Adding: why carrying works

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.600
Now, let's do the exact
same addition problem

00:00:02.600 --> 00:00:03.850
that we did in the last video.

00:00:03.850 --> 00:00:06.220
But I'm going to expand out
these numbers so that we really

00:00:06.220 --> 00:00:07.810
understand what's
going on when we're

00:00:07.810 --> 00:00:09.430
doing all of this carrying.

00:00:09.430 --> 00:00:11.490
So this 5 is in
the hundreds place.

00:00:11.490 --> 00:00:14.730
So it really represents
5 hundreds or 500.

00:00:14.730 --> 00:00:17.670
3 represents 3 tens because
it is in the tens place.

00:00:17.670 --> 00:00:19.150
So it represents 30.

00:00:19.150 --> 00:00:23.000
And the 6, well, it just
represents 6 ones or 6.

00:00:23.000 --> 00:00:26.940
Likewise, this 3 represents 300.

00:00:26.940 --> 00:00:31.180
This 9 is 9 tens or 90.

00:00:31.180 --> 00:00:35.240
And this 8 just
represents 8 ones or 8.

00:00:35.240 --> 00:00:37.590
And now we can add these two up.

00:00:37.590 --> 00:00:42.140
Now let's start in the
right-most column-- this ones

00:00:42.140 --> 00:00:42.670
column.

00:00:42.670 --> 00:00:45.100
6 plus 8, we've
already figured out,

00:00:45.100 --> 00:00:48.780
is equal to 14, which is
the same thing as 10 plus 4.

00:00:54.064 --> 00:00:55.480
So let's write the
part that's not

00:00:55.480 --> 00:00:57.390
a multiple of 10 in
this ones column.

00:00:57.390 --> 00:00:58.650
So let's put that 4 there.

00:00:58.650 --> 00:01:00.530
And the part that
is a multiple of 10,

00:01:00.530 --> 00:01:02.708
we can now carry into
this tens column.

00:01:02.708 --> 00:01:04.999
And that's just to keep track
of it-- just to make sure

00:01:04.999 --> 00:01:06.600
that we don't lose
that 10, we're

00:01:06.600 --> 00:01:08.230
putting it into the tens column.

00:01:08.230 --> 00:01:09.780
Now we can add all the tens.

00:01:09.780 --> 00:01:14.700
10 plus 30 plus 90, we've
already figured out is 130.

00:01:14.700 --> 00:01:18.220
Well the part that is
not a multiple of 100,

00:01:18.220 --> 00:01:21.357
we can write in this tens
column-- so the 30 part.

00:01:21.357 --> 00:01:23.190
And then the part that
is a multiple of 100,

00:01:23.190 --> 00:01:24.810
we can put in the
hundreds column.

00:01:24.810 --> 00:01:27.730
So we could put the
100 right over here.

00:01:27.730 --> 00:01:29.600
Notice, we've just
carried the 1.

00:01:29.600 --> 00:01:32.110
But essentially, we've carried
100, because we put a 1

00:01:32.110 --> 00:01:33.160
in the hundreds place.

00:01:33.160 --> 00:01:36.700
10 plus 30 plus
90 is 100 plus 30.

00:01:36.700 --> 00:01:41.120
This is equal to 100 plus 30.

00:01:41.120 --> 00:01:42.410
That's all we've done.

00:01:42.410 --> 00:01:44.300
Now we can add the hundreds.

00:01:44.300 --> 00:01:49.000
100 plus 500 plus 300 we've
already figured out is 900.

00:01:49.000 --> 00:01:51.520
So we can write it as 900.

00:01:51.520 --> 00:01:52.390
And we're done!

00:01:52.390 --> 00:01:54.640
We've figured out that
500 plus 30 plus 6,

00:01:54.640 --> 00:02:02.060
plus 300 plus 90 plus 8, is
equal to 900 plus 30 plus 4,

00:02:02.060 --> 00:02:05.215
which is the same thing as 934.

00:02:05.215 --> 00:02:07.340
So hopefully this gives
you a little bit more sense

00:02:07.340 --> 00:02:09.660
of what we're doing when we
"carry the 1" every time.

00:02:09.660 --> 00:02:11.520
6 plus 8 is 14.

00:02:11.520 --> 00:02:12.940
We carried the 1.

00:02:12.940 --> 00:02:14.347
That 1 represents 10.

00:02:14.347 --> 00:02:15.930
It represents this
10 right over here.

00:02:15.930 --> 00:02:17.380
Just so we don't
lose track of it.

00:02:17.380 --> 00:02:22.940
Then we say that 10 plus
30 plus 90 is equal to 130.

00:02:22.940 --> 00:02:25.190
So that's 30 plus 100.

00:02:25.190 --> 00:02:28.220
Then we add the hundreds
together and we get 900.


Adding three-digit numbers

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:02.849
Let's add 536 to 398.

00:00:02.849 --> 00:00:05.140
I'm going to do it two
different ways so that we really

00:00:05.140 --> 00:00:07.309
understand what this
carrying is all about.

00:00:07.309 --> 00:00:09.350
So first we'll do it in
the more traditional way.

00:00:09.350 --> 00:00:10.474
We start in the ones place.

00:00:10.474 --> 00:00:12.180
We say, well, what's 6 plus 8?

00:00:12.180 --> 00:00:14.955
Well, we know that 6
plus 8 is equal to 14.

00:00:18.540 --> 00:00:21.610
And so when we write it down
here in the sum, we could say,

00:00:21.610 --> 00:00:24.330
well, look, the four is in the
ones place, so it's equal to 4

00:00:24.330 --> 00:00:28.150
plus one 10 So let's write
that one 10 in the tens place.

00:00:28.150 --> 00:00:30.220
And now we focus
on the tens place.

00:00:30.220 --> 00:00:34.250
We have 1 ten, plus
3 tens, plus 9 tens.

00:00:34.250 --> 00:00:35.870
So what's that going to get us?

00:00:35.870 --> 00:00:42.290
1 plus 3 plus 9 is equal to 13.

00:00:45.240 --> 00:00:48.500
Now, we have to remind
ourselves, this is 13 tens.

00:00:48.500 --> 00:00:49.830
This is 13 tens.

00:00:49.830 --> 00:00:53.510
Or another way of thinking
about it, this is 3 tens.

00:00:53.510 --> 00:00:59.157
This is 3 tens and 100.

00:00:59.157 --> 00:01:00.240
You might say, wait, wait.

00:01:00.240 --> 00:01:01.740
How does that make sense?

00:01:01.740 --> 00:01:03.240
Remember, this is
in the tens place.

00:01:03.240 --> 00:01:06.500
When we're adding a 1 ten
plus the 3 tens plus 9 tens,

00:01:06.500 --> 00:01:14.170
we're actually adding 10 plus 30
plus 90, and we're getting 130.

00:01:14.170 --> 00:01:15.926
And so we're putting the 30.

00:01:15.926 --> 00:01:18.730
The 3 in the tens place
represents the 30.

00:01:18.730 --> 00:01:20.420
So this is the 3.

00:01:20.420 --> 00:01:21.690
The 3 represents the 30.

00:01:21.690 --> 00:01:26.390
And then we're placing this
1 in the hundreds place.

00:01:26.390 --> 00:01:29.550
10 tens is equal to 100.

00:01:29.550 --> 00:01:31.800
And now we're adding
up the hundreds place.

00:01:31.800 --> 00:01:40.650
1 plus 5 plus 3 is
equal to-- let's see,

00:01:40.650 --> 00:01:45.050
1 plus 5 is equal to 6,
plus 3 is equal to 9.

00:01:45.050 --> 00:01:47.440
But we have to remind
ourselves, this is 900.

00:01:47.440 --> 00:01:48.690
This is in the hundreds place.

00:01:48.690 --> 00:01:55.810
So this is actually 100-- I want
to make all colors the same.

00:01:55.810 --> 00:02:05.200
So this is actually
100 plus 500 plus 300.

00:02:05.200 --> 00:02:07.260
Let me get the
color coding right.

00:02:07.260 --> 00:02:14.350
Plus 300 is equal to 900.

00:02:14.350 --> 00:02:16.270
And that's exactly
what we got here.

00:02:16.270 --> 00:02:22.520
100 plus 500 plus 300 is
equal to 900, and we're done.

00:02:22.520 --> 00:02:24.690
This is equal to 934.


Rounding to the nearest 100

WEBVTT
Kind: captions
Language: en

00:00:00.820 --> 00:00:07.890
We're asked to round 152, 137,
245, and 354 to the nearest

00:00:07.890 --> 00:00:10.840
100, which is another
way of saying round each

00:00:10.840 --> 00:00:14.880
of these numbers to the
nearest multiple of 100.

00:00:14.880 --> 00:00:17.370
So let's think about
them one by one.

00:00:17.370 --> 00:00:19.890
So let's draw a
number line here.

00:00:19.890 --> 00:00:22.400
And here I'm counting
up by hundreds.

00:00:22.400 --> 00:00:25.290
What I've marked here,
100, 200, 300, 400, these

00:00:25.290 --> 00:00:26.619
are all multiples of 100.

00:00:26.619 --> 00:00:27.535
I could keep going up.

00:00:27.535 --> 00:00:30.990
I could go to 500, 600,
so on and so forth.

00:00:30.990 --> 00:00:33.690
Now, let's start with 152.

00:00:33.690 --> 00:00:35.420
Well, where does 152 sit?

00:00:35.420 --> 00:00:37.255
So halfway in between is 150.

00:00:37.255 --> 00:00:39.360
152 is going to be right
to the right of that.

00:00:39.360 --> 00:00:42.190
So that's 152 right over here.

00:00:42.190 --> 00:00:43.730
So what are our two options?

00:00:43.730 --> 00:00:45.060
We might round up.

00:00:45.060 --> 00:00:49.030
The multiple of 100
above 152 is 200.

00:00:49.030 --> 00:00:53.760
The multiple of 100
below 152 is 100.

00:00:53.760 --> 00:00:55.320
So which direction do we go in?

