The rule of 72 for compound interest

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Language: en

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>>In the last video, we
talked a little bit about

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compounding interest, and
our example was interest

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that compounds annually, not continuously,

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like we would see in a lot of banks,

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but I really just wanted
to let you understand that

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although the idea is simple,

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every year, you get 10% of the money

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that you started off with that year,

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and it's called compounding
because the next year,

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you get money not just
on your initial deposit,

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but you also get money or
interest on the interest

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from previous years.

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That's why it's called
compounding interest.

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Although that idea is pretty simple,

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we saw that the math
can get a little tricky.

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If you have a reasonable calculator,

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you can solve for some of these things,

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if you know how to do it,

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but it's nearly impossible
to actually do it

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in your head.

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For example,

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at the end of the last video,

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we said, "Hey, if I have
$100 and if I'm compounding

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"at 10% a year," that's
where this 1 comes from,

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"how long does it take for
me to double my money?"

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and end up with this equation.

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To solve that equation,

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most calculators don't
have a log (base 1.1),

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and I have shown this in other videos.

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This, you could also say

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x = log (base 10) 2 / log (base 1.1) 2.

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This is another way to
calculate log (base 1.1) 2.

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I say this ...

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Sorry.

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This should be log (base 10) 1.1.

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I say this because most calculators have

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a log (base 10) function,

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and this and this are equivalent,

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and I have proven it in other videos.

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In order to say, "How long does it take

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"to double my money at 10% a year?"

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you'd have to put that in your calculator,

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and let's try it out.

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Let's try it out right here.

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We're going to have 2,

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and we're going to take
the logarithm of that.

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It's 0.3 divided by ...

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divided by ...

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... I'll open parenthesis
here just to be careful ...

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... divided by 1.1 and
the logarithm of that,

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and we close the parentheses,

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is equal to 7.27 years,
so roughly 7.3 years.

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This is roughly equal to 7.3 years.

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As we saw in the last video,

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this not necessarily trivial to set up,

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but even if you understand the math here,

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it's not easy to do this in your head.

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It's literally almost impossible
to do it in your head.

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What I will show you is a rule

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to approximate this question.

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How long does it take for
you to double your money?

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That rule,

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this is called the Rule of 72.

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Sometimes it's the Rule
of 70 or the Rule of 69,

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but Rule of 72 tends to
be the most typical one,

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especially when you're
talking about compounding

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over set periods of time,

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maybe not continuous compounding.

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Continuous compounding,

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you'll get closer to 69 or 70,

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but I'll show you what I mean in a second.

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To answer that same question,

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let's say I have 10% compounding annually,

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compounding, compounding annually,

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10% interest compounding annually,

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using the Rule of 72, I
say how long does it take

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for me to double my money?

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I literally take 72.

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I take 72.

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That's why it's called the Rule of 72.

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I divide it by the percentage.

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The percentage is 10.

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Its decimal position is 0.1,

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but it's 10 per 100 percentage.

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So 72 / 10, and I get 7.2.

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It was annual, so 7.2 years.

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If this was 10% compounding monthly,

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it would be 7.2 months.

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I got 7.2 years, which
is pretty darn close

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to what we got by doing
all of that fancy math.

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Similarly,

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let's say that I am compounding ...

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Let's do another problem.

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Let's say I'm compounding 6.

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Let's say 6% compounding annually,

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compounding annually, so like that.

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Well, using the Rule of 72,

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I just take 72 / 6, and I
get 6 goes into 72 12 times,

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so it will take 12 years
for me to double my money

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if I am getting 6% on my money

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compounding annually.

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Let's see if that works out.

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We learned last time the
other way to solve this

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would literally be we would say x.

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The answer to this should be close to log,

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log base anything really
of 2 divided by ...

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This is where we get the
doubling our money from.

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The 2 means 2x our money,

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divided by log base
whatever this is, 10 of,

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in this case, instead of
1.1, it's going to be 1.06.

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You can already see it's a
little bit more difficult.

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Get our calculator out.

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We have 2, log of that
divided by 1.06, log of that,

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is equal to 11.89, so about 11.9.

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When you do all the fancy math,

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we got 11.9.

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Once again, you see,

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this is a pretty good approximation,

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and this math, this math
is much, much, much simpler

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than this math.

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I think most of us can
do this in our heads.

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This is actually a good
way to impress people.

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Just to get a better sense of how good

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this number 72 is,

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what I did is I plotted on a spreadsheet.

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I said, OK, here is the
different interest rates.

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This is the actual time
it would take to double.

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I'm actually using this formula right here

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to figure out the actual,
the precise amount of time

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it will take to double.

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Let's say this is in years,

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if we're compounding annually,

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so if you get 1%,

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it will take you 70 years
to double your money.

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At 25%, it will only take
you a little over three years

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to double your money.

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This is the actual, this is the correct,

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this is the correct,

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and I'll do this in blue,

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this is the correct number right here.

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This is actual right there.

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That right there is the actual.

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I plotted it here too.

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If you look at the blue line,

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that's the actual.

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I didn't plot all of them.

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I think I started at maybe 4%.

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If you look at 4%,

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it takes you 17.6 years
to double your money.

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So 4%, it takes 17.6 years
to double your money.

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That's that dot right there on the blue.

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At 5%, it takes you,

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at 5%, it takes you 14
years to double your money.

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This is also giving you an appreciation

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that every percentage really does matter

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when you're talking about
compounding interest.

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When it takes 2%,

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it takes you 35 years
to double your money.

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1% takes you 70 years,

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so you double your money twice as fast.

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It really is really important,

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especially if you're thinking about

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doubling your money, or
even tripling your money,

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for that matter.

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Now, in red,

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in red over here,

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I said what does the Rule of 72 predict?

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This is what the Rule ...

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So if you just take 72
and divide it by 1%,

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you get 72.

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If you take 72 / 4, you get 18.

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Rule of 72 says it will take you 18 years

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to double your money
at a 4% interest rate,

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when the actual answer is 17.7 years,

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so it's pretty close.

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That's what's in red right there.

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That's what's in red right there.

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You can see, so I have plotted it here,

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the curves are pretty close.

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For low interest rates,

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for low interest rates,

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so that's these interest rates over here,

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the Rule of 72,

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the Rule of 72 slightly,

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slightly overestimates
how long it will take

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to double your money.

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As you get to higher interest rates,

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it slightly underestimates
how long it will take you

00:07:51.998 --> 00:07:53.668
to double your money.

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Just if you had to think about,

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"Gee, is 72 really the best number?"

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this is what I did.

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If you just take the interest
rate and you multiply it

00:08:01.691 --> 00:08:03.962
by the actual doubling time,

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and here, you get a bunch of numbers.

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For low interest rates, 69 works good.

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For very high interest
rates, 78 works good.

00:08:09.994 --> 00:08:11.001
But if you look at this,

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72 looks like a pretty good approximation.

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You can see it took us
pretty well all the way from

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when I graphed here,
4% all the way to 25%,

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which is most of the
interest rates most of us

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are going to deal with
for most of our lives.

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Hopefully, you found that useful.

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It's a very easy way
to figure out how fast

00:08:28.963 --> 00:08:30.000
it's going to take you
to double your money.

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Let's do one more just for fun.

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I have a, I don't know, a 4 ...

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well, I already did that.

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Let's say I have a 9% annual compounding.

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How long does it take me for me

00:08:44.433 --> 00:08:46.028
to double my money?

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Well, 72 / 9 = 8 years.

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It will take me 8 years
to double my money.

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The actual answer, if this is using ...

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This is the approximate
answer using the Rule of 72

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The actual answer, 9% is 8.04 years.

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Once again, in our
head, we were able to do

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a very, very, very good approximation.


Traditional IRAs

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Language: en

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What I want to do in this video

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is talk a little bit
about traditional IRAs.

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IRA stands for Individual
Retirement Account.

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Individual

00:00:16.003 --> 00:00:20.830
Retirement

00:00:20.830 --> 00:00:22.270
Account.

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The focus on this video
is the traditional IRA.

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You'll hear of other types of IRAs,

00:00:28.164 --> 00:00:30.671
especially Roth IRA and SEP IRAs.

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This is only on Traditional.

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The just of all of them,

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is really it's the governments way

00:00:35.871 --> 00:00:39.603
of encouraging you to
save for your retirement.

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They all have slightly different details,

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so I'm just going to focus
on the traditional right now.

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Let's say we are in year 0.

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That's right now.

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Instead of year 0, let
me write "right now."

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You have 2 options.

00:00:55.536 --> 00:00:59.471
You could take advantage
of the traditional IRA.

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This is the IRA scenario.

00:01:02.537 --> 00:01:07.537
This is the no IRA scenario.

00:01:07.537 --> 00:01:09.622
Now, an IRA allows you

00:01:09.622 --> 00:01:14.072
to put up to a certain
amount of your income aside.

00:01:14.072 --> 00:01:16.536
Depending on your age and what year it is,

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that amount will change.

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In 2010 that number is $5,000

00:01:24.737 --> 00:01:27.137
if you are under the age of 50.

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For under 50.

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It's $6,000 ...

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This is for an individual,

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not for a family.

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It's $6,000 if you're over the age of 50.

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Over age of 50.

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I guess the rational was probably,

00:01:47.205 --> 00:01:48.620
"Gee, if you're over the age of 50,"

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"you better save even
more for your retirement,"

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"which might only be 10 or 15 years away."

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They gave a little bit more
lead way for over the age of 50.

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Let's say we're under the age of 50

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and we take full advantage of this IRA.

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We set aside $5,000.

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$5,000.

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Here we set aside nothing.

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Set aside nothing.

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In the very short term,

00:02:14.872 --> 00:02:18.804
the advantage is that
this $5,000 of our income

00:02:18.804 --> 00:02:21.071
will not be taxed.

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Let's say that my tax bracket ...

00:02:24.404 --> 00:02:27.537
Let's say that I'm in a 32% tax bracket.

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32% tax bracket.

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Let me write that on the side.

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It will apply to both scenarios.

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32% tax bracket today.

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I'm making some good money.

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Tax bracket today.

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On the $5,000 only,

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I'm only talking about
the taxes on the $5,000.

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You're going to have to pay taxes above

00:02:50.005 --> 00:02:51.403
and beyond that on the
rest of your income.

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Today, I'm going to pay
0 taxes on that $5,000.

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0 taxes on the $5,000.

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If I don't set aside
that $5,000 into an IRA,

00:03:06.938 --> 00:03:10.787
then I will have to pay
taxes on that $5,000.

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I'm going to have to pay $5,000 x 32%.

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Which is equal to what?

00:03:19.804 --> 00:03:23.138
I'll just get a calculator out.

00:03:23.138 --> 00:03:32.621
You get 5,000 x .32 = $1,600 in taxes,

00:03:32.621 --> 00:03:42.705
I'm going to pay $1,600 in taxes today.

00:03:42.705 --> 00:03:46.072
In the year that I
actually made that $5,000.

00:03:46.072 --> 00:03:49.774
I can't set aside $5,000
if I made less than $5,000.

00:03:49.774 --> 00:03:52.204
It's always the lower of your income

00:03:52.204 --> 00:03:55.137
or these IRA limits.

00:03:55.137 --> 00:03:57.454
Of course, you're going to
pay, even in this situation.

00:03:57.454 --> 00:03:59.706
Let's say you made $100,000.

00:03:59.706 --> 00:04:01.472
When you put the $5,000 aside,

00:04:01.472 --> 00:04:04.704
you're still going to have
to pay taxes on $95,000.

00:04:04.704 --> 00:04:07.806
In this situation, where you
didn't put the $5,000 aside,

00:04:07.806 --> 00:04:10.455
you're going to have to
pay taxes on $100,000.

00:04:10.455 --> 00:04:13.454
You're going to have to pay
taxes on the extra $5,000,

00:04:13.454 --> 00:04:15.955
which is $1,600.

00:04:15.955 --> 00:04:20.954
Let's say in either
situation, with that $5,000,

00:04:20.954 --> 00:04:25.202
you want to buy and sell some securities

00:04:25.202 --> 00:04:28.864
or some investments.

00:04:28.864 --> 00:04:32.005
Let's say right after you
put in the IRA account …

00:04:32.005 --> 00:04:34.121
Now everything is sitting
in our IRA account.

00:04:34.121 --> 00:04:35.621
All of our transactions are sitting

00:04:35.621 --> 00:04:38.371
in this special IRA account right here,

00:04:38.371 --> 00:04:41.071
where we can actually
buy and sell investments

00:04:41.071 --> 00:04:42.136
and trade them.

