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I could rewrite it as
100 times 1.1 squared,

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and that equals $121.

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And then in year two, this is
my new principal-- this is

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$121-- this is my
new principal.

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And now I have to in year
three-- so this is year two.

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I'm taking more space,
so this is year two.

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And now in year three, I'm
going to have to pay the $121

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that I owed at the end of year
two, plus 10% times the amount

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of money I owed going
into the year, $121.

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And so that's the same thing--
we could put parentheses around

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here-- so that's the same thing
as 1 times 121 plus 0.1 times

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121, so that's the same
thing as 1.1 times 121.

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Or another way of viewing it,
that's equal to our original

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principal times 1.1
to the third power.

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And if you keep doing this--
and I encourage you do it,

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because it'll really give you a
hands-on sense-- at the end of

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10 years, we will owe-- or you,
I forgot who's borrowing from

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whom-- $100 times 1.1
to the 10th power.

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And what does that equal?

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Let me get my spreadsheet out.

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Let me just pick a random cell.

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So plus 100 times 1.1
to the 10th power.

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So $259 and some change.

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So it might seem like a very
subtle distinction, but it ends

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up being a very big difference.

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When I compounded it 10% for
10 years using compound

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interest, I owe $259.

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When I did it using simple
interest, I only owe $200.

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So that $59 was kind of the
increment of how much more

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compound interest cost me.

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I'm about to run out of time,
so I'll do a couple more

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examples in the next video,
just you really get a deep

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understanding of how to do
compound interest, how the

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exponents work, and what
really is the difference.

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I'll see you in the next video.