00:00:55.320 --> 00:01:01.150
Do we round up to 200, or
do we round down to 100?

00:01:01.150 --> 00:01:04.530
Well, if we're rounding
to the nearest 100,

00:01:04.530 --> 00:01:07.696
we want to look at one
place to the right of that.

00:01:07.696 --> 00:01:09.070
We want to look
at the tens place

00:01:09.070 --> 00:01:12.170
to decide which multiple
of 100 it is closer to.

00:01:12.170 --> 00:01:13.820
And the rules are
very similar to when

00:01:13.820 --> 00:01:17.600
we're rounding to the nearest
tens place or really any place.

00:01:17.600 --> 00:01:19.510
We look one place
to the right of it.

00:01:19.510 --> 00:01:21.780
So in this case, we
look at the tens place.

00:01:21.780 --> 00:01:25.500
And we say, if this is 5
or larger, we round up.

00:01:25.500 --> 00:01:30.450
And this is 5 or larger, so
we're going to round up to 200.

00:01:30.450 --> 00:01:31.910
So this we're going to round.

00:01:31.910 --> 00:01:35.900
152, we're going to round to
200, which also makes sense.

00:01:35.900 --> 00:01:39.030
152 is a little
bit closer to 200.

00:01:39.030 --> 00:01:42.090
It's 48 away from to
200 than it to 100.

00:01:42.090 --> 00:01:44.090
It's 52 away from 100.

00:01:44.090 --> 00:01:51.040
So it makes sense to go up to
the nearest multiple of 100.

00:01:51.040 --> 00:01:55.200
Now, let's think about 137.

00:01:55.200 --> 00:01:56.970
And I encourage you
to now pause the video

00:01:56.970 --> 00:01:59.550
and try to round each of
these other three numbers

00:01:59.550 --> 00:02:01.351
to the nearest 100.

00:02:01.351 --> 00:02:05.710
Well, 137 is going to sit
someplace right over here.

00:02:05.710 --> 00:02:08.220
137 is going to be
right over there.

00:02:08.220 --> 00:02:12.450
So two options-- we
can round down to 100.

00:02:12.450 --> 00:02:15.470
That's the multiple
of 100 below 137.

00:02:15.470 --> 00:02:20.570
Or we could round up to 200.

00:02:20.570 --> 00:02:24.060
Well, 137, just looking at
it, is clearly closer to 100.

00:02:24.060 --> 00:02:25.900
Or we could apply our rule.

00:02:25.900 --> 00:02:28.235
If we're rounding
to the nearest 100,

00:02:28.235 --> 00:02:30.820
we want to look at one
place to the right of that.

00:02:30.820 --> 00:02:33.780
We want to look
at the tens place.

00:02:33.780 --> 00:02:36.290
If this is 5 or
larger, we round up.

00:02:36.290 --> 00:02:38.920
If it's less than
5, we round down.

00:02:38.920 --> 00:02:44.420
So in this case, we
would round down to 100.

00:02:44.420 --> 00:02:45.992
Let's do the same
thing with 245.

00:02:45.992 --> 00:02:47.950
If you haven't paused it
and tried it yourself,

00:02:47.950 --> 00:02:49.283
once again, I want to emphasize.

00:02:49.283 --> 00:02:52.300
That'll make it really valuable
for you to try it on your own.

00:02:52.300 --> 00:02:54.450
So let's plot where 245 is.

00:02:54.450 --> 00:02:58.050
So 245 is right
around-- this is 250,

00:02:58.050 --> 00:03:00.435
so 245 might be
right around here.

00:03:03.590 --> 00:03:04.910
Now, let's apply that rule.

00:03:04.910 --> 00:03:06.810
If we're trying to round
to the nearest 100,

00:03:06.810 --> 00:03:08.830
we would look to one
place to the right.

00:03:08.830 --> 00:03:10.560
We'll look at the tens place.

00:03:10.560 --> 00:03:12.370
We could ignore the ones place.

00:03:12.370 --> 00:03:14.400
We look at the tens place here.

00:03:14.400 --> 00:03:18.180
If it is greater than or
equal to 5, we round up.

00:03:18.180 --> 00:03:21.180
If it is less than
5, we round down.

00:03:21.180 --> 00:03:23.542
So here, we're clearly
going to round down.

00:03:23.542 --> 00:03:25.000
And when we round
down, we're going

00:03:25.000 --> 00:03:30.780
to round down to the multiple of
100 that's directly below 245.

00:03:30.780 --> 00:03:33.720
Well, we're going to
round down to 200.

00:03:33.720 --> 00:03:34.850
We had two options.

00:03:34.850 --> 00:03:37.400
If we rounded up, we
would have gone to 300.

00:03:37.400 --> 00:03:39.490
If we rounded down,
we would go to 200.

00:03:39.490 --> 00:03:41.350
We're clearly closer to 200.

00:03:41.350 --> 00:03:42.990
And we can verify
that with the rule.

00:03:42.990 --> 00:03:45.350
The tens place, we're
in the 40's here.

00:03:45.350 --> 00:03:46.640
The tens place is a 4.

00:03:46.640 --> 00:03:49.090
We're going to round down.

00:03:49.090 --> 00:03:53.680
Now let's think about 354.

00:03:53.680 --> 00:03:55.760
If we were to plot
that, this is 350.

00:03:55.760 --> 00:04:00.620
354 might be right over here.

00:04:00.620 --> 00:04:02.630
So if we rounded down,
we would go to 300.

00:04:02.630 --> 00:04:05.214
If we rounded up,
we would go to 400.

00:04:05.214 --> 00:04:06.880
Now let's apply our
rule, and let's also

00:04:06.880 --> 00:04:08.080
think about it on
the number line.

00:04:08.080 --> 00:04:09.955
This is all about finding
the multiple of 100

00:04:09.955 --> 00:04:11.230
that it's closest to.

00:04:11.230 --> 00:04:16.470
If you're trying to
round to the nearest 100,

00:04:16.470 --> 00:04:18.980
you want to look at
the tens place, a place

00:04:18.980 --> 00:04:22.019
to the right of the
place you're rounding to.

00:04:22.019 --> 00:04:24.810
If the tens place
is a 5 or larger,

00:04:24.810 --> 00:04:26.630
you're going to round up.

00:04:26.630 --> 00:04:36.100
This is a 5 or larger so we're
going to round up to 400.

00:04:36.100 --> 00:04:37.580
And that also makes sense.

00:04:37.580 --> 00:04:38.810
The rule is really valuable.

00:04:38.810 --> 00:04:40.519
If you're right at
350, right in between,

00:04:40.519 --> 00:04:43.101
then you would need the rule to
say, hey, let's look at this 5

00:04:43.101 --> 00:04:43.790
and round up.

00:04:43.790 --> 00:04:48.090
But 354 is also closer
to 400 than it is to 300.

00:04:48.090 --> 00:04:49.790
It's 54 away from 300.

00:04:49.790 --> 00:04:51.490
It's 46 away from 400.

00:04:51.490 --> 00:04:54.601
So it makes sense that
we would round up to 400.


Rounding to the nearest 10

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.520
Throughout your
mathematical life,

00:00:02.520 --> 00:00:06.034
you will find situations where
you will need to round numbers.

00:00:06.034 --> 00:00:07.450
And you might be
saying, well why?

00:00:07.450 --> 00:00:09.090
What situations might that be?

00:00:09.090 --> 00:00:10.660
Well, these would
be situations where

00:00:10.660 --> 00:00:12.550
you're trying to get
an estimate on things.

00:00:12.550 --> 00:00:14.758
Where you're trying to--
maybe you have a measurement

00:00:14.758 --> 00:00:17.721
and you want it to be a little
bit less exact to simplify

00:00:17.721 --> 00:00:18.220
things.

00:00:18.220 --> 00:00:20.719
Or you don't trust how
exact the measurement is.

00:00:20.719 --> 00:00:23.260
So here we're going to actually
think about what rounding is.

00:00:23.260 --> 00:00:27.680
And we're going to round each of
these numbers, 36, 34, 35, 26,

00:00:27.680 --> 00:00:28.550
and 12.

00:00:28.550 --> 00:00:31.650
We're going to round each
of them to the nearest 10.

00:00:31.650 --> 00:00:33.750
And I'll give you a
hint of what that means.

00:00:33.750 --> 00:00:36.080
That essentially says take
each of these numbers,

00:00:36.080 --> 00:00:39.940
and find the multiple of
10 that it is closest to.

00:00:39.940 --> 00:00:41.300
So what are multiples of 10?

00:00:41.300 --> 00:00:43.750
Well, 10 times 0
is 0, 10 times 1

00:00:43.750 --> 00:00:48.695
is 10, 20, 30, 40, 50,
60, so on and so forth.

00:00:48.695 --> 00:00:50.320
So I encourage you
to pause this video,

00:00:50.320 --> 00:00:52.300
and just based on what I just
told you, what is the nearest

00:00:52.300 --> 00:00:54.130
multiple of 10 to
each of these numbers?

00:00:54.130 --> 00:00:56.297
Try to think about that.

00:00:56.297 --> 00:00:58.380
Well, to think about it a
little bit deeper, let's

00:00:58.380 --> 00:01:00.550
actually put a number line here.

00:01:00.550 --> 00:01:02.590
I'll put two number
lines over here.

00:01:02.590 --> 00:01:05.050
So we've got some
number lines here.

00:01:05.050 --> 00:01:06.940
And let's think about
where these points

00:01:06.940 --> 00:01:09.350
would sit on this number line.

00:01:09.350 --> 00:01:11.710
So this first number,
36, where does it

00:01:11.710 --> 00:01:13.410
sit on this number line?

00:01:13.410 --> 00:01:15.360
Well, it's between 30 and 40.

00:01:15.360 --> 00:01:18.180
And this little blue mark
is 35, it's halfway between.

00:01:18.180 --> 00:01:21.440
So 36 is going to be a
little higher than that.

00:01:21.440 --> 00:01:25.490
So 36 is going to
be right over here.