00:04:42.136 --> 00:04:44.070
But, we can't cash them in

00:04:44.070 --> 00:04:45.405
and turn them into cash

00:04:45.405 --> 00:04:47.870
and then spend it on a new
car or something like that.

00:04:47.870 --> 00:04:49.071
If we did do that,

00:04:49.071 --> 00:04:52.373
before the age of 59 1/2, we
would have to pay a penalty.

00:04:52.373 --> 00:04:53.108
Let me write that down.

00:04:53.108 --> 00:04:53.856
You might immediately say,

00:04:53.856 --> 00:04:54.939
"Hey gee, this is a good idea."

00:04:54.939 --> 00:04:57.736
"Why doesn't everyone always do it?"

00:04:57.736 --> 00:05:01.372
The answer is, if I pull
it out before 59 1/2,

00:05:01.372 --> 00:05:03.004
I pay a penalty.

00:05:03.004 --> 00:05:04.005
Let me write this down,

00:05:04.005 --> 00:05:06.070
because that's important to keep in mind.

00:05:06.070 --> 00:05:22.672
Pay penalty and taxes if
withdrawn before 59 1/2.

00:05:22.672 --> 00:05:25.705
Once again, this is the Traditional IRA.

00:05:25.705 --> 00:05:27.136
The Roth IRA, for example,

00:05:27.136 --> 00:05:29.004
is a little bit more flexible on the

00:05:29.004 --> 00:05:32.204
actual principle amount that
you put into the account.

00:05:32.204 --> 00:05:33.138
We're just dealing with Traditional.

00:05:33.138 --> 00:05:34.623
This is an important
thing to keep in mind.

00:05:34.623 --> 00:05:37.138
This is kind of the
tradeoff that you're giving.

00:05:37.138 --> 00:05:38.072
The government is saying,

00:05:38.072 --> 00:05:38.737
"Hey, I'm giving you an
incentive to put this aside"

00:05:38.737 --> 00:05:42.738
"and I really want to make
sure that you leave this aside"

00:05:42.738 --> 00:05:44.621
"until you are ready to retire."

00:05:44.621 --> 00:05:46.703
"You don't get tempted, when
you see a nice sports car,"

00:05:46.703 --> 00:05:48.538
"to cash in your IRA and use it,"

00:05:48.538 --> 00:05:51.558
"because you're going to
have to pay a penalty."

00:05:51.558 --> 00:05:53.371
As long as you don't actually withdraw it

00:05:53.371 --> 00:05:54.288
and turn it into cash,

00:05:54.288 --> 00:05:58.371
you can actually buy and sell
securities within that IRA.

00:05:58.371 --> 00:06:01.804
Let's say, as soon as you put that $5,000,

00:06:01.804 --> 00:06:11.737
you buy $5,000 of stock A.

00:06:11.737 --> 00:06:14.372
Here, we don't have $5,000 anymore.

00:06:14.372 --> 00:06:18.005
We only have $3,400 of
our original amount,

00:06:18.005 --> 00:06:26.121
so we buy $3,400 of stock A.

00:06:26.121 --> 00:06:30.826
Let's say, I don't know,
10 years in the future.

00:06:30.826 --> 00:06:33.805
Let's say in 10 years ...

00:06:33.805 --> 00:06:36.024
This is going to be in either situation.

00:06:36.024 --> 00:06:41.602
In 10 years, let's say
that stock A has doubled,

00:06:41.602 --> 00:06:43.013
and you sell it.

00:06:43.013 --> 00:06:44.181
Now, you sell it.

00:06:44.181 --> 00:06:46.602
You have $10,000 here.

00:06:46.602 --> 00:06:52.470
You have $10,000 from sale of A.

00:06:52.470 --> 00:06:53.263
It's doubled.

00:06:53.263 --> 00:06:54.136
Here's it's doubled,

00:06:54.136 --> 00:06:56.597
but you only have $3,400 of stock A.

00:06:56.597 --> 00:07:01.015
Now, that $3,400 is worth $6,800.

00:07:01.015 --> 00:07:08.536
You have $6,800 from sale of A.

00:07:08.536 --> 00:07:12.765
Let's say you want to put
that into another stock.

00:07:12.765 --> 00:07:14.799
Let's say you put that all into stock B.

00:07:14.799 --> 00:07:16.604
I'm painting a very rosy picture.

00:07:16.604 --> 00:07:18.432
You can't always insure
that stocks will double.

00:07:18.432 --> 00:07:21.602
You buy $10,0000 in this situation.

00:07:21.602 --> 00:07:26.347
$10,000 of B.

00:07:26.347 --> 00:07:27.801
I'll hold off there.

00:07:27.801 --> 00:07:29.347
You buy $10,000 of B.

00:07:29.347 --> 00:07:30.136
Here you might say,

00:07:30.136 --> 00:07:32.266
"Oh, I'm going to buy $6,800 of B.

00:07:32.266 --> 00:07:36.932
Because you are not operating
within an IRA account,

00:07:36.932 --> 00:07:40.763
you're going to have to pay
taxes on the capital gains

00:07:40.763 --> 00:07:42.335
from this right here.

00:07:42.335 --> 00:07:46.765
Capital gains are gains made
from capital investments.

00:07:46.765 --> 00:07:50.347
In this case the capital
investment is investing in stocks.

00:07:50.347 --> 00:07:53.347
Since you owned your stock
for more that 1 year,

00:07:53.347 --> 00:07:56.469
you at least will only have to
pay long-term capital gains,

00:07:56.469 --> 00:07:59.847
which tends to be lower than
short-term capital gains.

00:07:59.847 --> 00:08:05.468
In this situation you
made a $3,400 profit.

00:08:05.468 --> 00:08:07.347
Not $340,000.

00:08:07.347 --> 00:08:11.347
You made $3,400 profit.

00:08:11.347 --> 00:08:14.802
You are going to have to
pay 15% capital gains.

00:08:14.802 --> 00:08:19.272
x 15%.

00:08:19.272 --> 00:08:24.097
Let's get the calculator out again.

00:08:24.097 --> 00:08:31.265
3,400 x .15 = $510.

00:08:31.265 --> 00:08:33.603
You're going to have to pay $510.

00:08:33.603 --> 00:08:35.682
This is $510.

00:08:35.682 --> 00:08:37.004
You take your $6,800,

00:08:37.004 --> 00:08:40.137
pay $510 to the IRS.

00:08:40.137 --> 00:08:49.682
You are going to be left with $6,290.

00:08:49.682 --> 00:08:51.535
Remember, the reason why
you have to pay taxes is

00:08:51.535 --> 00:08:53.932
this is not operating inside of an IRA.

00:08:53.932 --> 00:08:55.682
Here you are operating inside of an IRA,

00:08:55.682 --> 00:08:57.735
so you don't have to pay taxes.

00:08:57.735 --> 00:08:59.535
Let's say you invest in stock B

00:08:59.535 --> 00:09:00.932
and then over the next 10 years,

00:09:00.932 --> 00:09:03.070
stock B also doubles.

00:09:03.070 --> 00:09:06.098
Stock ... so this is 10 years.

00:09:06.098 --> 00:09:11.205
Stock B is now worth
$20,000 and you sell it.

00:09:11.205 --> 00:09:16.603
From sell of B.

00:09:16.603 --> 00:09:19.402
Once again, it's sitting
inside of your IRA,

00:09:19.402 --> 00:09:23.265
so you don't have to pay
any capital gains on it.

00:09:23.265 --> 00:09:26.849
In this situation, you use that $6,290

00:09:26.849 --> 00:09:29.202
to also invest in stock B,

00:09:29.202 --> 00:09:34.802
and after 10 years stock B doubles.

00:09:34.802 --> 00:09:35.748
It is now …

00:09:35.748 --> 00:09:36.515
What is that?

00:09:36.515 --> 00:09:40.137
$12,580.

00:09:40.137 --> 00:09:42.469
Once again, it's sitting
outside of your IRA.

00:09:42.469 --> 00:09:45.599
You have to pay 15% capital gains.

00:09:45.599 --> 00:09:49.433
You had a $6,290 gain.

00:09:49.433 --> 00:09:55.349
$6,290 gain x 15%.

00:09:55.349 --> 00:09:57.599
Let's see what that is.

00:09:57.599 --> 00:09:59.131
I'll get the calculator.

00:09:59.131 --> 00:09:59.870
Where's my calculator?

00:09:59.870 --> 00:10:01.871
There is it.

00:10:01.871 --> 00:10:08.469
You have $6,290 x 15%.

00:10:08.469 --> 00:10:10.016
That's equal to 943.

00:10:10.016 --> 00:10:14.017
Let me take that from my 12,580.

00:10:14.017 --> 00:10:23.348
12,580 - 943.5 is equal to ...

00:10:23.348 --> 00:10:26.598
I have $11,636.

00:10:26.598 --> 00:10:33.683
I now have $11,636.

00:10:33.683 --> 00:10:35.181
Let's say 20 years have past.

00:10:35.181 --> 00:10:37.598
We are now over the age of 59 1/2.

00:10:37.598 --> 00:10:42.433
We can now withdraw from our IRA.

00:10:42.433 --> 00:10:45.203
Of course, this situation,
this is cash that we have.

00:10:45.203 --> 00:10:46.468
We can do anything with it.

00:10:46.468 --> 00:10:48.004
Maybe we're now over 60 years old.

00:10:48.004 --> 00:10:49.869
This could be used for our retirement,

00:10:49.869 --> 00:10:51.536
for our everyday expenses.

00:10:51.536 --> 00:10:53.183
This money that was sitting in IRA,

00:10:53.183 --> 00:10:55.849
now that we're over the age of 60,

00:10:55.849 --> 00:10:59.137
we're over 60 now, or over 59 1/2

00:10:59.137 --> 00:11:00.766
if you want to be particular.

00:11:00.766 --> 00:11:02.015
Now that we're over 60

00:11:02.015 --> 00:11:05.469
we can withdraw the IRA
without paying any penalty,

00:11:05.469 --> 00:11:09.008
but we will have to pay taxes.

00:11:09.008 --> 00:11:12.737
We're going to withdraw.

00:11:12.737 --> 00:11:14.099
No penalties.

00:11:14.099 --> 00:11:15.870
We will have to pay taxes,

00:11:15.870 --> 00:11:17.203
but the huge advantage here is,

00:11:17.203 --> 00:11:20.469
once we're over 60, we're
probably earning less money.

00:11:20.469 --> 00:11:22.536
The actual tax bracket that we're in

00:11:22.536 --> 00:11:24.603
is probably going to be lower.

00:11:24.603 --> 00:11:28.349
Let's say we're in a 25% tax bracket.

00:11:28.349 --> 00:11:31.868
Remember, when we first made that $5,000

00:11:31.868 --> 00:11:33.765
we were in a 32% tax bracket,

00:11:33.765 --> 00:11:36.098
because we were this young gun

00:11:36.098 --> 00:11:37.802
at the peak of his or her career,

00:11:37.802 --> 00:11:39.433
making a lot of money.

00:11:39.433 --> 00:11:40.764
Now, we're making less money.

00:11:40.764 --> 00:11:42.470
We're trying to live off of our savings,

00:11:42.470 --> 00:11:45.099
so we have to pay 25% income tax on it.

00:11:45.099 --> 00:11:47.671
If we pay 25% on $20,000 ...

00:11:47.671 --> 00:11:49.349
Remember, now we're
actually withdrawing it.

00:11:49.349 --> 00:11:50.684
We're actually putting it
in our checking account

00:11:50.684 --> 00:11:51.937
so we can spend it for living

00:11:51.937 --> 00:11:54.469
or whatever we want to do with it.

00:11:54.469 --> 00:12:01.357
25% of $20,00 is equal to $5,000 in taxes.

00:12:01.357 --> 00:12:07.805
We will be left with $15,000

00:12:07.805 --> 00:12:11.070
to do anything that we want with it.

00:12:11.070 --> 00:12:11.689
Compare this.

00:12:11.689 --> 00:12:16.022
This is $15,000 verses $11,636.

00:12:16.022 --> 00:12:19.003
Everything that we did
was completely identical,

00:12:19.003 --> 00:12:24.106
except for, over here we took the $5,000

00:12:24.106 --> 00:12:26.071
and invested within an IRA.

00:12:26.071 --> 00:12:28.022
Here, we took the $5,000,

00:12:28.022 --> 00:12:29.939
we had to pay taxes on it.

00:12:29.939 --> 00:12:32.440
Then, we invested it
in the exact same way.

00:12:32.440 --> 00:12:34.938
We actually made very
good stock investments

00:12:34.938 --> 00:12:36.468
in both situations

00:12:36.468 --> 00:12:39.773
and we ended up with a
significant less amount of money.

00:12:39.773 --> 00:12:43.274
This is $15,000 verses $11,000.

00:12:43.274 --> 00:12:44.736
That's almost … What is that?

00:12:44.736 --> 00:12:45.940
30 something % difference

00:12:45.940 --> 00:12:47.607
in the total amount of money you have.

00:12:47.607 --> 00:12:48.605
Not only that,

00:12:48.605 --> 00:12:51.606
but this tax we had to pay,

00:12:51.606 --> 00:12:53.067
we don't have to pay this …

00:12:53.067 --> 00:12:55.204
this is only in situations
where you have a 25% tax rate.

00:12:55.204 --> 00:12:56.357
When you're retired you might even

00:12:56.357 --> 00:12:58.271
have a lower tax rate than that

00:12:58.271 --> 00:12:59.773
and it's deferred a good bit.

00:12:59.773 --> 00:13:01.689
The real thing to think about is just,

00:13:01.689 --> 00:13:04.669
20 years in the future
you're sitting on $15,000

00:13:04.669 --> 00:13:07.071
verses if you didn't
participate it in the IRA

00:13:07.071 --> 00:13:11.136
you're sitting on only
a little over $11,500.

00:13:11.136 --> 00:13:13.803
Of course, the main trade off here is

00:13:13.803 --> 00:13:16.080
that in the IRA situation,

00:13:16.080 --> 00:13:17.773
you really couldn't touch your money.

00:13:17.773 --> 00:13:18.772
If you had an emergency

00:13:18.772 --> 00:13:20.536
and you had to withdraw the money,

00:13:20.536 --> 00:13:24.000
you would have had to pay penalties on it.


Unemployment rate primer

WEBVTT
Kind: captions
Language: en

00:00:00.647 --> 00:00:02.861
Voiceover: What I want to do in this
video is think a little bit about

00:00:02.861 --> 00:00:07.176
how the unemployment
rate is actually computed

00:00:07.176 --> 00:00:10.009
by the Bureau of Labor Statistics.

00:00:10.009 --> 00:00:14.330
So to figure that out let's just start
off with the entire U.S. population.

00:00:14.330 --> 00:00:17.597
So let me draw a big
circle here that represents

00:00:17.597 --> 00:00:20.264
the entire U.S. population.

00:00:20.264 --> 00:00:26.402
U.S. population and right now
if my numbers are correct,

00:00:26.402 --> 00:00:31.931
the latest numbers are 304 million people.

00:00:31.931 --> 00:00:37.403
Now, not all of those 304 million
people are capable of working,

00:00:37.403 --> 00:00:42.263
including my two and a half year
old son or my newborn daughter

00:00:42.263 --> 00:00:44.485
so you have to think of, when
you think about unemployment,

00:00:44.485 --> 00:00:46.735
you want to think about the
percentage of these people

00:00:46.735 --> 00:00:48.998
that are actually old enough to work.

00:00:48.998 --> 00:00:51.664
That actually can be
employed theoretically.

00:00:51.664 --> 00:00:54.402
So let's take a subset
of that U.S. population

00:00:54.402 --> 00:00:58.197
and let's think about who's essentially
an adult, who's working age.

00:00:58.197 --> 00:01:04.402
So this subset right over
here is 16 years and older,

00:01:04.402 --> 00:01:08.320
so people who can legally work
and the numbers I have here

00:01:08.320 --> 00:01:10.331
is that this is 100-

00:01:10.331 --> 00:01:14.736
sorry, this right here
is 237 million people.

00:01:14.736 --> 00:01:17.736
237 million people.

00:01:17.736 --> 00:01:21.184
Now we can't just say all of
these people could possibly work

00:01:21.184 --> 00:01:24.518
because a lot of them are in college,
some of them are in high school,

00:01:24.518 --> 00:01:27.117
some of them might not
have the ability to work,

00:01:27.117 --> 00:01:28.678
some of them might be retired.

00:01:28.678 --> 00:01:31.261
So what we want to do is take
a subset of this population,

00:01:31.261 --> 00:01:37.517
that is essentially part of the
labor force in that they are working

00:01:37.517 --> 00:01:40.316
or they are actively looking for work.

00:01:40.316 --> 00:01:43.785
So let me draw that right over here.

00:01:43.785 --> 00:01:48.183
So this right over here
is the labor force.

00:01:48.183 --> 00:01:52.678
Labor force, so these are not
retirees or people who are in college.

00:01:52.678 --> 00:01:55.052
Those people would be sitting
right over there assuming

00:01:55.052 --> 00:01:56.718
they're 16 years or older.

00:01:56.718 --> 00:02:01.011
The labor force, so this is working or-

00:02:01.011 --> 00:02:04.116
or I should say working and
actively looking for work,

00:02:04.116 --> 00:02:07.344
and we'll think about what
actively looking for work means

00:02:07.344 --> 00:02:09.583
in a little bit more
depth in a few minutes.

00:02:09.583 --> 00:02:15.260
Actively looking for work.

00:02:15.260 --> 00:02:19.860
And that number if my numbers are
correct is right around 154 million

00:02:19.860 --> 00:02:21.260
although the numbers
here aren't so important,

00:02:21.260 --> 00:02:24.666
the more important thing is
how the unemployment rate

00:02:24.666 --> 00:02:26.335
itself is calculated.

00:02:26.335 --> 00:02:29.335
And so then within the labor
force you have a subset,

00:02:29.335 --> 00:02:32.860
so this is working and actively
looking for work, so you have a subset

00:02:32.860 --> 00:02:37.260
of the labor force that is
actively looking for work.

00:02:37.260 --> 00:02:40.002
So they don't have a job but
they're actively looking.

00:02:40.002 --> 00:02:49.198
So this right here is
unemployed and actively looking.

00:02:49.198 --> 00:02:51.948
Actively looking and this
actively looking is probably

00:02:51.948 --> 00:02:55.395
more important than you
might realize at first.

00:02:55.395 --> 00:02:57.794
And this number, let's just
say for the sake of argument,

00:02:57.794 --> 00:03:00.735
this is sitting at
around 15 million people.

00:03:00.735 --> 00:03:02.085
15 million people.

00:03:02.085 --> 00:03:05.498
So if you have a job
you're right over here,

00:03:05.498 --> 00:03:08.308
if you don't have a job
but are actively looking

00:03:08.308 --> 00:03:10.390
you're going to be right over here.

00:03:10.390 --> 00:03:15.122
What we're going to see in a little
bit is if you don't have a job

00:03:15.122 --> 00:03:18.123
but you are not actively looking
but you could be working,

00:03:18.123 --> 00:03:20.922
you would actually be sitting out here.

00:03:20.922 --> 00:03:22.807
This is going to be
interesting when we think about

00:03:22.807 --> 00:03:26.057
trends in the unemployment
rate when it goes up or down.

00:03:26.057 --> 00:03:28.456
But just to see how the
unemployment rate is calculated,

00:03:28.456 --> 00:03:30.391
let's just do it for this example.

00:03:30.391 --> 00:03:32.390
So the unemployment rate-

00:03:32.390 --> 00:03:42.474
unemployment rate is literally
just the number of unemployed

00:03:42.474 --> 00:03:45.224
over the entire labor force.

00:03:45.224 --> 00:03:49.322
So in this situation
it would be 15 million-

00:03:49.322 --> 00:03:52.457
so that's just the number of
unemployed and actively looking

00:03:52.457 --> 00:03:54.922
over the entire labor force.

00:03:54.922 --> 00:04:02.063
Over 154 million and so if
we get my handy TI-85 out,

00:04:02.063 --> 00:04:05.390
that gives us in this
example right over here,

00:04:05.390 --> 00:04:11.657
an unemployment rate of
15 divided by 154 million.

00:04:11.657 --> 00:04:17.722
So it's about 9.7, if we write
it as a decimal it's 0.097,

00:04:17.722 --> 00:04:22.256
if we write it as a percentage
this would be 9.7 percent.

00:04:22.256 --> 00:04:28.323
This is approximately 9.7 percent.

00:04:28.323 --> 00:04:31.475
Now I told you that the details
are going to be important

00:04:31.475 --> 00:04:34.308
and the reason why they are is
because interesting things happen

00:04:34.308 --> 00:04:38.891
when people stop looking for work
or when they start looking for work.

00:04:38.891 --> 00:04:43.590
So I said unemployed and actively looking
puts you in this bucket over here.

00:04:43.590 --> 00:04:44.989
If you're unemployed,
if you don't have a job,

00:04:44.989 --> 00:04:48.989
and you're not actively looking you're
actually not in the labor force.

00:04:48.989 --> 00:04:51.657
And so you might be saying,
"Sal, what does it mean

00:04:51.657 --> 00:04:54.257
"to be actively looking for work?"

00:04:54.257 --> 00:04:57.722
And this means that you've looked for
a job or you are actively searching

00:04:57.722 --> 00:05:03.856
in the past, let me do this in a
new color, in the past four weeks.

00:05:03.856 --> 00:05:06.260
Past four weeks.

00:05:06.260 --> 00:05:11.677
And you might say, "Sal, how do they
know whether these 15 million people

00:05:11.677 --> 00:05:16.427
"have actively searched for
jobs in the past four weeks?"

00:05:16.427 --> 00:05:17.657
And the answer is they do a survey.

00:05:17.657 --> 00:05:20.791
They're not going to survey every
human being in the labor force

00:05:20.791 --> 00:05:24.262
or the U.S. population or all
15 million that are unemployed,

00:05:24.262 --> 00:05:26.094
that would be logistically impossible.

00:05:26.094 --> 00:05:28.456
What they do is they do a
survey and right now they do

00:05:28.456 --> 00:05:32.522
about 60,000 people every month
and they essentially ask them

00:05:32.522 --> 00:05:35.594
are you employed, are you
unemployed, if you are unemployed

00:05:35.594 --> 00:05:38.927
have you looked for a job
in the past four weeks?

00:05:38.927 --> 00:05:41.011
If you have looked for a
job in the past four weeks

00:05:41.011 --> 00:05:44.093
as an unemployed person you get
thrown into this bucket right here,

00:05:44.093 --> 00:05:45.191
you're actively looking.

00:05:45.191 --> 00:05:47.011
You're still part of the labor force.

00:05:47.011 --> 00:05:51.011
But if you've gotten so discouraged
that you're no longer looking for work,

00:05:51.011 --> 00:05:58.655
maybe you've given up, then you
get thrown out of the labor force.

00:05:58.655 --> 00:06:01.390
And that is what most
people don't realize.

00:06:01.390 --> 00:06:03.989
If things get bad enough and
people get really discouraged,

00:06:03.989 --> 00:06:10.122
you have people actually
exiting the entire labor force.

00:06:10.122 --> 00:06:11.855
To see how that affects the numbers,

00:06:11.855 --> 00:06:13.057
imagine a situation.

00:06:13.057 --> 00:06:14.855
So this is the unemployment
rate right now.

00:06:14.855 --> 00:06:17.723
There's 15 million
people who are unemployed

00:06:17.723 --> 00:06:19.512
and actively looking for work.

00:06:19.512 --> 00:06:22.992
Let's say that this is just a
horrible recession or depression

00:06:22.992 --> 00:06:26.791
and five million of these
people get so discouraged

00:06:26.791 --> 00:06:31.456
they don't, in the last four weeks,
they do not look for work anymore.

00:06:31.456 --> 00:06:34.724
So they maybe even stop altogether
or they want to take a break.

00:06:34.724 --> 00:06:37.593
So what we're going to do is we're
going to take five million people

00:06:37.593 --> 00:06:40.057
out of this bucket over here.

00:06:40.057 --> 00:06:42.791
So we're going to take five
million people and move them

00:06:42.791 --> 00:06:46.989
out over here, outside of the labor force.

00:06:46.989 --> 00:06:49.057
If you did that, what happens?

00:06:49.057 --> 00:06:54.593
Well now the official unemployed
number is now going to be 10 million,

00:06:54.593 --> 00:06:56.722
it's now going to be 10 million.

00:06:56.722 --> 00:06:58.456
And what's the labor force number?

00:06:58.456 --> 00:07:01.927
Remember they went completely out
of this green circle over here.

00:07:01.927 --> 00:07:04.011
So they've also left the labor force.

00:07:04.011 --> 00:07:08.454
So the labor force number
is now 149 million.

00:07:08.454 --> 00:07:13.124
So in this bad situation where
people have left the labor force

00:07:13.124 --> 00:07:16.103
the unemployment rate would
now be 10 million people

00:07:16.103 --> 00:07:19.854
unemployed and actively looking
for work over a labor force

00:07:19.854 --> 00:07:25.354
of 149 million, the labor force has
shrunk because they're so discouraged.