00:01:25.490 --> 00:01:28.430
And if we zoom in
between 30 and 40.

00:01:28.430 --> 00:01:33.170
So if we say that this
is 30, and this is 40,

00:01:33.170 --> 00:01:34.650
where is 36 going to be?

00:01:34.650 --> 00:01:36.110
So once again, this is 35.

00:01:36.110 --> 00:01:37.870
36 is one notch above that.

00:01:37.870 --> 00:01:41.700
So 36 is going to
be right over here.

00:01:41.700 --> 00:01:45.190
So if we want to round to the
nearest 10, to the nearest

00:01:45.190 --> 00:01:48.740
multiple of 10, what are
the two possibilities here?

00:01:48.740 --> 00:01:54.230
Well, I could take 36
and I could round up

00:01:54.230 --> 00:01:58.000
to the multiple of 10
above it, which is 40.

00:01:58.000 --> 00:02:02.100
So I could round up to
40, or I could round down

00:02:02.100 --> 00:02:08.160
to the multiple of 10
below it, which is 30.

00:02:08.160 --> 00:02:10.280
And so I need to figure
out which of these numbers

00:02:10.280 --> 00:02:11.600
is it closer to.

00:02:11.600 --> 00:02:14.335
Well, when you just look at
that, even just eyeballing it,

00:02:14.335 --> 00:02:14.960
you can see it.

00:02:14.960 --> 00:02:17.830
But you could also say 36
is only four away from 40,

00:02:17.830 --> 00:02:20.670
and it's six away from
30, it's closer to 40.

00:02:20.670 --> 00:02:22.820
So we are going to round up.

00:02:22.820 --> 00:02:25.240
We are going to round up to 40.

00:02:25.240 --> 00:02:27.460
This is literally
called rounding up.

00:02:27.460 --> 00:02:29.540
Now let's try some of
these other numbers.

00:02:29.540 --> 00:02:31.970
What about 34?

00:02:31.970 --> 00:02:34.126
And I encourage you
to pause the video.

00:02:34.126 --> 00:02:35.500
Think about what
number you would

00:02:35.500 --> 00:02:38.040
get if you were to try to
round it up or round it down,

00:02:38.040 --> 00:02:40.970
and then which one it
is actually closer to.

00:02:40.970 --> 00:02:46.950
Well, 34 is right over
here on this number line,

00:02:46.950 --> 00:02:52.220
where we zoom in, 34
is right over here.

00:02:52.220 --> 00:02:54.170
And we have two options.

00:02:54.170 --> 00:02:57.060
The multiple of
10 above 34-- let

00:02:57.060 --> 00:03:02.920
me do those same colors-- the
multiple of 10 above 34 is 40.

00:03:02.920 --> 00:03:06.809
Multiple of 10 below
34, again, is 30.

00:03:06.809 --> 00:03:08.100
Now, which one is it closer to?

00:03:08.100 --> 00:03:10.780
Well it's only four away from
30, and six away from 40,

00:03:10.780 --> 00:03:12.750
so it's closer to 30.

00:03:12.750 --> 00:03:15.700
So we are going to
round down to 30.

00:03:19.750 --> 00:03:21.280
And notice we went to 30.

00:03:21.280 --> 00:03:22.863
You might say, hey,
when we rounded it

00:03:22.863 --> 00:03:26.280
up the 10's place increased
from 3 to 4, from 30 to 40.

00:03:26.280 --> 00:03:28.020
Maybe when we round
down, the 10's place

00:03:28.020 --> 00:03:30.970
will decrease from
30 to 20, but no, 30

00:03:30.970 --> 00:03:33.210
is the multiple of 10 below 34.

00:03:33.210 --> 00:03:35.460
So when you round
down, you just go--

00:03:35.460 --> 00:03:40.060
you keep the multiple of 10,
but the ones place becomes a 0.

00:03:40.060 --> 00:03:42.220
Now let's try a really
interesting one.

00:03:42.220 --> 00:03:48.165
Let's think about rounding the
number 35 to the nearest 10.

00:03:48.165 --> 00:03:49.790
And first, before we
even try to do it,

00:03:49.790 --> 00:03:51.090
let's think about
the two options.

00:03:51.090 --> 00:03:52.256
Well, we've already seen it.

00:03:52.256 --> 00:03:54.450
35 is sitting right over here.

00:03:54.450 --> 00:03:57.760
On this number line, that
is 35, and once again we

00:03:57.760 --> 00:03:59.200
have two options.

00:03:59.200 --> 00:04:07.270
35, we can round it up to 40,
or we could round it down to 30.

00:04:07.270 --> 00:04:10.430
And I encourage you to pause
the video and think about this.

00:04:10.430 --> 00:04:12.600
Well this one is a
little bit of a conundrum

00:04:12.600 --> 00:04:14.790
because it's five away
from both elements.

00:04:14.790 --> 00:04:17.339
It's five away from 40,
and five away from 30.

00:04:17.339 --> 00:04:19.050
So the mathematical
community has

00:04:19.050 --> 00:04:21.380
decided to define
what to do in the case

00:04:21.380 --> 00:04:23.710
where you have a 5
in the ones place.

00:04:23.710 --> 00:04:27.690
If you have five or more in the
ones place, you will round up.

00:04:27.690 --> 00:04:28.730
This is just a rule.

00:04:28.730 --> 00:04:31.850
Five or more in the ones
place, you round up.

00:04:31.850 --> 00:04:35.450
So 35, you round up to 40.

00:04:35.450 --> 00:04:39.940
Notice, a 6 in the ones
place was five or more.

00:04:39.940 --> 00:04:43.320
So if you're rounding to the
nearest 10, you round up to 40.

00:04:43.320 --> 00:04:49.091
A 4 in the ones place is not 5
or greater, so we rounded down.

00:04:49.091 --> 00:04:50.590
And so this gives
a pretty good clue

00:04:50.590 --> 00:04:52.120
for these other two numbers.

00:04:52.120 --> 00:04:56.230
Let's try-- let's see
what happens with 26.

00:04:56.230 --> 00:04:58.350
26, what are the two options?

00:04:58.350 --> 00:05:00.370
What is a multiple
of 10 above 26,

00:05:00.370 --> 00:05:03.810
and what is a multiple
of 10 below 26.?

00:05:03.810 --> 00:05:08.460
Well, the multiple
of 10 above 26 is 30,

00:05:08.460 --> 00:05:12.400
and the multiple of
10 below 26 is 20.

00:05:12.400 --> 00:05:14.030
So if we round up, we go to 30.

00:05:14.030 --> 00:05:17.290
If we round down, we go to 20.

00:05:17.290 --> 00:05:19.040
Well, if we're rounding
to the nearest 10,

00:05:19.040 --> 00:05:20.130
we look at the 10's place.

00:05:20.130 --> 00:05:20.980
That's what we're
going to round--

00:05:20.980 --> 00:05:22.890
we're going to round
to the nearest 10--

00:05:22.890 --> 00:05:24.500
but then we look
at the ones place.

00:05:24.500 --> 00:05:26.370
The ones place is
going to decide it.

00:05:26.370 --> 00:05:31.510
And we see here this
is 5 or greater.

00:05:31.510 --> 00:05:34.410
Or you could say this is
greater than or equal to 5.

00:05:34.410 --> 00:05:36.460
So we round up.

00:05:36.460 --> 00:05:41.580
26 rounded to the nearest
10, we round up to 30.

00:05:41.580 --> 00:05:44.060
Now what about 12?

00:05:44.060 --> 00:05:46.480
And I think you're
getting the hang of this.

00:05:46.480 --> 00:05:49.750
Well let's think about the
multiple of 10 above 12.

00:05:49.750 --> 00:05:51.810
So we could either
round up to 20.

00:05:51.810 --> 00:05:54.790
So 12 is sitting
right around here.

00:05:54.790 --> 00:05:59.230
We either round up to 20
or we round down to 10.

00:05:59.230 --> 00:06:01.430
Well, if we're going to
round to the nearest 10,

00:06:01.430 --> 00:06:03.590
we have to look
at the ones place.

00:06:03.590 --> 00:06:06.440
We have to look at the
ones place right over here.

00:06:06.440 --> 00:06:09.090
This is less than 5.

00:06:09.090 --> 00:06:11.670
Since it's less than
five, we round down,

00:06:11.670 --> 00:06:13.670
which makes sense because
it's also closer to 10

00:06:13.670 --> 00:06:15.020
than it is to 20.

00:06:15.020 --> 00:06:19.100
So we round down, and
rounding 12 to the nearest 10,

00:06:19.100 --> 00:06:21.610
you actually get 10.


Examples rounding to the nearest 10 and 100

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:02.160
We've got four numbers here.

00:00:02.160 --> 00:00:04.850
What I want to do is try
to round each of these

00:00:04.850 --> 00:00:07.720
to the nearest 10 and
to the nearest hundred.

00:00:07.720 --> 00:00:11.130
So I encourage you to pause the
video and try that right now.

00:00:11.130 --> 00:00:12.360
So let's make two columns.

00:00:12.360 --> 00:00:16.900
Let's make one first
for the nearest 10

00:00:16.900 --> 00:00:22.612
and then make another
column for the nearest 100.

00:00:22.612 --> 00:00:25.120
And let's start with 154.

00:00:25.120 --> 00:00:30.370
So 154, what is the
multiple of 10 above 154?

00:00:30.370 --> 00:00:32.189
Well, it's 160.

00:00:32.189 --> 00:00:37.640
And the multiple of
10 below 154 is 150.

00:00:37.640 --> 00:00:41.950
So we're going to round
up to 160 or down to 150.

00:00:41.950 --> 00:00:44.300
Well, when we're rounding
to the nearest 10,

00:00:44.300 --> 00:00:45.990
we need to look
at the ones place.

00:00:45.990 --> 00:00:48.830
One place to the right of the
place that we're rounding.

00:00:48.830 --> 00:00:51.150
So we look at this
4 in the ones place.

00:00:51.150 --> 00:00:58.320
Since 4 is less than 5,
we round down to 150.