00:07:25.354 --> 00:07:27.454
So what do we get there
as our unemployment rate?

00:07:27.454 --> 00:07:36.271
We have 10 divided by 149,
it gives us 6.7 percent.

00:07:36.271 --> 00:07:38.854
So this is fascinating.

00:07:38.854 --> 00:07:43.021
If things get bad enough and people
actually exit the labor force,

00:07:43.021 --> 00:07:48.388
then the unemployment rate could go down
because the labor force is shrinking.

00:07:48.388 --> 00:07:51.653
The other thing could also happen,
maybe things get really good,

00:07:51.653 --> 00:07:55.269
maybe things get really good
and you have 10 million people

00:07:55.269 --> 00:08:01.022
who are sitting out here, they're
either marginally attached workers

00:08:01.022 --> 00:08:04.455
which are people who are hoping
to get a job but haven't looked

00:08:04.455 --> 00:08:07.271
for a job in the past four weeks,
or they could be discouraged workers

00:08:07.271 --> 00:08:09.388
who have altogether, they
wouldn't mind working,

00:08:09.388 --> 00:08:12.187
but they've given up altogether
looking, but you can imagine it

00:08:12.187 --> 00:08:16.021
when the economy gets good, let's say
we're starting from this baseline here,

00:08:16.021 --> 00:08:19.521
when the economy gets good and all
of these people who are unemployed

00:08:19.521 --> 00:08:24.124
but not part of the labor force all
of a sudden start looking for work.

00:08:24.124 --> 00:08:27.189
So then they'd be part of
the official unemployed.

00:08:27.189 --> 00:08:30.187
So this 10 million would
grow to 20 million,

00:08:30.187 --> 00:08:33.322
20 million so now this
number is 20 million

00:08:33.322 --> 00:08:36.272
and this green area would
go up by 10 million.

00:08:36.272 --> 00:08:38.791
So now this would be 159 million.

00:08:38.791 --> 00:08:43.389
So in this situation, the official
unemployed would be 20 million,

00:08:43.389 --> 00:08:47.355
and the entire labor force
would be 159 million,

00:08:47.355 --> 00:08:50.122
and now you would get a situation-

00:08:50.122 --> 00:08:55.188
so you have 20 divided by 159 million,

00:08:55.188 --> 00:08:58.271
which is 12.6 percent.

00:08:58.271 --> 00:09:01.925
12.6 percent, approximately 12.6 percent.

00:09:01.925 --> 00:09:05.353
So the whole point of this video, I'm
not saying that the unemployment rate,

00:09:05.353 --> 00:09:08.603
the way it's calculated is wrong or
that's it supposed to be misleading,

00:09:08.603 --> 00:09:12.055
I just want to give you a little
bit of nuance that it doesn't always

00:09:12.055 --> 00:09:15.124
give the complete picture, in
particular that one number,

00:09:15.124 --> 00:09:18.937
and there's other unemployment rates
that give a little bit more nuance here,

00:09:18.937 --> 00:09:22.655
but this one headline unemployment rate
that is typically given on the news

00:09:22.655 --> 00:09:24.456
doesn't capture the whole story.

00:09:24.456 --> 00:09:28.861
In particular it doesn't
capture the people who might
be exiting the labor force

00:09:28.861 --> 00:09:32.260
when things are bad, so in that
situation the unemployment rate

00:09:32.260 --> 00:09:35.394
would probably be understating
how bad things are,

00:09:35.394 --> 00:09:38.745
and it also doesn't capture the people
who are entering the labor force,

00:09:38.745 --> 00:09:41.728
and that situation the unemployment
rate would probably make things

00:09:41.728 --> 00:09:46.000
look worse than they are when
things might actually be improving.


What it means to buy a company's stock

WEBVTT
Kind: captions
Language: en

00:00:00.475 --> 00:00:02.273
Voiceover: Let's talk a
little bit about what it means

00:00:02.273 --> 00:00:06.068
to own shares or stock in a company,

00:00:06.068 --> 00:00:07.812
so shares or stock.

00:00:07.812 --> 00:00:09.405
I think we all have a general sense,

00:00:09.405 --> 00:00:10.352
but what I want to do in this video

00:00:10.352 --> 00:00:11.669
is make it a little bit more tangible

00:00:11.669 --> 00:00:14.102
to really understand
exactly what you're buying

00:00:14.102 --> 00:00:16.809
when you buy a share of stock.

00:00:16.809 --> 00:00:17.956
So the general sense,

00:00:17.956 --> 00:00:19.951
and this is exactly what it really is,

00:00:19.951 --> 00:00:22.136
is when you buy stock or you buy shares,

00:00:22.136 --> 00:00:23.952
you're essentially becoming a partial

00:00:23.952 --> 00:00:26.470
or a part owner of the company.

00:00:26.470 --> 00:00:31.254
Part owner of company.

00:00:31.254 --> 00:00:33.543
Just to contrast this with bonds

00:00:33.543 --> 00:00:35.597
because they're often kind of used

00:00:35.597 --> 00:00:36.874
in the same phrasing,

00:00:36.874 --> 00:00:38.697
"Oh, I'm gonna go buy
some stocks or bonds,"

00:00:38.697 --> 00:00:40.258
or "I deal with stocks and bonds."

00:00:40.258 --> 00:00:41.722
Bonds.

00:00:42.430 --> 00:00:46.877
Bonds, you become part
lender to the company.

00:00:46.877 --> 00:00:53.425
Part lender to the company.

00:00:53.425 --> 00:00:57.945
So, for example, if you buy a,

00:00:57.945 --> 00:01:00.743
well, I'll just say a face value bond

00:01:00.743 --> 00:01:03.214
of, let's say, it's $10.

00:01:03.214 --> 00:01:04.597
Let's say it's $1,000,

00:01:04.597 --> 00:01:06.546
and there's 1,000 people who do that.

00:01:06.546 --> 00:01:10.089
Each of you all are lending
$1,000 to the company

00:01:10.089 --> 00:01:11.803
and since there's 1,000 of you,

00:01:11.803 --> 00:01:14.009
you're lending $1 million to the company.

00:01:14.009 --> 00:01:15.348
I'm not going to go into detail in that

00:01:15.348 --> 00:01:17.844
because the focus of this
is going to be stock,

00:01:17.844 --> 00:01:19.014
but it's good to keep in mind

00:01:19.014 --> 00:01:20.490
that they're very different things.

00:01:20.490 --> 00:01:22.097
Here, you're owning the company.

00:01:22.097 --> 00:01:23.946
Here, you're lending to the company.

00:01:23.946 --> 00:01:26.099
So just to make this a
little bit more tangible

00:01:26.099 --> 00:01:27.803
of exactly what we're owning,

00:01:27.803 --> 00:01:29.348
let me draw a simple balance sheet

00:01:29.348 --> 00:01:31.347
for some company X.

00:01:31.347 --> 00:01:33.101
So this is Company ...

00:01:33.101 --> 00:01:35.471
Let me do a new color.

00:01:35.471 --> 00:01:41.764
Let's say we're dealing
with Company X right here,

00:01:41.764 --> 00:01:44.269
and let's say if we looked
at Company X's assets,

00:01:44.269 --> 00:01:45.404
and when we talk about assets,

00:01:45.404 --> 00:01:47.345
it really is the same thing that we mean

00:01:47.345 --> 00:01:48.919
in the real world, or in our everyday life

00:01:48.919 --> 00:01:50.144
when we talk about assets.

00:01:50.144 --> 00:01:51.650
The things that have value.

00:01:51.650 --> 00:01:53.255
Things that are going to give us

00:01:53.255 --> 00:01:54.838
some type of future benefit.

00:01:54.838 --> 00:01:56.392
A house is an asset because it gives us

00:01:56.392 --> 00:01:58.450
the future benefit of
being able to live in it

00:01:58.450 --> 00:02:01.184
and protecting us from
cold weather and rain.

00:02:01.184 --> 00:02:03.485
Cars are assets because they give,

00:02:03.485 --> 00:02:05.320
provide us some transportation.

00:02:05.320 --> 00:02:07.864
Cash is an asset because
it can be exchanged

00:02:07.864 --> 00:02:09.661
for things we need in the future.

00:02:09.661 --> 00:02:10.303
All of these ...

00:02:10.303 --> 00:02:12.896
A loan to someone else is an asset

00:02:12.896 --> 00:02:13.943
because in the future,

00:02:13.943 --> 00:02:15.319
they will pay us back.

00:02:15.319 --> 00:02:17.060
A loan to me is a liability,

00:02:17.060 --> 00:02:18.394
which we'll talk about in a second,

00:02:18.394 --> 00:02:21.591
but anyway, let's just in
the very abstract sense,

00:02:21.591 --> 00:02:24.013
say this is Company X's assets.

00:02:24.013 --> 00:02:27.390
Let's say that they're worth $100 million.

00:02:28.143 --> 00:02:30.841
$100 million,

00:02:30.841 --> 00:02:32.233
and I'm not going to go into exactly

00:02:32.233 --> 00:02:33.520
how this number is determined

00:02:33.520 --> 00:02:34.653
or who's determining it,

00:02:34.653 --> 00:02:36.386
or who's saying this is 100 million,

00:02:36.386 --> 00:02:37.869
but let's just say this is,

00:02:37.869 --> 00:02:39.790
we agree that this is how much their land

00:02:39.790 --> 00:02:42.154
and their patents and their copyrights

00:02:42.154 --> 00:02:46.024
and their cash and their buildings

00:02:46.024 --> 00:02:47.724
and everything else they have is worth.

00:02:47.724 --> 00:02:50.154
All of the things that
will generate future value.

00:02:50.154 --> 00:02:51.165
Now, let's say that Company X

00:02:51.165 --> 00:02:53.500
has also borrowed some money,

00:02:53.500 --> 00:02:55.924
and maybe they borrowed
it by issuing bonds,

00:02:55.924 --> 00:02:58.072
which I will not go into detail on.

00:02:58.072 --> 00:03:00.451
Let's say they borrowed some money,

00:03:00.451 --> 00:03:03.862
and so they owe some people collectively

00:03:03.862 --> 00:03:05.919
$80 million.

00:03:05.919 --> 00:03:07.522
$80 million.

00:03:07.522 --> 00:03:10.534
This could have been a straight debt

00:03:10.534 --> 00:03:11.185
from a bank,

00:03:11.185 --> 00:03:12.952
or this could have been via a bond issue.

00:03:12.952 --> 00:03:14.837
They might have issued,

00:03:14.837 --> 00:03:16.807
maybe they issued a million bonds,

00:03:16.807 --> 00:03:18.727
where each of those essentially represent

00:03:18.727 --> 00:03:20.901
a debt of $80.

00:03:20.901 --> 00:03:22.063
I won't go into that too much,

00:03:22.063 --> 00:03:23.318
but I think you get
the idea of what I mean

00:03:23.318 --> 00:03:24.479
of part lender,

00:03:24.479 --> 00:03:25.475
but this is debt.

00:03:25.475 --> 00:03:28.071
$80 million of debt right here.

00:03:28.071 --> 00:03:29.818
Let's say that's all of their liabilities.

00:03:29.818 --> 00:03:32.452
There are other liabilities
other than debt,

00:03:33.343 --> 00:03:34.527
but for simplicity,

00:03:34.527 --> 00:03:36.567
let's say that's their only liability

00:03:36.567 --> 00:03:38.787
and debt tends to be the biggest.

00:03:38.787 --> 00:03:41.410
Now, what's left for the owners?

00:03:41.410 --> 00:03:44.333
A good way to think about that is

00:03:44.333 --> 00:03:47.043
what would happen if
this company were sold

00:03:47.043 --> 00:03:48.413
and the debt paid off.

00:03:48.413 --> 00:03:49.612
So, if the company were sold

00:03:49.612 --> 00:03:51.813
and these assets really
are able to be sold

00:03:51.813 --> 00:03:53.490
for $100 million,

00:03:53.490 --> 00:03:55.014
you get $100 million.

00:03:55.014 --> 00:03:56.989
You'd have to pay the debt holders,

00:03:56.989 --> 00:03:58.728
you'd have to pay off the debt first,

00:03:58.728 --> 00:04:00.687
so you'd have 100 minus 80,

00:04:00.687 --> 00:04:03.790
you'd have $20 million
left for the owners.

00:04:03.790 --> 00:04:05.682
I'll do that in this other green color.

00:04:05.682 --> 00:04:08.499
So you'd have $20 million left.

00:04:08.499 --> 00:04:10.418
$20 million left,

00:04:10.418 --> 00:04:11.590
and this is called the equity,

00:04:11.590 --> 00:04:13.662
or the owner's equity.

00:04:13.662 --> 00:04:18.396
Owner's equity.

00:04:18.396 --> 00:04:20.072
This is completely the same idea

00:04:20.072 --> 00:04:22.273
as when people talk about
having equity in a house.

00:04:22.273 --> 00:04:24.652
If I have a $300,000 house,

00:04:24.652 --> 00:04:28.063
and I still have $200,000
left on the mortgage,

00:04:28.063 --> 00:04:30.585
then I have $100,000 in equity.

00:04:30.585 --> 00:04:32.065
It's completely analogous.

00:04:32.065 --> 00:04:34.588
You can see, very simply, that assets.

00:04:34.588 --> 00:04:35.323
I'll write this down.

00:04:35.323 --> 00:04:36.424
You're getting a little bit of

00:04:36.424 --> 00:04:38.470
an introduction to accounting right here,

00:04:38.470 --> 00:04:42.274
but assets are going to
always be equal to liabilities

00:04:42.274 --> 00:04:44.320
plus equity.

00:04:44.320 --> 00:04:46.519
Because essentially, or
you can view it this way:

00:04:46.519 --> 00:04:48.553
If you subtract liabilities
from both sides,

00:04:48.553 --> 00:04:51.801
assets minus liabilities
is equal to equity.

00:04:51.801 --> 00:04:53.657
This might be a little bit more intuitive.

00:04:53.657 --> 00:04:56.203
What we have leftover
is always what we own

00:04:56.203 --> 00:04:57.523
minus what we owe.

00:04:57.523 --> 00:04:59.811
That is what the owners have.

00:04:59.811 --> 00:05:03.132
Now, when we say that I'm
part-owner of a company,

00:05:03.132 --> 00:05:06.888
that means that I have a
piece of this pie right here.

00:05:06.888 --> 00:05:10.324
This is what I am a
part-owner of, the equity.

00:05:10.324 --> 00:05:12.998
So, for example, if we have,

00:05:12.998 --> 00:05:14.560
if there are 2 million shares,

00:05:14.560 --> 00:05:20.941
so Company X, let's say
they have 2 million shares,

00:05:20.941 --> 00:05:22.815
and let's say that the equity

00:05:22.815 --> 00:05:25.330
is really worth $20 million.

00:05:25.330 --> 00:05:26.660
How much is each share worth

00:05:26.660 --> 00:05:28.733
if we believe all of these numbers?

00:05:28.733 --> 00:05:30.946
Well, we have $20 million of equity,

00:05:30.946 --> 00:05:40.393
20 million of equity
divided by 2 million shares,

00:05:40.393 --> 00:05:42.648
divided by 2 million shares,

00:05:42.648 --> 00:05:51.899
which gets us $10 of equity per share.

00:05:51.899 --> 00:05:53.922
If we believe all of these numbers,

00:05:53.922 --> 00:05:57.119
and we know that Company
X has 2 million shares,

00:05:57.119 --> 00:05:59.793
then we would say that
each share is worth $10,

00:05:59.793 --> 00:06:00.897
and if we like these numbers

00:06:00.897 --> 00:06:02.768
and if someone is willing
to sell us a share

00:06:02.768 --> 00:06:04.595
for less than that, we would buy it.

00:06:04.595 --> 00:06:06.989
If someone was willing
to pay more than that,

00:06:06.989 --> 00:06:08.244
maybe we would sell it.

00:06:08.244 --> 00:06:11.071
Just to make all of this a
little bit more tangible,

00:06:11.071 --> 00:06:12.858
let's look at an actual
example of a company

00:06:12.858 --> 00:06:15.599
to show you that I'm not
making all of this stuff up.

00:06:15.599 --> 00:06:18.459
I got this off of your
traditional financial sources.

00:06:18.459 --> 00:06:19.927
This is actually from the filings

00:06:19.927 --> 00:06:21.816
of this unnamed company,

00:06:21.816 --> 00:06:23.145
and you'll get extra bonus points

00:06:23.145 --> 00:06:24.653
if you figure out what this company is,

00:06:24.653 --> 00:06:27.174
and this is their actual
stock-trading activity,

00:06:27.174 --> 00:06:29.161
and I just want to draw the same diagram

00:06:29.161 --> 00:06:30.742
that I drew up here,

00:06:30.742 --> 00:06:33.086
the same diagram that I drew up here,

00:06:33.086 --> 00:06:34.588
to really, on this company,

00:06:34.588 --> 00:06:35.922
so you can kind of see that this

00:06:35.922 --> 00:06:37.530
actually happens in the real world,

00:06:37.530 --> 00:06:40.585
so first let's draw their assets.

00:06:40.585 --> 00:06:42.819
Let's say this is Company X,

00:06:42.819 --> 00:06:45.989
and let's say these are
its assets right there.

00:06:45.989 --> 00:06:47.213
Its assets.

00:06:47.213 --> 00:06:48.921
Let's go to its balance sheet.

00:06:48.921 --> 00:06:50.383
This is actually what they reported.

00:06:50.383 --> 00:06:52.144
This is June 30th,

00:06:53.174 --> 00:06:56.209
well, we want to take
the more recent date.

00:06:56.209 --> 00:06:57.533
They're just trying to compare to

00:06:57.533 --> 00:06:59.852
what they had before.

00:06:59.852 --> 00:07:01.590
Let's look at these,

00:07:01.590 --> 00:07:02.924
this is some time ago,

00:07:02.924 --> 00:07:03.655
but it doesn't matter.

00:07:03.655 --> 00:07:04.326
We're learning.

00:07:04.326 --> 00:07:05.354
This is, we're not trying to decide

00:07:05.354 --> 00:07:07.072
whether we want to
invest in this right now.

00:07:07.072 --> 00:07:09.041
This is a very old financial statement,

00:07:09.041 --> 00:07:11.452
but let's just look at
what they're saying.

00:07:11.452 --> 00:07:13.324
They have our total assets here.

00:07:13.324 --> 00:07:15.806
30 million, I'll just do in round numbers.

00:07:15.806 --> 00:07:18.049
$30 million right there,

00:07:18.049 --> 00:07:20.794
so $30 million.

00:07:20.794 --> 00:07:21.823
You might be curious about,

00:07:21.823 --> 00:07:23.879
"Hey, what's all this
current asset business?"

00:07:24.078 --> 00:07:26.794
Those are things that are either cash

00:07:26.794 --> 00:07:28.474
or that can be turned into cash

00:07:28.474 --> 00:07:29.708
within the next year.

00:07:29.708 --> 00:07:31.996
So, for example, accounts receivable.

00:07:31.996 --> 00:07:35.070
That's money that other
maybe vendors owe them,

00:07:35.070 --> 00:07:36.302
that they're going to pay very soon.

00:07:36.302 --> 00:07:38.730
Inventories, these are
things that they have

00:07:38.730 --> 00:07:40.206
maybe in the warehouse that they can sell

00:07:40.206 --> 00:07:41.703
and turn into cash very quickly.

00:07:41.703 --> 00:07:44.133
Other current assets, maybe that's stock

00:07:44.133 --> 00:07:46.210
or some other type of
investment that they could sell

00:07:46.210 --> 00:07:47.393
and turn into cash.

00:07:47.393 --> 00:07:50.484
So they have 18 million of current assets,

00:07:50.484 --> 00:07:52.919
that's things that they can
turn into cash very easily

00:07:52.919 --> 00:07:53.629
and very quickly,

00:07:53.629 --> 00:07:56.126
definitely within the next year.

00:07:56.126 --> 00:07:57.887
Then you have some property,
plant and equipment.

00:07:57.887 --> 00:08:02.600
this is kind of that land
and buildings and machinery

00:08:02.600 --> 00:08:03.405
that I talked about,

00:08:03.405 --> 00:08:05.123
and then who knows what
these other assets are.

00:08:05.123 --> 00:08:07.391
Maybe those are trademarks or patents,

00:08:07.391 --> 00:08:08.736
or who knows what they are?

00:08:08.736 --> 00:08:12.099
But all in all, they have
$30 million of assets.

00:08:12.099 --> 00:08:13.573
Now let's go to the liabilities.

00:08:13.573 --> 00:08:16.857
They have some current liabilities,

00:08:16.857 --> 00:08:18.294
16 million.

00:08:18.294 --> 00:08:19.727
Current liabilities, just so you know,

00:08:19.727 --> 00:08:20.828
those are liabilities.

00:08:20.828 --> 00:08:22.953
These are things that
they have to pay in cash

00:08:22.953 --> 00:08:23.843
within the next year.

00:08:23.843 --> 00:08:26.061
It could be debt, it could be payables.

00:08:26.061 --> 00:08:27.725
They have to pay some other vendors.

00:08:27.725 --> 00:08:28.885
Who knows what it is?

00:08:28.885 --> 00:08:31.277
But you can kind of view
it as debt on some level,

00:08:31.277 --> 00:08:33.282
maybe debt that you have
to pay in the next year.

00:08:33.282 --> 00:08:37.220
Then the have long-term
debt of 5.5 million.

00:08:37.220 --> 00:08:38.680
If you add these two up,

00:08:38.680 --> 00:08:42.475
you get pretty close to about 22 million,

00:08:42.475 --> 00:08:46.793
so just for simplicity, I'll
put it over here as 22 million.

00:08:46.793 --> 00:08:52.281
So this company has 22
million in liabilities.

00:08:52.281 --> 00:08:57.284
22 million liabilities.

00:08:57.284 --> 00:08:58.532
These are their assets,

00:08:58.532 --> 00:09:00.469
just to get all the labeling right.

00:09:00.469 --> 00:09:01.731
So what's left for equity?

00:09:01.731 --> 00:09:04.397
We'll just draw it on this simple diagram.

00:09:04.397 --> 00:09:08.225
We have 8 million left for equity.

00:09:08.225 --> 00:09:09.326
8 million left for equity,

00:09:09.326 --> 00:09:11.397
and actually, they did the
calculation here for us.

00:09:11.397 --> 00:09:16.760
The exact number is 8.39
or 8.4 million in equity,

00:09:16.760 --> 00:09:18.529
but this is a nice round
number for us to show.

00:09:18.529 --> 00:09:21.421
This is real-world stuff
that we're dealing with,

00:09:21.421 --> 00:09:23.009
and if you wanted to know, kind of,

00:09:23.009 --> 00:09:24.529
if you believe these numbers,

00:09:24.529 --> 00:09:26.489
if you believe that this company's assets

00:09:26.489 --> 00:09:29.062
really are worth $30 million,

00:09:29.062 --> 00:09:30.525
what should you pay for it?

00:09:30.525 --> 00:09:31.865
Well, then you're going to divide by

00:09:31.865 --> 00:09:33.565
the total number of shares,

00:09:33.565 --> 00:09:35.471
and you'll see this in
some financial statements,

00:09:35.471 --> 00:09:36.813
and I won't go into the details

00:09:36.813 --> 00:09:38.727
of the difference between
basic and diluted,

00:09:38.727 --> 00:09:40.815
but the numbers are very, very close,

00:09:40.815 --> 00:09:43.414
so we don't have to
worry about it too much.

00:09:43.414 --> 00:09:47.057
But let's just say that
this company has 2.7,

00:09:47.057 --> 00:09:51.330
looks like 2.78 million shares.

00:09:51.330 --> 00:09:54.733
So if the book value is 8.396.

00:09:54.733 --> 00:09:56.257
I mean, I wrote 8 here,

00:09:56.257 --> 00:09:58.329
how much should each of these shares,

00:09:58.329 --> 00:09:59.723
how much should each of these,

00:09:59.723 --> 00:10:00.726
and when I say book value,

00:10:00.726 --> 00:10:02.727
I mean these are their books.

00:10:02.727 --> 00:10:04.326
According to their books,

00:10:04.326 --> 00:10:06.987
the equity is worth 8.4 million.

00:10:06.987 --> 00:10:10.468
If we really believe that the
equity's worth 8.4 million,

00:10:10.468 --> 00:10:12.605
how much should each share be worth?

00:10:12.605 --> 00:10:16.474
Well, we'll just divide 8.4 million,

00:10:16.474 --> 00:10:19.464
we'll just have to divide 8.4 million,

00:10:19.464 --> 00:10:20.808
8.4 million.

00:10:20.808 --> 00:10:22.725
This is actually an 8.4.

00:10:22.725 --> 00:10:23.966
I wrote 8 there for simpicity.

00:10:23.966 --> 00:10:27.727
Divided by the number
of shares, 2.78 million.

00:10:27.727 --> 00:10:30.009
So that's a million, and that's a million,

00:10:30.009 --> 00:10:34.664
and I'll get a calculator
out for this one right here.