00:00:58.320 --> 00:01:00.400
Now, let's think about
that same number,

00:01:00.400 --> 00:01:05.442
rounding to the nearest hundred,
so 154 to the nearest hundred.

00:01:05.442 --> 00:01:07.650
So now we need to think
about if we were to round up,

00:01:07.650 --> 00:01:10.680
what's the multiple
of 100 above 154?

00:01:10.680 --> 00:01:14.980
160 isn't the multiple of 100
The multiple of 100 above 154

00:01:14.980 --> 00:01:16.550
is 200.

00:01:16.550 --> 00:01:19.490
What's the multiple
of 100 below 154?

00:01:19.490 --> 00:01:22.300
Well, that's going to be 100.

00:01:22.300 --> 00:01:24.860
So if we're going to round
to the nearest hundred-- so

00:01:24.860 --> 00:01:26.260
we look at the hundreds place.

00:01:26.260 --> 00:01:27.850
We'll look one
place to the right

00:01:27.850 --> 00:01:29.750
of that, which is
the tens place.

00:01:29.750 --> 00:01:33.320
If that place is 5 or
greater, we round up.

00:01:33.320 --> 00:01:35.730
If it's less than
5, we round down.

00:01:35.730 --> 00:01:39.272
Well, this is clearly 5
or greater so we round up.

00:01:39.272 --> 00:01:40.230
So this is interesting.

00:01:40.230 --> 00:01:42.720
When we rounded to the
nearest 10, since we had a 4

00:01:42.720 --> 00:01:44.710
in the ones place,
we rounded down.

00:01:44.710 --> 00:01:46.660
But when rounded to
the nearest hundreds,

00:01:46.660 --> 00:01:51.760
since we had a 5 in the tens
place, we rounded up to 200.

00:01:51.760 --> 00:01:52.960
Let's do some more of these.

00:01:52.960 --> 00:01:53.770
This is fun.

00:01:53.770 --> 00:02:00.270
So 4,674.

00:02:00.270 --> 00:02:08.110
The multiple of 10
above that is 4,680.

00:02:08.110 --> 00:02:13.620
The multiple of 10
below that, 4,670.

00:02:13.620 --> 00:02:16.560
Remember, we're concerned
only with the multiple of 10.

00:02:16.560 --> 00:02:19.000
So do we round up or down?

00:02:19.000 --> 00:02:22.400
Well, we're thinking about
rounding the tens place.

00:02:22.400 --> 00:02:25.520
So that's why it's either going
to be an 8 if we round up,

00:02:25.520 --> 00:02:27.380
or a 7 if we round down.

00:02:27.380 --> 00:02:30.330
To figure that out, we
look at the ones place.

00:02:30.330 --> 00:02:32.440
If the ones place is 5
or greater, we round up.

00:02:32.440 --> 00:02:34.410
If it's less than
5, we round down.

00:02:34.410 --> 00:02:41.053
It's, once again, less than
5, so we round down to 4,670.

00:02:41.053 --> 00:02:43.344
Now let's round the same
number to the nearest hundred.

00:02:46.270 --> 00:02:48.610
What's the multiple
of 100 below this?

00:02:48.610 --> 00:02:52.900
Well, the multiple of
100 below this is 4,600.

00:02:52.900 --> 00:02:57.510
The multiple of 100
above this is 4,700.

00:02:57.510 --> 00:02:59.780
If we're trying to think
about rounding to the nearest

00:02:59.780 --> 00:03:02.980
hundred, we want to
look at the tens place.

00:03:02.980 --> 00:03:09.840
The tens place is 5 or greater,
so we round up to 4,700.

00:03:09.840 --> 00:03:13.790
Now let's tackle 9,995.

00:03:13.790 --> 00:03:15.297
And once again,
always try to pause

00:03:15.297 --> 00:03:16.880
these, if you haven't
done so already,

00:03:16.880 --> 00:03:19.020
to try to do this on your own.

00:03:19.020 --> 00:03:22.890
So 9,995.

00:03:22.890 --> 00:03:25.880
What is the multiple
of 10 below this.

00:03:25.880 --> 00:03:30.180
Well the multiples of
10 below this is 9,990.

00:03:30.180 --> 00:03:32.400
And what's the multiple
of 10 above this?

00:03:32.400 --> 00:03:38.785
Well, if you increase this by
10, you actually get to 10,000.

00:03:38.785 --> 00:03:41.160
So you might say, hey, well
isn't this a multiple of 100,

00:03:41.160 --> 00:03:42.720
and actually this is a
multiple of a thousand--

00:03:42.720 --> 00:03:44.280
it's also a multiple of 10,000.

00:03:44.280 --> 00:03:46.260
It's all of those,
but the multiple

00:03:46.260 --> 00:03:50.610
of 10 right above
9,995 is 10,000.

00:03:50.610 --> 00:03:53.090
You just have to add a little
bit to this to get to 10,000.

00:03:53.090 --> 00:03:56.990
Or the multiple of 10
below it is clearly 9,990.

00:03:56.990 --> 00:04:00.560
10 more than that
gets you to 10,000.

00:04:00.560 --> 00:04:01.990
So how do we around this?

00:04:01.990 --> 00:04:04.880
Well, once again, if we're
rounding to the nearest 10,

00:04:04.880 --> 00:04:07.300
we want to look
at the ones place.

00:04:07.300 --> 00:04:13.890
The ones place is 5 or greater
so we round up to 10,000.

00:04:13.890 --> 00:04:16.450
Now, let's round to
the nearest hundreds.

00:04:16.450 --> 00:04:18.260
You should be getting
used to this now.

00:04:18.260 --> 00:04:21.529
To the nearest hundreds, what
is the hundreds below this?

00:04:21.529 --> 00:04:26.120
Well, it's 9,900.

00:04:26.120 --> 00:04:29.590
What is 100 above this, the
next multiple of 100 above this?

00:04:29.590 --> 00:04:35.230
Well, if you add 100 to 9,900
you once again get 10,000.

00:04:35.230 --> 00:04:37.564
So how do we decide whether
to round up or down?

00:04:37.564 --> 00:04:39.480
Well, we don't look at
the ones place anymore.

00:04:39.480 --> 00:04:41.040
We're now rounding to
the nearest hundred.

00:04:41.040 --> 00:04:42.831
So we want to round to
the nearest hundred.

00:04:42.831 --> 00:04:44.850
To do that, we look
one place to the right,

00:04:44.850 --> 00:04:46.730
which is the tens place.

00:04:46.730 --> 00:04:49.140
If this is 5 or
greater, we round up.

00:04:49.140 --> 00:04:51.240
If it's less than
5, we round down.

00:04:51.240 --> 00:04:56.830
It is 5 or greater so once
again we round up to 10,000.

00:04:56.830 --> 00:05:06.590
Now we have one more, 8,346.

00:05:06.590 --> 00:05:12.860
The multiple of 10
below it is 8,340.

00:05:12.860 --> 00:05:19.550
Multiple of 10
above that is 8,350.

00:05:19.550 --> 00:05:22.000
If we're going to round
to the nearest 10,

00:05:22.000 --> 00:05:24.120
we need to look
at the ones place.

00:05:24.120 --> 00:05:28.500
The ones place is 5 or
greater, so we round up.

00:05:28.500 --> 00:05:30.672
Now, let's round to
the nearest hundred.

00:05:30.672 --> 00:05:40.640
8,346, the multiple of
100 above this is 8,400.

00:05:40.640 --> 00:05:45.179
The multiple of 100
below this is 8,300.

00:05:45.179 --> 00:05:47.095
Notice we're rounding
to the nearest hundreds.

00:05:47.095 --> 00:05:50.710
If we were to round up, the
hundreds place becomes a 4.

00:05:50.710 --> 00:05:53.030
If we round down, the
hundreds place stays at 3,

00:05:53.030 --> 00:05:54.997
but it's followed by zeroes.

00:05:54.997 --> 00:05:56.830
If we want to round to
the nearest hundreds,

00:05:56.830 --> 00:05:59.170
we need to look
at the tens place.

00:05:59.170 --> 00:06:05.189
The tens place here is less than
5, so we round down to 8,300.

00:06:05.189 --> 00:06:07.230
Notice, again, when we
round to the nearest tens,

00:06:07.230 --> 00:06:10.000
we rounded up to 8,350.

00:06:10.000 --> 00:06:11.620
When we round to the
nearest hundreds,

00:06:11.620 --> 00:06:15.120
we rounded down to 8,300.


Institutional roles in issuing and processing credit cards

WEBVTT
Kind: captions
Language: en

00:00:00.818 --> 00:00:02.873
Voiceover: What I want to
do in this video is try

00:00:02.873 --> 00:00:04.781
to give a reasonable understanding

00:00:04.781 --> 00:00:08.947
of the different players
involved that issue and process

00:00:08.947 --> 00:00:10.537
your credit cards.

00:00:10.537 --> 00:00:13.835
Let's start off with the processors.

00:00:16.003 --> 00:00:18.089
Sometimes you could say that the network,

00:00:18.089 --> 00:00:20.089
or the processors are
the people that maintain

00:00:20.089 --> 00:00:22.089
the credit card networks.

00:00:22.089 --> 00:00:29.453
Examples of those are Visa, Mastercard,

00:00:29.453 --> 00:00:33.188
American Express, Discover.

00:00:33.188 --> 00:00:36.388
What they do is they,
essentially, maintain networks

00:00:36.388 --> 00:00:38.930
of IT and policies that connect

00:00:38.930 --> 00:00:40.187
a bunch of banks together.

00:00:40.187 --> 00:00:43.470
For just the sake of this
video, we'll do very simple.

00:00:43.470 --> 00:00:48.836
Let's say that this is
network 1, maybe that's Visa.

00:00:49.089 --> 00:00:51.125
Maybe this right here is network 2.

00:00:51.125 --> 00:00:53.959
This right here could be Mastercard.

00:00:56.136 --> 00:00:57.926
Right now the networks are
just circles, but you'll see

00:00:57.926 --> 00:01:01.658
that they're networks as I
build out this explanation.