00:10:34.664 --> 00:10:41.859
So, let's see, we're
here doing 8.4 million

00:10:41.859 --> 00:10:46.476
divided by 2.78 million shares.

00:10:46.476 --> 00:10:47.067
So according,

00:10:47.067 --> 00:10:50.056
if we believe these numbers,
if we believe the books,

00:10:50.056 --> 00:10:51.724
the book value of the shares is about

00:10:51.724 --> 00:10:55.327
$3.02 per share,

00:10:55.327 --> 00:11:02.407
so this is $3.02 per share,

00:11:02.407 --> 00:11:04.221
book value per share.

00:11:04.221 --> 00:11:06.470
That's what we should be
willing to pay for this,

00:11:06.470 --> 00:11:08.377
or what we think a fair price per share

00:11:08.377 --> 00:11:09.551
of this company is

00:11:09.551 --> 00:11:12.928
if we think these assets are
really worth $30 million.

00:11:12.928 --> 00:11:14.654
Now, what are people actually paying

00:11:14.654 --> 00:11:15.995
for these shares?

00:11:15.995 --> 00:11:16.929
Well, that's,

00:11:16.929 --> 00:11:20.077
we look at this information right here,

00:11:20.077 --> 00:11:23.977
and we see that the last
trade here was for $2.58,

00:11:23.977 --> 00:11:25.826
so people are paying a discount

00:11:25.826 --> 00:11:27.478
to the number we just calculated,

00:11:27.478 --> 00:11:28.999
so the only reason why people are paying

00:11:28.999 --> 00:11:30.077
less than that,

00:11:30.077 --> 00:11:32.723
or someone's willing to
sell for less than $3,

00:11:32.723 --> 00:11:34.259
is that someone out there,

00:11:34.259 --> 00:11:35.802
especially the person selling,

00:11:35.802 --> 00:11:37.638
thinks that this company really,

00:11:37.638 --> 00:11:38.731
the assets of this company

00:11:38.731 --> 00:11:40.660
really aren't worth $30 million.

00:11:40.660 --> 00:11:42.991
He or she thinks of the
assets of this company

00:11:42.991 --> 00:11:44.587
are worth less than $30 million,

00:11:44.587 --> 00:11:46.475
and maybe they think that
the company's prospects

00:11:46.475 --> 00:11:47.556
aren't as good.

00:11:47.556 --> 00:11:49.135
They're product isn't,

00:11:49.135 --> 00:11:50.317
the sales are going to go down.

00:11:50.317 --> 00:11:51.128
Who knows?

00:11:51.128 --> 00:11:52.396
Maybe the person buying it,

00:11:52.396 --> 00:11:54.192
maybe they think it is worth $3 a share,

00:11:54.192 --> 00:11:56.658
and that's why they're
willing to pay $2.58 for it

00:11:56.658 --> 00:11:58.327
because they think it's going to go up.

00:11:58.327 --> 00:12:00.977
Just so that we get some
of the other details

00:12:00.977 --> 00:12:04.259
that we see here, this bid,

00:12:04.259 --> 00:12:05.135
this bid right here.

00:12:05.135 --> 00:12:07.662
This is what someone has explicitly said

00:12:07.662 --> 00:12:10.139
that they're willing to pay for a share.

00:12:10.139 --> 00:12:12.475
The ask is what someone
has explicitly said

00:12:12.475 --> 00:12:15.075
they're willing to sell a share for.

00:12:15.075 --> 00:12:17.674
This 52-week range is the range of prices

00:12:17.674 --> 00:12:18.553
that the shares have sold,

00:12:18.553 --> 00:12:19.923
so in the past year,

00:12:19.923 --> 00:12:23.096
these shares sold for as low as $1.20,

00:12:23.096 --> 00:12:24.333
and that was actually a great deal

00:12:24.333 --> 00:12:26.726
because they went up, even now,

00:12:26.726 --> 00:12:29.225
where they're selling at $2.58.

00:12:29.225 --> 00:12:31.400
the average volume right here,

00:12:31.400 --> 00:12:35.660
this is the number of shares sold per day,

00:12:35.660 --> 00:12:36.891
exchanged per day.

00:12:36.891 --> 00:12:38.890
The market cap, right here,

00:12:38.890 --> 00:12:40.393
you've probably heard that word before.

00:12:40.393 --> 00:12:43.192
That's essentially the market's sense

00:12:43.192 --> 00:12:45.636
of what this number really is.

00:12:45.636 --> 00:12:47.868
We're saying that the
books of this company

00:12:47.868 --> 00:12:49.998
are saying this company
is worth $8 million,

00:12:49.998 --> 00:12:51.476
but the market cap is saying

00:12:51.476 --> 00:12:53.673
what the equity of the company is worth

00:12:53.673 --> 00:12:55.327
in the market's mind,

00:12:55.327 --> 00:12:56.261
and to get that number,

00:12:56.261 --> 00:12:58.928
they're taking the $2.58.

00:12:58.928 --> 00:13:02.996
they're taking the $2.58
times the number of shares.

00:13:02.996 --> 00:13:07.394
Times the 2.78 million shares.

00:13:07.394 --> 00:13:09.673
If we do that, we're going to get,

00:13:09.673 --> 00:13:17.073
let's see, 2.58 times
2.78 is equal to exactly,

00:13:17.073 --> 00:13:18.596
well, it's a little
different than what they had.

00:13:18.596 --> 00:13:20.025
Maybe it's a little round-off error,

00:13:20.025 --> 00:13:24.224
but roughly 7 million in market cap.

00:13:24.224 --> 00:13:26.995
Like I said before, the
market is not paying $3.

00:13:26.995 --> 00:13:28.930
It's paying $2.58,

00:13:28.930 --> 00:13:31.139
and so the market is
saying that the equity,

00:13:31.139 --> 00:13:33.328
this piece right here
is closer to 7 million,

00:13:33.328 --> 00:13:34.526
even though the books are saying

00:13:34.526 --> 00:13:37.659
that this number right
here is above 8 million.

00:13:37.659 --> 00:13:40.070
Well, anyway, hopefully
that was a little bit useful

00:13:40.070 --> 00:13:41.324
and gives you a little bit of a sense

00:13:41.324 --> 00:13:45.074
of what it actually means to buy shares

00:13:45.074 --> 00:13:46.525
in a company.


Finding width from perimeter and length

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:05.220
Mike built a rectangular dog
pen that is 21 feet long,

00:00:05.220 --> 00:00:08.410
and it has a
perimeter of 78 feet.

00:00:08.410 --> 00:00:11.930
What is the width
of Mike's dog pen?

00:00:11.930 --> 00:00:13.550
So let's try to
draw this dog pen.

00:00:13.550 --> 00:00:16.710
So it's going to
have some width,

00:00:16.710 --> 00:00:20.050
and I'll just label
that as the width.

00:00:20.050 --> 00:00:23.820
And it's going to have
a length of 21 feet.

00:00:23.820 --> 00:00:27.339
So this distance right over
here is going to be 21,

00:00:27.339 --> 00:00:28.630
and of course, this is as well.

00:00:28.630 --> 00:00:30.140
It's a rectangle,
so this is also

00:00:30.140 --> 00:00:32.479
going to be a distance of 21.

00:00:32.479 --> 00:00:34.470
And of course, this
distance down here

00:00:34.470 --> 00:00:39.700
is also going to be the width.

00:00:39.700 --> 00:00:42.210
Now, how do you calculate
the perimeter of this?

00:00:42.210 --> 00:00:44.240
They tell us that the
perimeter is 78 feet,

00:00:44.240 --> 00:00:46.550
but how do we calculate
the perimeter using

00:00:46.550 --> 00:00:47.930
this information?

00:00:47.930 --> 00:00:49.470
Well, the perimeter
is just the sum

00:00:49.470 --> 00:00:52.410
of these two widths
and these two lengths.

00:00:52.410 --> 00:00:59.090
So the perimeter is going to
be the width plus the width

00:00:59.090 --> 00:01:04.430
plus the two lengths,
plus 21 plus 21.

00:01:04.430 --> 00:01:05.930
This will give us
the distance if we

00:01:05.930 --> 00:01:09.420
go around this
rectangular dog pen.

00:01:09.420 --> 00:01:14.670
And they tell us that this thing
needs to be equal to 78 feet.

00:01:14.670 --> 00:01:15.785
Let me do the same color.

00:01:19.970 --> 00:01:22.450
Now, we could simplify
this expression

00:01:22.450 --> 00:01:24.420
on the left hand
side a little bit.

00:01:24.420 --> 00:01:32.820
We know that the width plus the
width plus the sum of the two

00:01:32.820 --> 00:01:39.010
lengths-- which are
both the same-- plus 42

00:01:39.010 --> 00:01:41.990
is going to equal 78.

00:01:41.990 --> 00:01:45.390
So what must the width
plus the width be equal to?

00:01:45.390 --> 00:01:49.640
So, I have something--
I have this thing

00:01:49.640 --> 00:01:53.820
plus 42 is equal to 78.

00:01:53.820 --> 00:01:56.970
So if I have something
plus 42 is equal to 78,

00:01:56.970 --> 00:02:00.200
that means that this
something must be 78 minus 42.

00:02:00.200 --> 00:02:01.980
So let's write that down.

00:02:01.980 --> 00:02:11.540
Width plus width is going
to be equal to 78 minus 42,

00:02:11.540 --> 00:02:17.800
which is-- I'll do it in a
new color-- 78 minus 42 is 36.

00:02:17.800 --> 00:02:19.040
And you can verify this.

00:02:19.040 --> 00:02:22.170
If this thing right over
here is equal to 36,

00:02:22.170 --> 00:02:24.450
if the sum of my two
widths-- or essentially

00:02:24.450 --> 00:02:26.190
this is 2 times the width.

00:02:26.190 --> 00:02:30.480
If 2 times the width is 36,
then width plus width is 36.

00:02:30.480 --> 00:02:33.470
Then this right over here is 36.

00:02:33.470 --> 00:02:36.970
36 plus 42 is
indeed equal to 78.

00:02:36.970 --> 00:02:41.230
So we figure out a width so that
if I add the width to itself,

00:02:41.230 --> 00:02:44.340
I get 36, because when we
add those two, you get 36,

00:02:44.340 --> 00:02:48.680
plus 21 plus 21 is equal to 78.

00:02:48.680 --> 00:02:52.200
So what number plus itself
is going to be equal to 36?

00:02:52.200 --> 00:02:55.230
Another way to rewrite this
is a number plus itself

00:02:55.230 --> 00:02:57.810
is the same thing as
2 times that number.

00:02:57.810 --> 00:03:04.747
So 2 times the width is
going to be equal to 36.

00:03:04.747 --> 00:03:06.830
And later on when we learn
algebra in a little bit

00:03:06.830 --> 00:03:11.500
more detail, you'll see that
essentially what we're doing

00:03:11.500 --> 00:03:15.200
is actually algebra, but it
just comes out of common sense,

00:03:15.200 --> 00:03:16.750
out of logic.

00:03:16.750 --> 00:03:21.140
So if I say 2 times some
value is equal to 36,

00:03:21.140 --> 00:03:24.490
what is that value going to be?

00:03:24.490 --> 00:03:35.500
Well, 2 times 18 is 36, so
the width is equal to 18.

00:03:35.500 --> 00:03:38.400
And you might say well,
how did I figure out

00:03:38.400 --> 00:03:39.650
that the width is equal to 18?

00:03:39.650 --> 00:03:41.691
Well, there's a couple of
ways to think about it.

00:03:41.691 --> 00:03:44.020
If 2 times the width
is equal to 36,

00:03:44.020 --> 00:03:49.440
then the width must be
equal to 36 divided by 2,

00:03:49.440 --> 00:03:55.539
must be equal to 36 over 2,
which would also get you 18.

00:03:55.539 --> 00:03:57.330
So there's a lot of
ways to think about it,

00:03:57.330 --> 00:03:59.413
and later on when we learn
algebra in a little bit

00:03:59.413 --> 00:04:02.026
more details, things like this
will seem even more obvious.

00:04:02.026 --> 00:04:04.150
But I just wanted to show
you that you can actually

00:04:04.150 --> 00:04:07.999
reason this through just with
what we know about perimeter.


Introduction to perimeter

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:02.650
When people use the
word "perimeter"

00:00:02.650 --> 00:00:04.830
in everyday language,
they're talking

00:00:04.830 --> 00:00:07.690
about the boundary of some area.

00:00:07.690 --> 00:00:09.732
And when we talk about
perimeter in math,

00:00:09.732 --> 00:00:11.190
we're talking about
a related idea.