00:01:01.658 --> 00:01:04.977
Let's say that I'm some bank out there.

00:01:05.191 --> 00:01:08.730
Let me call myself bank A.

00:01:10.856 --> 00:01:12.792
I decide that, you know
what, it would be good

00:01:12.792 --> 00:01:15.393
for my business for me
to issue a credit card.

00:01:15.393 --> 00:01:18.124
I could extend credit to my customers,

00:01:18.124 --> 00:01:20.262
they'll pay me interest,
maybe I'll make some fees

00:01:20.262 --> 00:01:23.524
off of that, and it'll be
good business for my bank.

00:01:23.524 --> 00:01:26.389
I go up to Visa and I say,
"Hey, can I be a member

00:01:26.389 --> 00:01:27.427
"of your network?"

00:01:27.427 --> 00:01:30.455
Visa has some policies and
if you're a legitimate bank

00:01:30.455 --> 00:01:31.792
and you agree to all those policies,

00:01:31.792 --> 00:01:34.858
you'll become a member of that network.

00:01:34.858 --> 00:01:36.762
I've joined the network
and I'm, of course,

00:01:36.762 --> 00:01:38.347
not the only person on that network.

00:01:38.347 --> 00:01:41.057
There's tons of other
banks on that network.

00:01:41.057 --> 00:01:45.261
That could be bank B,
this could be bank C,

00:01:45.261 --> 00:01:47.845
this could be bank D.

00:01:47.845 --> 00:01:50.124
Of course, each of these are
networks, so they all have

00:01:50.124 --> 00:01:52.259
their own member banks on them.

00:01:52.259 --> 00:01:56.225
That's Mastercard's network right there.

00:01:57.333 --> 00:02:01.192
In this situation, let's say
I'm a customer of bank A.

00:02:01.192 --> 00:02:02.737
They say, "You want a credit
card?" and I say, "Sure.

00:02:02.737 --> 00:02:05.405
"That'll be convenient, I
don't like carrying cash

00:02:05.405 --> 00:02:07.572
"in my pocket, so give me a credit card."

00:02:07.572 --> 00:02:11.822
They'll issue a credit card
that looks something like this.

00:02:11.822 --> 00:02:15.259
The credit card, I think
we've all seen credit cards,

00:02:15.259 --> 00:02:18.892
It'll say Bank A really big up at the top.

00:02:18.904 --> 00:02:23.459
Bank A, I'll have a credit
card number that's unique

00:02:23.459 --> 00:02:27.327
to me, my credit card number,
my name will be there,

00:02:27.327 --> 00:02:30.655
some type of expiration
date, and then here

00:02:30.655 --> 00:02:32.926
in the bottom right corner,
they're going to say

00:02:32.926 --> 00:02:34.657
what network I'm a part of.

00:02:34.657 --> 00:02:37.453
In this case, it would be Visa.

00:02:37.527 --> 00:02:39.989
A credit card issued over
here would say Mastercard

00:02:39.989 --> 00:02:41.260
or if it was American Express, they'd put

00:02:41.260 --> 00:02:43.194
American Express here, or
maybe there's some type

00:02:43.194 --> 00:02:44.822
of a hologram.

00:02:44.822 --> 00:02:46.822
Great, I have a credit card here.

00:02:46.822 --> 00:02:48.155
I think we all have a general sense.

00:02:48.155 --> 00:02:50.925
I could use it and then
I'll build a balance

00:02:50.925 --> 00:02:53.074
and then in the future I
could pay off that balance

00:02:53.074 --> 00:02:55.993
to this bank or I could carry a balance

00:02:55.993 --> 00:02:58.089
and they'll charge me
interest, which is usually

00:02:58.089 --> 00:02:59.821
reasonably high interest,
so I want to pay it off

00:02:59.821 --> 00:03:02.259
fairly quickly, but how
does this actually work

00:03:02.259 --> 00:03:04.905
in the context of a network?

00:03:04.905 --> 00:03:08.158
Let's say I go to the local grocery store.

00:03:08.194 --> 00:03:10.322
Let me draw that in orange.

00:03:10.322 --> 00:03:13.404
Let's say I go to some
grocery store over here.

00:03:13.404 --> 00:03:15.573
I'll say G for grocery.

00:03:15.573 --> 00:03:17.927
I buy $100 worth of
groceries and I want to pay

00:03:17.927 --> 00:03:20.738
with my newly issued credit card.

00:03:20.738 --> 00:03:21.489
Let me write this down.

00:03:21.489 --> 00:03:23.994
This is the issuing, issuer.

00:03:23.994 --> 00:03:25.738
This is the issuing bank.

00:03:25.738 --> 00:03:27.593
I go to the grocery store,
I say, "Hey, I'd like to pay

00:03:27.593 --> 00:03:29.259
"with a credit card."

00:03:29.259 --> 00:03:31.327
The grocery store, if
they accept credit cards,

00:03:31.327 --> 00:03:34.904
they need to have some
relationship with another bank

00:03:34.904 --> 00:03:37.260
someplace on this Visa
network, in order for them

00:03:37.260 --> 00:03:39.403
to accept a Visa card.

00:03:39.403 --> 00:03:42.738
Let's say that they have
a relationship with bank B

00:03:42.738 --> 00:03:43.987
over here.

00:03:43.987 --> 00:03:46.407
This would be the merchant
bank, or we could say

00:03:46.407 --> 00:03:50.064
the retailer's bank, or it's
often in credit card lingo called

00:03:50.064 --> 00:03:52.898
the acquiring bank or the acquirer.

00:03:52.898 --> 00:03:55.192
You might wonder why is
it called the acquirer?

00:03:55.192 --> 00:03:57.067
It's called the acquirer
because this is the player

00:03:57.067 --> 00:03:59.594
that goes out and goes
to each of the merchants

00:03:59.594 --> 00:04:02.065
and says, "Hey, right
now you only accept cash

00:04:02.065 --> 00:04:04.069
"or you only accept American Express.

00:04:04.069 --> 00:04:06.067
"Wouldn't it be great if
you also accepted Visa

00:04:06.067 --> 00:04:07.399
"or Mastercard?

00:04:07.399 --> 00:04:10.397
"That way you'll have more
appeal to more customers

00:04:10.397 --> 00:04:13.258
"and it'll be more
convenient for your customers

00:04:13.258 --> 00:04:15.147
"and every time a transaction
happens, we'll just take

00:04:15.147 --> 00:04:17.650
"a little bit of a cut
of that transaction."

00:04:17.650 --> 00:04:20.402
So they go out and acquire
different retailers.

00:04:20.402 --> 00:04:23.660
This was the grocer, maybe bank B goes off

00:04:23.660 --> 00:04:28.129
and acquires the shoemaker, maybe he goes

00:04:28.129 --> 00:04:31.727
and he gets the tailor on the network.

00:04:31.727 --> 00:04:33.261
These are all different
retailers who will now,

00:04:33.261 --> 00:04:34.925
all of a sudden, accept Visa,

00:04:34.925 --> 00:04:39.509
because their merchant bank is a member

00:04:39.509 --> 00:04:40.511
of the Visa network.

00:04:40.511 --> 00:04:41.527
Likewise, it could've been a member

00:04:41.527 --> 00:04:43.526
of the Mastercard network,
it doesn't matter.

00:04:43.526 --> 00:04:46.785
This is the processor and
this is their network.

00:04:46.785 --> 00:04:51.985
Now, this guy, in this
context, he would accept Visa.

00:04:51.985 --> 00:04:54.388
I would give him my Visa
card and the first process

00:04:54.388 --> 00:04:57.099
is called authorization.

00:05:01.998 --> 00:05:04.852
That's literally to check
whether I'm good for the money,

00:05:04.852 --> 00:05:08.451
whether this card is
valid to buy $100 worth

00:05:08.451 --> 00:05:10.118
of groceries.

00:05:10.118 --> 00:05:12.491
When I swipe the card or
when the grocer swipes

00:05:12.491 --> 00:05:14.852
the card, it's going to send a message

00:05:14.852 --> 00:05:17.919
from that little unit, from
the point of sale unit,

00:05:17.919 --> 00:05:20.319
to the acquiring bank.

00:05:20.319 --> 00:05:22.719
That's going to be forwarded to Visa.

00:05:22.719 --> 00:05:24.941
Then Visa will say, "Oh,
that's bank A's card,"

00:05:24.941 --> 00:05:26.941
and they'll give a number to bank A

00:05:26.941 --> 00:05:29.691
on their own proprietary network.

00:05:29.691 --> 00:05:31.523
Then bank A will look into
their database and say,

00:05:31.523 --> 00:05:34.607
"Oh yeah, Sal's got $1,000
of credit, he hasn't used

00:05:34.607 --> 00:05:36.025
"any of it, he is good for it.

00:05:36.025 --> 00:05:37.718
"I authorize the transaction."

00:05:37.718 --> 00:05:40.025
That message goes back through the network

00:05:40.025 --> 00:05:43.394
to bank B, so then we get authorized.

00:05:43.394 --> 00:05:46.227
Then the transaction goes
forward and eventually,

00:05:46.227 --> 00:05:49.649
as you could imagine,
you can't just authorize

00:05:49.649 --> 00:05:54.556
a transaction and then I
walk away with the groceries.

00:05:54.645 --> 00:05:57.115
At some point, this guy here expects

00:05:57.115 --> 00:06:00.849
to get his money back for
giving me the groceries.

00:06:00.849 --> 00:06:03.144
He expects to get $100 back.

00:06:03.144 --> 00:06:07.316
That $100 is going to come from bank A,

00:06:07.316 --> 00:06:09.393
but he's not going to get a complete $100,

00:06:09.393 --> 00:06:11.984
because obviously, each of these players,

00:06:11.984 --> 00:06:13.726
they're providing a service.

00:06:13.726 --> 00:06:15.894
This guy, he's plugged into the network

00:06:15.894 --> 00:06:18.643
and he's offering credit.

00:06:22.859 --> 00:06:25.342
The network operator or
the processor is offering

00:06:25.342 --> 00:06:29.989
their network and there's other services

00:06:29.989 --> 00:06:32.125
they might provide, different
security mechanisms.

00:06:32.125 --> 00:06:35.061
They say, "Sal lives in
Chicago, but all of a sudden,

00:06:35.061 --> 00:06:41.335
"he's buying $100 worth
of groceries in Salzburg

00:06:41.335 --> 00:06:45.057
"or someplace that seems unlikely."

00:06:45.057 --> 00:06:46.592
Then it might send some
type of a warning trigger,

00:06:46.592 --> 00:06:48.754
so people might have their
own security mechanisms.

00:06:48.754 --> 00:06:50.792
They're all providing a service.

00:06:50.792 --> 00:06:53.060
This guy is going out
there, he might be providing

00:06:53.060 --> 00:06:55.919
the actual point of sale
terminals, the actual network,

00:06:55.919 --> 00:06:59.737
so they're all going to get a
little bit of a cut of things.

00:06:59.737 --> 00:07:04.371
Out of the $100, I got
$100 worth of groceries.

00:07:09.520 --> 00:07:12.188
There'll be a 2%, and it's not always 2%,

00:07:12.188 --> 00:07:16.417
that's a round number,
but it also is a ballpark,

00:07:16.417 --> 00:07:19.405
not completely outlandish,
relative to what tends

00:07:19.405 --> 00:07:20.856
to be the case.

00:07:20.856 --> 00:07:26.253
Of that $100 that this guy could've gotten

00:07:26.253 --> 00:07:29.818
for his groceries, he has to pay a 2% ...

00:07:31.429 --> 00:07:32.349
Yeah, let's write it that way.

00:07:32.349 --> 00:07:34.847
He's got to pay a 2%, or in this case $2,

00:07:34.847 --> 00:07:36.791
that's 2% of $100.

00:07:36.791 --> 00:07:51.219
He's got to pay a $2 discount
rate to his acquiring bank.

00:07:53.337 --> 00:07:55.089
You might say, "Gee, the
acquirer, that's great.

00:07:55.089 --> 00:07:59.335
"They get 2% of all of
these guys' transactions,"

00:07:59.335 --> 00:08:00.455
but of course they're
going to have to share it

00:08:00.455 --> 00:08:03.417
with these other people up here.

00:08:03.417 --> 00:08:07.587
Actually, the bulk of
it ends up with bank A.

00:08:07.587 --> 00:08:11.335
Of this $2, and I'm doing
it in roundabout numbers,

00:08:11.335 --> 00:08:14.669
bank A, now we're going
to split up the $2,

00:08:14.669 --> 00:08:18.678
bank A is going to get,
let's just say, $1.70.

00:08:18.678 --> 00:08:20.751
These aren't that far off
from what the real numbers

00:08:20.751 --> 00:08:22.919
might be and they change
and they depend on the banks

00:08:22.919 --> 00:08:24.391
and the network and all of that.

00:08:24.391 --> 00:08:26.457
The networks might change their rates.

00:08:26.457 --> 00:08:31.189
$1.70 goes to bank A.

00:08:31.189 --> 00:08:34.420
The issuing bank, besides now that I have

00:08:34.420 --> 00:08:36.335
a credit balance, it'll be
able to charge interest on it.

00:08:36.335 --> 00:08:40.131
It also got $1.70 for that transaction.

00:08:40.131 --> 00:08:44.821
That $1.70 of the $2, this
is called an interchange fee.

00:08:44.925 --> 00:08:48.154
This right here is an interchange fee.

00:08:50.537 --> 00:08:54.288
It generally gets set by
the individual networks.

00:08:54.288 --> 00:08:56.803
Although, the networks don't
share that interchange fee.

00:08:56.803 --> 00:08:58.956
They just say, "Our standard
interchange fee is X%

00:08:58.956 --> 00:09:02.801
"of transactions plus $0.10,"
and that's what bank B

00:09:02.801 --> 00:09:04.467
is going to pay to bank A.

00:09:04.467 --> 00:09:07.214
It's essentially bank A's
cut of the discount rate,

00:09:07.214 --> 00:09:10.629
of the $2 this guy is charging that guy.

00:09:10.629 --> 00:09:13.047
Then, the network, they make their money

00:09:13.047 --> 00:09:15.046
in several ways, but in
general, they make money

00:09:15.046 --> 00:09:16.848
off of every transaction, as well.

00:09:16.848 --> 00:09:20.046
In this situation, they
make roughly about 1000th

00:09:20.046 --> 00:09:22.714
of the transaction or .1%

00:09:22.714 --> 00:09:26.447
In this example, $0.10
of this discount rate

00:09:26.447 --> 00:09:32.516
that this guy charged
would go to the processor

00:09:34.916 --> 00:09:36.582
or the network.

00:09:36.582 --> 00:09:38.519
Every time you transact,
the processor gets

00:09:38.519 --> 00:09:41.649
a small fraction of your actual purchase.

00:09:41.649 --> 00:09:44.527
Then, this guy will be left with 30 -

00:09:44.527 --> 00:09:45.157
Well, let's see.

00:09:45.157 --> 00:09:46.940
$1.70, $0.10, $1.80.

00:09:46.940 --> 00:09:48.938
We're coming from $2, this
guy's going to be left

00:09:48.938 --> 00:09:50.461
with $0.20.

00:09:50.461 --> 00:09:52.327
When the whole transaction gets settled,

00:09:52.327 --> 00:09:54.190
which essentially means
everyone gets the money

00:09:54.190 --> 00:09:58.595
they need to get, this bank
is going to send Visa's

00:09:58.595 --> 00:10:01.940
settlement bank $100 minus the $1.70

00:10:01.940 --> 00:10:04.938
that it gets to keep as
part of its interchange fee.

00:10:04.938 --> 00:10:07.794
It's going to send Visa, what is that,

00:10:07.794 --> 00:10:14.023
that's $98.30 to Visa.

00:10:14.023 --> 00:10:17.605
Visa will keep $0.10 of it,
send it to the acquirer,

00:10:17.605 --> 00:10:23.823
so the acquirer is going to get $98.20.

00:10:23.994 --> 00:10:25.856
Then the acquirer is going
to keep $0.20 for itself

00:10:25.856 --> 00:10:30.991
and give the retailer $98.

00:10:30.991 --> 00:10:32.460
My numbers aren't exact,
but I want to give you

00:10:32.460 --> 00:10:35.644
the general idea of how all this works.

00:10:35.994 --> 00:10:37.538
In order for this retailer
to be able to use all

00:10:37.538 --> 00:10:40.759
of this infrastructure out
there, he essentially had to pay

00:10:40.759 --> 00:10:43.008
2% of the actual transaction.

00:10:43.008 --> 00:10:44.935
That's always not going
to be 2%, but it gives you

00:10:44.935 --> 00:10:46.760
a nice, round figure.

00:10:46.760 --> 00:10:49.204
This guy benefits because
he gets access to a network,

00:10:49.204 --> 00:10:51.427
it's convenient for the customers.

00:10:51.427 --> 00:10:53.604
This guy, obviously, is
getting some type of fee.

00:10:53.604 --> 00:10:56.534
The more retailers he signs
on, or the more retailers

00:10:56.534 --> 00:10:59.270
he acquires, the more cuts of transactions

00:10:59.270 --> 00:11:00.468
he's going to make.

00:11:00.468 --> 00:11:04.203
Visa makes a small cut on
many, many transactions,

00:11:04.203 --> 00:11:05.534
so that's where they make their money.

00:11:05.534 --> 00:11:07.342
They obviously have to
use some of that money

00:11:07.342 --> 00:11:09.869
to support all of this infrastructure.

00:11:09.869 --> 00:11:13.135
Then bank A is going to
make that interchange fee,

00:11:13.135 --> 00:11:15.676
which was the bulk of that discount rate,

00:11:15.676 --> 00:11:17.936
that retailer discount
rate, not related at all

00:11:17.936 --> 00:11:20.202
to the federal funds discount rate.

00:11:20.202 --> 00:11:22.469
Then, of course, they
extended credit to me,

00:11:22.469 --> 00:11:24.602
so that $100 might not
be paid immediately.

00:11:24.602 --> 00:11:27.202
They might be able to charge me 15-20%

00:11:27.202 --> 00:11:31.426
annualized percentage rate
interest on that money

00:11:31.426 --> 00:11:32.426
until I pay it off.

00:11:32.426 --> 00:11:35.214
Of course I have some
type of minimum balances

00:11:35.214 --> 00:11:35.963
to pay.

00:11:35.963 --> 00:11:38.212
Hopefully that explains
things a little bit.

00:11:38.212 --> 00:11:41.000
I'll see you in the next video.


Introduction to bonds

WEBVTT
Kind: captions
Language: en

00:00:00.480 --> 00:00:01.072
Voiceover: In this video,

00:00:01.072 --> 00:00:04.343
I want to give you a general
idea of what a bond is

00:00:04.343 --> 00:00:06.681
and why a company might even issue them

00:00:06.681 --> 00:00:07.736
in the first place.

00:00:07.736 --> 00:00:09.029
And just at a very high level,

00:00:09.029 --> 00:00:12.207
a bond is essentially a way for someone

00:00:12.207 --> 00:00:14.880
to participate in lending to a company,

00:00:14.880 --> 00:00:16.607
so you're a partial lender,

00:00:16.607 --> 00:00:19.504
partial lender,

00:00:19.996 --> 00:00:20.937
to a company,

00:00:20.937 --> 00:00:22.336
and just to make that more concrete,

00:00:22.336 --> 00:00:24.343
let's imagine some type of company

00:00:24.343 --> 00:00:26.940
that has $10 million in assets,

00:00:26.940 --> 00:00:29.854
so these are its assets right there,

00:00:29.854 --> 00:00:31.288
assets,

00:00:31.827 --> 00:00:35.674
and it has $10 million in assets.