00:00:11.190 --> 00:00:13.273
But now we're not just
talking about the boundary.

00:00:13.273 --> 00:00:15.900
We're actually talking about
the length of the boundary.

00:00:15.900 --> 00:00:18.520
How far do you have to
go around the boundary

00:00:18.520 --> 00:00:21.440
to essentially go completely
around the figure,

00:00:21.440 --> 00:00:24.100
completely go around the area?

00:00:24.100 --> 00:00:26.600
So let's look at this first
triangle right over here.

00:00:26.600 --> 00:00:27.630
It has three sides.

00:00:27.630 --> 00:00:29.000
That's why it's a triangle.

00:00:29.000 --> 00:00:30.360
So what's its perimeter?

00:00:30.360 --> 00:00:32.150
Well, here, all the
sides are the same,

00:00:32.150 --> 00:00:33.930
so the perimeter
for this triangle

00:00:33.930 --> 00:00:39.790
is going to be 4 plus 4 plus
4, and whatever units this is.

00:00:39.790 --> 00:00:42.300
If this is 4 feet,
4 feet and 4 feet,

00:00:42.300 --> 00:00:44.660
then it would be 4 feet
plus 4 feet plus 4 feet

00:00:44.660 --> 00:00:47.670
is equal to 12 feet.

00:00:47.670 --> 00:00:50.280
Now, I encourage you
to now pause the video

00:00:50.280 --> 00:00:54.720
and figure out the parameters
of these three figures.

00:00:54.720 --> 00:00:56.240
Well, it's the exact same idea.

00:00:56.240 --> 00:00:59.190
We would just add the
lengths of the sides.

00:00:59.190 --> 00:01:01.780
So let's say that
these distances, let's

00:01:01.780 --> 00:01:03.020
say they're in meters.

00:01:03.020 --> 00:01:06.740
So let's say this is 3 meters,
and this is also 3 meters.

00:01:06.740 --> 00:01:08.670
This is a rectangle here,
so this is 5 meters.

00:01:08.670 --> 00:01:10.300
This is also 5 meters.

00:01:10.300 --> 00:01:13.870
So what is the perimeter of
this rectangle going to be?

00:01:13.870 --> 00:01:16.420
What is the distance
around the rectangle

00:01:16.420 --> 00:01:18.520
that bounds this area?

00:01:18.520 --> 00:01:24.430
Well, it's going to
be 3 plus 5 plus 3

00:01:24.430 --> 00:01:27.910
plus 5, which is
equal to-- let's see,

00:01:27.910 --> 00:01:31.230
that's 3 plus 3 is 6,
plus 5 plus 5 is 10.

00:01:31.230 --> 00:01:33.280
So that is equal to 16.

00:01:33.280 --> 00:01:35.540
And if we're saying
these are all in meters,

00:01:35.540 --> 00:01:40.370
these are all in meters, then
it's going to be 16 meters.

00:01:40.370 --> 00:01:42.130
Now, what about this pentagon?

00:01:42.130 --> 00:01:45.450
Let's say that each
of these sides are 2--

00:01:45.450 --> 00:01:47.840
and I'll make up a unit here.

00:01:47.840 --> 00:01:49.100
Let's say they're 2 gnus.

00:01:51.840 --> 00:01:56.320
That's a new unit of
distance that I've just

00:01:56.320 --> 00:02:02.140
invented-- 2 gnus.

00:02:02.140 --> 00:02:06.860
So what is the perimeter
of this pentagon in gnus?

00:02:06.860 --> 00:02:11.640
Well, it's 2 plus 2 plus
2 plus 2 plus 2 gnus.

00:02:11.640 --> 00:02:19.620
Or we're essentially
taking 1, 2, 3, 4, 5 sides.

00:02:19.620 --> 00:02:21.170
Each have a length of 2 gnus.

00:02:21.170 --> 00:02:25.270
So the perimeter here, we could
add 2 repeatedly five times.

00:02:25.270 --> 00:02:30.620
Or you could just say this
is 5 times 2 gnus, which

00:02:30.620 --> 00:02:33.860
is equal to 10 gnus,
where gnu is a completely

00:02:33.860 --> 00:02:36.950
made-up unit of length
that I just made up.

00:02:36.950 --> 00:02:41.530
Here we have a more irregular
polygon, but same exact idea.

00:02:41.530 --> 00:02:43.420
How would you figure
out its perimeter?

00:02:43.420 --> 00:02:45.444
Well, you just add up
the lengths of its sides.

00:02:45.444 --> 00:02:46.860
And here I'll just
do it unitless.

00:02:46.860 --> 00:02:49.450
I'll just assume that this
is some generic units.

00:02:49.450 --> 00:02:54.330
And here the perimeter
will be 1 plus 4

00:02:54.330 --> 00:02:58.610
plus 2 plus 2-- let me
scroll over to the right

00:02:58.610 --> 00:03:02.900
a little bit-- plus 4 plus 6.

00:03:02.900 --> 00:03:04.590
So what is this
going to be equal to?

00:03:04.590 --> 00:03:11.490
1 plus 4 is 5, plus 2 is 7,
plus 2 is 9, plus 4 is 13,

00:03:11.490 --> 00:03:13.540
plus 6 is 19.

00:03:13.540 --> 00:03:16.050
So this figure has
a perimeter of 19

00:03:16.050 --> 00:03:20.280
in whatever units these
distances are actually given.


Calculating the square footage of a house

WEBVTT
Kind: captions
Language: en

00:00:00.700 --> 00:00:02.685
You are thinking
about buying a house,

00:00:02.685 --> 00:00:04.059
but you really
want to figure out

00:00:04.059 --> 00:00:06.740
how much area does
the house cover.

00:00:06.740 --> 00:00:09.350
What is the square
footage of the house?

00:00:09.350 --> 00:00:12.530
Or what is the area of the
foundation of the house?

00:00:12.530 --> 00:00:14.910
So right here, we have the
floor plan of the house.

00:00:14.910 --> 00:00:16.761
And you're tasked
with finding its area.

00:00:16.761 --> 00:00:18.510
And you're given the
dimensions of a bunch

00:00:18.510 --> 00:00:19.530
of walls of the house.

00:00:19.530 --> 00:00:21.290
This wall right here is 18 feet.

00:00:21.290 --> 00:00:22.620
This is 8 feet.

00:00:22.620 --> 00:00:27.640
This is 20 feet, 20 feet,
5 feet, 26 feet, 15 feet,

00:00:27.640 --> 00:00:28.812
and 25 feet.

00:00:28.812 --> 00:00:30.020
But you're a little confused.

00:00:30.020 --> 00:00:31.880
You know how to find
the area of rectangles,

00:00:31.880 --> 00:00:35.170
but how do you find an area
of a strange shape like this?

00:00:35.170 --> 00:00:37.030
So I encourage you
to pause this video

00:00:37.030 --> 00:00:41.850
and try to figure out the area
of this strange house footprint

00:00:41.850 --> 00:00:44.700
shape, floor plan shape,
using the techniques

00:00:44.700 --> 00:00:47.450
that you already know about.

00:00:47.450 --> 00:00:49.170
So what you already
do know about

00:00:49.170 --> 00:00:51.750
is how to find the
area of rectangles.

00:00:51.750 --> 00:00:54.390
So if we can break
this house's floor plan

00:00:54.390 --> 00:00:56.410
into a series of
rectangles and find out

00:00:56.410 --> 00:00:58.410
the areas of those
rectangles, then we

00:00:58.410 --> 00:01:00.830
can figure out the area
of this entire house.

00:01:00.830 --> 00:01:03.740
So let's break it into a
bunch of simpler rectangles.

00:01:03.740 --> 00:01:05.269
So I could have
one rectangle here.

00:01:05.269 --> 00:01:10.190
It has a width of 20 feet, and
it has a length of 20 feet.

00:01:10.190 --> 00:01:14.290
So that would be a
rectangle right over there.

00:01:14.290 --> 00:01:16.590
We should be able to
figure out its area.

00:01:16.590 --> 00:01:18.200
Then I could set up
another rectangle

00:01:18.200 --> 00:01:23.930
that has a width of 26
feet and has a length.

00:01:23.930 --> 00:01:25.461
That's its length
right over there.

00:01:25.461 --> 00:01:26.960
And we could think
about in a second

00:01:26.960 --> 00:01:28.475
what that length actually is.

00:01:28.475 --> 00:01:29.850
Actually, let's
think about that.

00:01:29.850 --> 00:01:33.590
How would we figure out what
this length actually is?

00:01:33.590 --> 00:01:37.310
Well, this length
plus 5 feet is going

00:01:37.310 --> 00:01:39.570
to be the same thing as
this length over here.

00:01:39.570 --> 00:01:43.690
It's the same as the opposite
wall of this rectangle.

00:01:43.690 --> 00:01:45.940
So this length plus
5 feet is 20 feet.

00:01:45.940 --> 00:01:48.550
Well, this must be 15 feet.

00:01:48.550 --> 00:01:52.827
So this blue rectangle is 15
feet long and 26 feet wide.

00:01:52.827 --> 00:01:54.160
Now let's add another rectangle.

00:01:54.160 --> 00:01:56.630
We could have one
that's 18 feet long

00:01:56.630 --> 00:01:59.880
and then goes the entire
length of the house.

00:01:59.880 --> 00:02:03.190
Goes the entire length
of the house like that.

00:02:03.190 --> 00:02:06.060
And you might say, wait, how
do we figure out its width?

00:02:06.060 --> 00:02:09.699
How do we figure out the
width of this rectangle?

00:02:09.699 --> 00:02:12.160
Well, we know that
this is 8 feet.

00:02:12.160 --> 00:02:15.010
We know that this
is 20 feet, and we

00:02:15.010 --> 00:02:17.460
know that this is 26 feet.

00:02:17.460 --> 00:02:21.670
So the entire width is going
to be 26 feet plus 20 feet.

00:02:21.670 --> 00:02:25.360
So 26 plus 20 gets us to 46.

00:02:25.360 --> 00:02:28.730
Plus 8 gets us to 54 feet.

00:02:28.730 --> 00:02:34.150
So this is 54 feet
right over here.

00:02:34.150 --> 00:02:35.030
Did I do that right?

00:02:35.030 --> 00:02:35.530
Let's see.

00:02:35.530 --> 00:02:39.040
8 plus 36 would be 34,
plus 20 is 54 feet.

00:02:39.040 --> 00:02:41.929
And then finally we have one
last rectangle to deal with,

00:02:41.929 --> 00:02:43.470
this rectangle right
over here, which

00:02:43.470 --> 00:02:50.210
is 15 feet long
and 25 feet wide.

00:02:50.210 --> 00:02:52.360
And so now we can
calculate the areas

00:02:52.360 --> 00:02:54.480
of the different rectangles.

00:02:54.480 --> 00:02:58.930
So the total area is going to
be the 20 feet by the 20 feet.

00:02:58.930 --> 00:03:00.340
So let's just multiply them.

00:03:00.340 --> 00:03:03.580
So it's going to be 20 times 20.

00:03:03.580 --> 00:03:07.040
That's this area
right over here.

00:03:07.040 --> 00:03:08.956
Plus 15 times 26.

00:03:14.320 --> 00:03:18.420
That's this area
right over there.

00:03:18.420 --> 00:03:30.180
Plus 18 times 54, which is
this area right over there.

00:03:30.180 --> 00:03:38.240
And then finally,
plus 15 times 25,

00:03:38.240 --> 00:03:43.880
which is this area
right over here.

00:03:43.880 --> 00:03:46.220
So we just have to now
evaluate these things.

00:03:46.220 --> 00:03:48.440
So what is 20 times 20?

00:03:48.440 --> 00:03:51.040
Well, this is going to be 400.

00:03:51.040 --> 00:03:52.350
What's 15 times 26?

00:03:52.350 --> 00:03:53.640
Well, let's multiply it out.

00:03:53.640 --> 00:03:56.720
26 times 15.

00:03:56.720 --> 00:03:59.146
6 times 5 is 30.

00:03:59.146 --> 00:04:03.320
2 times 5 is 10, plus 3 is 13.

00:04:03.320 --> 00:04:07.770
Now I'm going to multiply a
10 times 26, gets us to 260.

00:04:07.770 --> 00:04:09.380
And you add these two together.

00:04:09.380 --> 00:04:11.110
You get 390.

00:04:11.110 --> 00:04:14.620
So it's 400 plus 390.

00:04:14.620 --> 00:04:18.552
Now we've got to multiply
18 times 54, or 54 times 18.

00:04:18.552 --> 00:04:19.260
So let's do that.

00:04:19.260 --> 00:04:21.660
54 times 18.

00:04:21.660 --> 00:04:25.430
8 times 4 is 32.

00:04:25.430 --> 00:04:28.970
8 times 5 is 40, plus 3 is 43.

00:04:28.970 --> 00:04:31.720
Now we're multiplying
this 10 times 54.

00:04:31.720 --> 00:04:33.720
Gets us to 540.

00:04:33.720 --> 00:04:34.500
And we add.

00:04:34.500 --> 00:04:37.100
2 plus 0 is 2.

00:04:37.100 --> 00:04:39.970
This 30 plus the
40 gets us to a 70.

00:04:39.970 --> 00:04:42.320
In other words, a 3 plus
a 4 in the tens place.

00:04:42.320 --> 00:04:44.930
And then 400 plus 500 is 900.

00:04:44.930 --> 00:04:47.730
So we get to 972.

00:04:47.730 --> 00:04:51.300
And one more of these
multiplications.

00:04:51.300 --> 00:04:52.939
25 times 15.

00:04:52.939 --> 00:04:54.730
And actually, we could
do that in our head.

00:04:54.730 --> 00:04:58.300
This is 26 times
15, so 25 times 15

00:04:58.300 --> 00:05:00.860
is going to be this minus 15.

00:05:00.860 --> 00:05:02.090
So it's going to be 300.

00:05:02.090 --> 00:05:04.250
Let's see, if you subtract
10, you get to 380.

00:05:04.250 --> 00:05:07.870
Subtract another 5, 375.

00:05:07.870 --> 00:05:10.070
Let me do it in that same color.

00:05:10.070 --> 00:05:16.120
So plus 375.

00:05:16.120 --> 00:05:17.700
And now let's add
up these numbers.

00:05:17.700 --> 00:05:33.770
So we have 375 plus
972, plus 390, plus 400.

00:05:33.770 --> 00:05:37.920
And so this gets us to 5--
this is the home stretch.

00:05:37.920 --> 00:05:39.620
We deserve a drum roll now.

00:05:39.620 --> 00:05:42.341
5 plus 2 is 7.

00:05:42.341 --> 00:05:47.390
7 plus 7 is 14, plus 9 is 23.

00:05:47.390 --> 00:05:53.710
2 plus 3 is 5, plus
9 is 14, 17, 21.

00:05:53.710 --> 00:05:55.620
So the square footage
of this house?

00:05:55.620 --> 00:05:57.335
2,137 square feet.


Area of rectangles and the distributive property

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:03.950
I have this rectangle here, and
I want to figure out its area.

00:00:03.950 --> 00:00:06.860
I want to figure out how
much space it is taking up

00:00:06.860 --> 00:00:08.950
on my screen right over here.

00:00:08.950 --> 00:00:10.650
And I encourage you
to pause this video

00:00:10.650 --> 00:00:13.320
and try to figure out the
area of this entire rectangle.

00:00:13.320 --> 00:00:15.584
And when you do it, think
about the two different ways

00:00:15.584 --> 00:00:16.250
you could do it.

00:00:16.250 --> 00:00:18.040
You could either
multiply the length

00:00:18.040 --> 00:00:20.120
of the rectangle times
the entire width,

00:00:20.120 --> 00:00:22.420
so just figure out the
area of the entire thing.

00:00:22.420 --> 00:00:24.480
Or you could
separately figure out

00:00:24.480 --> 00:00:28.380
the area of this red or
this purple rectangle

00:00:28.380 --> 00:00:30.920
and then separately figure
out this blue rectangle

00:00:30.920 --> 00:00:33.090
and realize that their
combined areas is

00:00:33.090 --> 00:00:36.399
the exact same thing as
the entire rectangle.

00:00:36.399 --> 00:00:37.940
So I encourage you
to pause the video

00:00:37.940 --> 00:00:41.839
and try both of
those strategies out.

00:00:41.839 --> 00:00:43.380
So let's just try
them out ourselves.

00:00:43.380 --> 00:00:46.050
First, let's look at
the overall dimensions

00:00:46.050 --> 00:00:47.510
of the larger rectangle.

00:00:47.510 --> 00:00:50.220
The length is 9, and
we're going to multiply

00:00:50.220 --> 00:00:51.940
that times the width.

00:00:51.940 --> 00:00:53.700
But what's width here?

00:00:53.700 --> 00:00:57.720
Well, the width is
going to be 8 plus 12.

00:00:57.720 --> 00:01:01.750
This entire distance right
over here is 8 plus 12.

00:01:01.750 --> 00:01:04.705
So it's 9 times 8 plus 12.

00:01:08.080 --> 00:01:10.060
This is one way that
we could figure out

00:01:10.060 --> 00:01:12.120
the area of this entire thing.

00:01:12.120 --> 00:01:15.420
This is just the
length times the width.

00:01:15.420 --> 00:01:18.095
8 plus 12 is obviously
going to be equal to 20.

00:01:18.095 --> 00:01:19.720
But the other way
that we could do it--

00:01:19.720 --> 00:01:22.011
and this must be equivalent,
because we're figuring out

00:01:22.011 --> 00:01:24.480
the area of the same
thing-- is to separate out

00:01:24.480 --> 00:01:26.982
the area of these
two sub-rectangles.

00:01:26.982 --> 00:01:27.690
So let's do that.

00:01:27.690 --> 00:01:29.310
And this must be
equal to this thing.

00:01:29.310 --> 00:01:31.804
So what's the area of
this purple rectangle?

00:01:31.804 --> 00:01:33.220
Well, it's going
to be the length.

00:01:33.220 --> 00:01:34.800
It's going to be 9.

00:01:34.800 --> 00:01:36.400
Let me do it in that same color.

00:01:36.400 --> 00:01:40.750
It's going to be 9 times
the width, which is 8.

00:01:40.750 --> 00:01:44.340
It's going to be 9 times 8.

00:01:44.340 --> 00:01:47.970
And then what's the area
of this the blue rectangle?

00:01:47.970 --> 00:01:51.250
Well, that's going
to be 9 times--

00:01:51.250 --> 00:01:53.700
so the height here is 9 still.

00:01:53.700 --> 00:01:54.650
The height is 9.

00:01:54.650 --> 00:01:55.990
And what's the width?

00:01:55.990 --> 00:01:58.700
Well, the width is 12.

00:01:58.700 --> 00:02:00.410
And what's the area
of the combined

00:02:00.410 --> 00:02:02.942
if you wanted to combine the
area of the purple rectangle

00:02:02.942 --> 00:02:03.650
and the blue one?

00:02:03.650 --> 00:02:05.608
Well, you'd just add
these two things together.

00:02:08.840 --> 00:02:11.090
And of course, when you add
these two things together,

00:02:11.090 --> 00:02:13.100
you get the area of
the entire thing.

00:02:13.100 --> 00:02:16.020
So these things
must be equivalent.

00:02:16.020 --> 00:02:18.430
They are calculating
the same area.

00:02:18.430 --> 00:02:20.890
Now, what's neat
about this is we just

00:02:20.890 --> 00:02:24.530
showed ourselves the
distributive property

00:02:24.530 --> 00:02:26.134
when we're dealing
with these numbers.

00:02:26.134 --> 00:02:27.800
You could try these
out for any numbers.

00:02:27.800 --> 00:02:29.341
They'll work for
any numbers, because

00:02:29.341 --> 00:02:31.800
the distributive property
works for any numbers.

00:02:31.800 --> 00:02:35.920
You see 9 times the
sum of 8 plus 12

00:02:35.920 --> 00:02:39.570
is equal to 9 times
8 plus 9 times 12.

00:02:39.570 --> 00:02:44.940
We essentially have
distributed the 9-- 9 times 8

00:02:44.940 --> 00:02:47.360
plus 9 times 12.

00:02:47.360 --> 00:02:49.270
And let's actually
calculate it just

00:02:49.270 --> 00:02:51.500
to satisfy ourselves
about the area.

00:02:51.500 --> 00:02:57.830
So if you multiply the length
times the entire width,

00:02:57.830 --> 00:03:00.820
so that's 9 times
8 plus 12, that's

00:03:00.820 --> 00:03:05.610
the same thing as 9
times 20, which is 180.

00:03:05.610 --> 00:03:07.820
And over here, if you
calculate the area

00:03:07.820 --> 00:03:14.050
of this purple rectangle,
that is 9 times 8.

00:03:14.050 --> 00:03:16.980
So that is going
to be equal to 72.

00:03:19.640 --> 00:03:20.910
That's the purple rectangle.

00:03:20.910 --> 00:03:27.162
The area of the blue rectangle,
9 times 12, well, that's 108.

00:03:27.162 --> 00:03:28.912
And we're going to
take the sum of the two

00:03:28.912 --> 00:03:32.340
to find the area of
the larger rectangle.

00:03:32.340 --> 00:03:34.760
What is 72 plus 108?

00:03:34.760 --> 00:03:39.340
Well, 72 plus 108 is
also equal to 180.

00:03:39.340 --> 00:03:40.180
So we've verified.

00:03:40.180 --> 00:03:43.172
These, indeed, are equal to each
other when we calculate them.

00:03:43.172 --> 00:03:44.630
And they make sense,
because we are

00:03:44.630 --> 00:03:48.263
calculating the same exact area.


Comparing areas of plots of land

WEBVTT
Kind: captions
Language: en

00:00:00.750 --> 00:00:04.460
Diya is looking to buy a plot
of land to build her home on.

00:00:04.460 --> 00:00:07.020
She finally narrows
her search to two plots

00:00:07.020 --> 00:00:09.090
that both have good locations.

00:00:09.090 --> 00:00:15.530
The plot at 314159 Apple
Lane has a width of 30 meters

00:00:15.530 --> 00:00:17.930
and a length of 40 meters.

00:00:17.930 --> 00:00:24.340
The plot at 11235 Fibonacci
Drive has a width of 50 meters

00:00:24.340 --> 00:00:26.520
and a length of 20 meters.

00:00:26.520 --> 00:00:30.410
They are each being
sold for $36,000.

00:00:30.410 --> 00:00:33.850
Which one is a better deal?

00:00:33.850 --> 00:00:35.670
So they're the same
price, and they're

00:00:35.670 --> 00:00:37.350
in comparable neighborhoods.

00:00:37.350 --> 00:00:39.480
So really, the better
deal is the one

00:00:39.480 --> 00:00:42.390
that actually gets me more area.

00:00:42.390 --> 00:00:44.640
So I encourage you to pause
the video and think about,

00:00:44.640 --> 00:00:48.300
which one of these am
I getting more land

00:00:48.300 --> 00:00:51.632
for the same amount of money?

00:00:51.632 --> 00:00:53.590
Well, to think about how
much land I'm getting,

00:00:53.590 --> 00:00:55.298
I'm really thinking
about, how much space

00:00:55.298 --> 00:00:56.394
is that plot taking up?

00:00:56.394 --> 00:00:57.810
Or I'm really
thinking about, what

00:00:57.810 --> 00:01:00.670
is the area of each
of these plots?

00:01:00.670 --> 00:01:02.640
And we've already
figured out that you

00:01:02.640 --> 00:01:05.690
can calculate the
area of a rectangle

00:01:05.690 --> 00:01:09.120
by multiplying its
length times its width.

00:01:09.120 --> 00:01:18.670
So the area of Apple Lane is 40
meters times 30 meters, which

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is equal to-- 40 times 3 is 120.

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40 times 30 is 1,200.

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And then it's
meters times meters.

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Or you can view this as square
meters, 1,200 square meters.

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Now let's think
about what the area

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of the plot at
Fibonacci Drive is.

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So its length is 20.

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Its width is 50.

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So here the area is 20
meters times 50 meters, which

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is equal to-- 20 times 5 is 100.

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20 times 50 is
1,000 square meters.

00:02:07.680 --> 00:02:10.090
So it's pretty clear when
you calculate the area

00:02:10.090 --> 00:02:13.880
that Apple Lane, you're getting
more square meters than you

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would get at Fibonacci Drive.

00:02:15.550 --> 00:02:17.940
And literally, when we say
1,200 square meters, that

00:02:17.940 --> 00:02:22.390
means if you were to
put a 1 meter by 1

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meter square here--
so a really small one

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like that-- then you
could fit 1,200 of these

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on this plot of land, while you
could only fit 1,000 of them

00:02:31.270 --> 00:02:36.080
on this plot of land-- of these
1 meter by 1 meter squares.

00:02:36.080 --> 00:02:39.190
So we have a larger area, same
neighborhood or comparable

00:02:39.190 --> 00:02:40.890
neighborhood for the same price.

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I would go with Apple Lane
being the better deal.