00:00:35.674 --> 00:00:37.681
Let's say just for the sake of simplicity,

00:00:37.681 --> 00:00:40.031
it has no liabilities,

00:00:40.031 --> 00:00:43.155
so all of that value,
all of that $10 million

00:00:43.155 --> 00:00:46.089
is what is owned by the owners,

00:00:46.089 --> 00:00:48.078
or by the equity, this owner's equity,

00:00:48.078 --> 00:00:50.096
so this is $10 million,

00:00:50.096 --> 00:00:53.281
$10 million in equity.

00:00:53.281 --> 00:00:56.720
And if we had, let's
say, a million shares.

00:00:56.720 --> 00:00:57.391
I'll write it down.

00:00:57.391 --> 00:00:59.608
If we have a million shares,

00:00:59.608 --> 00:01:02.342
and if we believe this $10 million number,

00:01:02.342 --> 00:01:07.547
that implies that each share
is worth $10 per share.

00:01:07.547 --> 00:01:09.282
Now let's say this company
is doing really well

00:01:09.282 --> 00:01:10.343
and it wants to expand.

00:01:10.343 --> 00:01:13.800
It wants to increase
its assets by $5 million

00:01:13.800 --> 00:01:16.536
so it can go out and buy
a $5 million factory,

00:01:16.536 --> 00:01:17.605
so it wants,

00:01:17.605 --> 00:01:18.839
let me draw it right here.

00:01:18.839 --> 00:01:23.203
It wants another $5 million in assets

00:01:23.203 --> 00:01:24.607
that it needs to build that factory,

00:01:24.607 --> 00:01:27.270
or essentially a $5 million factory.

00:01:27.270 --> 00:01:28.340
The question is,

00:01:28.340 --> 00:01:30.343
how does it finance it?

00:01:30.343 --> 00:01:33.683
Well, one way is they could
just issue more equity.

00:01:33.683 --> 00:01:36.125
If they're able to get a
price of $10 per share,

00:01:36.125 --> 00:01:40.127
they could issue another 500,000 shares,

00:01:40.127 --> 00:01:47.543
500,000 shares at $10 per share,

00:01:47.543 --> 00:01:49.865
and then that would essentially,

00:01:49.865 --> 00:01:52.395
it would produce $5 million.

00:01:52.395 --> 00:01:54.128
This is scenario one.

00:01:54.128 --> 00:01:57.041
They issue 500,000 shares at $10 a share.

00:01:57.041 --> 00:02:00.861
They now have 1.5 million shares,

00:02:00.861 --> 00:02:03.664
but these new owners
gave them, collectively,

00:02:03.664 --> 00:02:05.477
$5 million dollars,

00:02:05.477 --> 00:02:09.492
so this, the equity
would grow by $5 million.

00:02:09.492 --> 00:02:12.263
We now have 1.5 million shares,

00:02:12.263 --> 00:02:15.600
so this would now be 1.5 million shares,

00:02:15.600 --> 00:02:16.791
not one million,

00:02:16.791 --> 00:02:19.917
and that new money from
these new shareholders

00:02:19.917 --> 00:02:21.789
would go into the asset side,

00:02:21.789 --> 00:02:22.679
and then we would use that

00:02:22.679 --> 00:02:25.829
to actually buy the factory.

00:02:25.829 --> 00:02:28.263
What I just described is
essentially issuing equity,

00:02:28.263 --> 00:02:30.822
or financing via equity.

00:02:30.822 --> 00:02:35.495
Financing via equity,

00:02:35.495 --> 00:02:37.529
or by issuing stock.

00:02:37.529 --> 00:02:39.263
Now, the other way to do it

00:02:39.263 --> 00:02:41.199
is to borrow the money,

00:02:41.199 --> 00:02:42.102
to borrow the money,

00:02:42.102 --> 00:02:44.740
so let me redraw this company.

00:02:44.740 --> 00:02:48.092
I'll leave this up here just
so we can compare the two.

00:02:48.092 --> 00:02:52.573
Once again, we have $10 million of assets.

00:02:52.573 --> 00:02:55.605
That's our $10 million of assets.

00:02:55.605 --> 00:02:59.190
We have $10 million of
equity to start off with,

00:02:59.697 --> 00:03:02.577
$10 million of equity,

00:03:03.424 --> 00:03:06.936
and instead of issuing
stock to get the $5 million,

00:03:06.936 --> 00:03:09.330
we're going to borrow the money

00:03:09.330 --> 00:03:13.198
so we could, we're
essentially issuing debt,

00:03:13.198 --> 00:03:14.075
so we issue,

00:03:14.075 --> 00:03:16.203
we essentially could go to a bank and say,

00:03:16.203 --> 00:03:18.345
"Hey, bank. Can I borrow $5 million?"

00:03:18.345 --> 00:03:21.926
So we would have a $5 million liability,

00:03:21.926 --> 00:03:22.757
it would be debt.

00:03:22.757 --> 00:03:24.421
$5 million of debt,

00:03:24.421 --> 00:03:27.196
and the bank would give
us $5 million of cash

00:03:27.196 --> 00:03:30.400
that we can then go
use to buy our factory.

00:03:30.400 --> 00:03:32.130
So in either situation,

00:03:32.130 --> 00:03:33.733
in either situation,

00:03:33.733 --> 00:03:36.272
the asset side of our
balance sheet looks identical

00:03:36.272 --> 00:03:38.277
or the assets of the
company are identical.

00:03:38.277 --> 00:03:40.009
We had our $10 million of assets,

00:03:40.009 --> 00:03:41.590
and now we have a factory,

00:03:41.590 --> 00:03:42.902
but in this first situation,

00:03:42.902 --> 00:03:46.092
I was able to raise
that money by increasing

00:03:46.092 --> 00:03:47.618
the number of shareholders

00:03:47.618 --> 00:03:49.010
by increasing the number of people

00:03:49.010 --> 00:03:53.662
that I have to split the
profits of this company with.

00:03:53.662 --> 00:03:54.867
In this situation,

00:03:54.867 --> 00:03:57.977
I was able to raise the
money by borrowing it.

00:03:58.700 --> 00:04:01.433
The people that I'm
borrowing this money from,

00:04:01.433 --> 00:04:03.070
the people that I'm borrowing this money,

00:04:03.070 --> 00:04:05.142
this is borrowed money,

00:04:05.834 --> 00:04:07.266
borrowed money.

00:04:07.266 --> 00:04:10.344
They don't get a cut of the
profits of this company.

00:04:10.344 --> 00:04:12.512
What they do is they get paid interest

00:04:12.512 --> 00:04:14.396
on their money that they're lending to us

00:04:14.396 --> 00:04:17.129
before these guys get any profits at all.

00:04:17.129 --> 00:04:19.528
In fact, that interest
is considered an expense,

00:04:19.528 --> 00:04:23.205
so these guys get interest,

00:04:23.729 --> 00:04:24.689
get interest.

00:04:24.689 --> 00:04:26.869
And even if this company
does super, super well,

00:04:26.869 --> 00:04:28.676
and becomes very, very profitable,

00:04:28.676 --> 00:04:31.151
these guys only get their interest.

00:04:31.151 --> 00:04:33.015
Likewise, if the company does really bad

00:04:33.015 --> 00:04:34.183
and these guys suffer,

00:04:34.183 --> 00:04:35.928
as long as the company
doesn't go bankrupt,

00:04:35.928 --> 00:04:38.428
these guys are still going
to get their interest,

00:04:38.428 --> 00:04:41.356
so they're going to be a lot safer than,

00:04:41.356 --> 00:04:43.793
well, they don't get as much of the reward

00:04:43.793 --> 00:04:45.866
as the new equity holders would.

00:04:45.866 --> 00:04:48.019
They also don't get as much of the risk.

00:04:48.019 --> 00:04:49.968
Now, this is just straight up debt,

00:04:49.968 --> 00:04:52.013
and you could just get this from any bank

00:04:52.013 --> 00:04:53.197
if they were willing to.

00:04:53.197 --> 00:04:55.513
If they said, "You're
a good, safe company.

00:04:55.513 --> 00:04:57.610
"We're willing to lend you $5 million."

00:04:57.610 --> 00:05:00.266
But let's say that no bank wants to

00:05:00.266 --> 00:05:02.011
individually take on
that risk, so you say,

00:05:02.011 --> 00:05:05.825
"Hey, instead of borrowing
$5 million from one entity,

00:05:05.825 --> 00:05:09.498
"Why don't I borrow it
from 5,000 entities?"

00:05:09.774 --> 00:05:11.428
What I can do instead,

00:05:12.196 --> 00:05:13.792
instead of borrowing it from one entity,

00:05:13.792 --> 00:05:16.764
I could issue these certificates.
I could issue bonds.

00:05:17.380 --> 00:05:18.990
That's the topic of this video.

00:05:18.990 --> 00:05:20.861
I issue these certificates.

00:05:20.861 --> 00:05:24.528
They have a face value of $1,000.

00:05:24.528 --> 00:05:28.354
$1,000. This is my face value.

00:05:28.354 --> 00:05:29.230
Face value,

00:05:29.230 --> 00:05:33.181
or sometimes you'll hear
the notion of par value,

00:05:34.304 --> 00:05:35.978
of par value,

00:05:35.978 --> 00:05:38.809
and I'll say what interest
I'm going to pay on it,

00:05:38.809 --> 00:05:43.396
so let's say I say it
has a 10% annual coupon,

00:05:44.164 --> 00:05:46.529
annual coupon,

00:05:46.529 --> 00:05:47.335
and it's actually called,

00:05:47.335 --> 00:05:48.726
even though this is the interest,

00:05:48.726 --> 00:05:51.143
I'm essentially going to pay $100 a year.

00:05:51.143 --> 00:05:52.900
It's called a coupon because when they,

00:05:52.900 --> 00:05:54.612
when bonds were first issued,

00:05:54.612 --> 00:05:56.671
they would actually throw
these little coupons

00:05:56.671 --> 00:05:58.695
on the bond itself,

00:05:58.695 --> 00:06:00.627
and the owner of the
certificate could rip off

00:06:00.627 --> 00:06:02.167
or cut off one of these coupons,

00:06:02.167 --> 00:06:05.421
and then go to the person borrowing,

00:06:05.421 --> 00:06:06.995
or the entity borrowing the money,

00:06:06.995 --> 00:06:08.811
and get their actual interest payment.

00:06:08.811 --> 00:06:10.556
That's why it's actually called "coupons",

00:06:10.556 --> 00:06:13.012
but they don't actually
attach those coupons anymore.

00:06:13.012 --> 00:06:14.238
And it has some maturity date,

00:06:14.238 --> 00:06:16.464
the date that not only will
I pay your interest back,

00:06:16.464 --> 00:06:18.402
but I'll pay the entire principle,

00:06:18.402 --> 00:06:19.624
the entire face value,

00:06:19.624 --> 00:06:22.565
so let's say the maturity,

00:06:22.565 --> 00:06:25.633
maturity is in two years,

00:06:25.633 --> 00:06:27.057
is in two years.

00:06:27.057 --> 00:06:28.220
In this situation,

00:06:28.220 --> 00:06:31.158
in order to raise $5 million,

00:06:31.158 --> 00:06:34.014
i'm going to have to issue 5,000 of these

00:06:34.014 --> 00:06:38.173
because 5,000 times 1,000 is 5 million,

00:06:38.173 --> 00:06:41.741
so times 5,000.

00:06:41.741 --> 00:06:45.554
If you wanted to lend
$1,000 to this company

00:06:45.554 --> 00:06:47.126
so that they could expand,

00:06:47.126 --> 00:06:49.058
and if you think 10% is
a good interest rate,

00:06:49.058 --> 00:06:50.422
and it's a safe company,

00:06:50.422 --> 00:06:53.099
you would essentially
buy one of these bonds.

00:06:53.099 --> 00:06:55.668
Maybe you buy it for $1,000,

00:06:55.668 --> 00:06:58.582
and when you buy that bond for $1,000,

00:06:58.582 --> 00:07:01.357
you are essentially lending this company

00:07:01.357 --> 00:07:04.750
that $1,000, and if you
did that 5,000 times,

00:07:04.750 --> 00:07:06.413
or if that happened 5,000 times

00:07:06.413 --> 00:07:07.893
amongst a bunch of different people,

00:07:07.893 --> 00:07:09.458
this company would be able to raise

00:07:09.458 --> 00:07:11.413
its $5 million.

00:07:11.828 --> 00:07:14.465
Now just to be clear how
the actual payments work.

00:07:15.126 --> 00:07:18.549
The coupons tend to
get paid semi-annually,

00:07:18.549 --> 00:07:21.667
so let me draw a little timeline here,

00:07:22.160 --> 00:07:23.784
and this tends to be the case in the US

00:07:23.784 --> 00:07:24.753
and western Europe.

00:07:24.753 --> 00:07:27.324
If this is today.

00:07:27.324 --> 00:07:28.642
This is today.

00:07:28.642 --> 00:07:30.815
This is in 6 months.

00:07:30.815 --> 00:07:33.629
This is in 12 months, or 1 year.

00:07:33.629 --> 00:07:35.658
This is in 18 months,

00:07:36.857 --> 00:07:38.834
and this is in 24 months,

00:07:38.834 --> 00:07:40.314
and I'm only going up to 24 months

00:07:40.314 --> 00:07:43.828
because I said this bond
matures in 24 months.

00:07:43.828 --> 00:07:44.617
What is this,

00:07:44.617 --> 00:07:48.272
if you own, if you hold
this bond, this certificate,

00:07:48.272 --> 00:07:49.783
what do you get?

00:07:49.783 --> 00:07:52.329
Well, it's going to pay you 10% annually,

00:07:52.329 --> 00:07:54.150
so $100 a year.

00:07:54.520 --> 00:07:56.581
$100 per year.

00:07:56.581 --> 00:07:58.891
But they actually pay the
coupons semi-annually,

00:07:58.891 --> 00:08:00.127
so you get $100 a year,

00:08:00.127 --> 00:08:02.636
but you get half of it every 6 months,

00:08:02.636 --> 00:08:05.422
so you're going to get $50 after 6 months.

00:08:05.422 --> 00:08:08.067
You're going to get $50 after 12 months,

00:08:08.067 --> 00:08:09.494
or after another 6 months.

00:08:09.494 --> 00:08:11.116
You're going to get another $50 here.

00:08:11.116 --> 00:08:13.683
You're going to get a final $50 there,

00:08:13.683 --> 00:08:15.693
and they're also going
to have to pay you back

00:08:15.693 --> 00:08:17.338
the original amount of the loan.

00:08:17.338 --> 00:08:20.049
They're also going to have
to pay you the $1,000,

00:08:20.049 --> 00:08:22.288
so that last payment's
going to be the coupon of 50

00:08:22.288 --> 00:08:23.968
plus the $1,000,

00:08:23.968 --> 00:08:25.833
and so you will have
essentially been getting

00:08:25.833 --> 00:08:28.221
this 10% annual interest.

00:08:28.221 --> 00:08:29.611
Now, when the company does this,

00:08:29.611 --> 00:08:31.948
they'll probably have to
issue some type of new bond

00:08:31.948 --> 00:08:32.647
because all of a sudden,

00:08:32.647 --> 00:08:34.116
they have to pay all of these people

00:08:34.116 --> 00:08:36.448
this huge lump sum of money

00:08:36.448 --> 00:08:37.778
if they haven't been able to earn it

00:08:37.778 --> 00:08:38.817
from the factories yet,

00:08:38.817 --> 00:08:41.161
and we could talk about
that in a future video.


Compound interest introduction

WEBVTT
Kind: captions
Language: en

00:00:00.376 --> 00:00:01.471
Male Voice: What I want
to do in this video

00:00:01.471 --> 00:00:06.939
is talk a little bit
about compounding interest

00:00:06.939 --> 00:00:08.425
and then have a little bit of a discussion

00:00:08.425 --> 00:00:12.340
of a way to quickly, kind
of an approximate way,

00:00:12.340 --> 00:00:14.759
to figure out how quickly
something compounds.

00:00:14.759 --> 00:00:16.427
Then we'll actually see how good

00:00:16.427 --> 00:00:18.935
of an approximation this really is.

00:00:18.935 --> 00:00:20.678
Just as a review, let's say I'm running

00:00:20.678 --> 00:00:23.207
some type of a bank and I tell you that I

00:00:23.207 --> 00:00:33.401
am offering 10% interest
that compounds annually.

00:00:33.401 --> 00:00:35.308
That's usually not the
case in a real bank;

00:00:35.308 --> 00:00:37.683
you would probably compound continuously,

00:00:37.683 --> 00:00:39.406
but I'm just going to
keep it a simple example,

00:00:39.406 --> 00:00:41.329
compounding annually.
There are other videos

00:00:41.329 --> 00:00:43.681
on compounding continuously.
This makes the math

00:00:43.681 --> 00:00:46.350
a little simpler. All that
means is that let's say

00:00:46.350 --> 00:00:53.014
today you deposit $100
in that bank account.

00:00:53.014 --> 00:00:56.145
If we wait one year,
and you just keep that

00:00:56.145 --> 00:01:01.473
in the bank account, then
you'll have your $100

00:01:01.473 --> 00:01:04.704
plus 10% on your $100 deposit.

00:01:04.704 --> 00:01:08.973
10% of 100 is going to be another $10.

00:01:08.973 --> 00:01:14.918
After a year you're going to have $110.

00:01:14.918 --> 00:01:17.250
You can just say I added 10% to the 100.

00:01:17.250 --> 00:01:22.382
After two years, or a year
after that first year,

00:01:22.382 --> 00:01:24.981
after two years, you're going to get 10%

00:01:24.981 --> 00:01:28.327
not just on the $100,
you're going to get 10%

00:01:28.327 --> 00:01:32.606
on the $110. 10% on 110 is you're going

00:01:32.606 --> 00:01:36.185
to get another $11, so 10% on 110 is $11,

00:01:36.185 --> 00:01:39.863
so you're going to get 110 ...

00:01:39.863 --> 00:01:42.058
That was, you can imagine,
your deposit entering

00:01:42.058 --> 00:01:45.528
your second year, then
you get plus 10% on that,

00:01:45.528 --> 00:01:47.434
not 10% on your initial deposit.

00:01:47.434 --> 00:01:49.456
That's why we say it compounds.

00:01:49.456 --> 00:01:53.397
You get interest on the
interest from previous years.

00:01:53.397 --> 00:01:57.869
So 110 plus now $11. Every year the amount

00:01:57.869 --> 00:01:59.518
of interest we're getting, if
we don't withdraw anything,

00:01:59.518 --> 00:02:04.532
goes up. Now we have $121.

00:02:04.532 --> 00:02:06.944
I could just keep doing
that. The general way

00:02:06.944 --> 00:02:11.325
to figure out how much you
have after let's say n years

00:02:11.325 --> 00:02:17.326
is you multiply it. I'll use
a little bit of algebra here.

00:02:17.326 --> 00:02:21.727
Let's say this is my original
deposit, or my principle,

00:02:21.727 --> 00:02:25.282
however you want to
view it. After x years,

00:02:25.282 --> 00:02:27.325
so after one year you
would just multiply it ...

00:02:27.325 --> 00:02:31.542
To get to this number right
here you multiply it by 1.1.

00:02:31.542 --> 00:02:32.693
Actually, let me do it this way.

00:02:32.693 --> 00:02:34.442
I don't want to be too abstract.

00:02:34.442 --> 00:02:37.793
Just to get the math here,
to get to this number

00:02:37.793 --> 00:02:40.260
right here, we just multiplied that number

00:02:40.260 --> 00:02:48.101
right there is 100 times 1
plus 10%, or you could say 1.1.

00:02:48.101 --> 00:02:50.125
This number right here is going to be,

00:02:50.125 --> 00:02:55.548
this 110 times 1.1 again.
It's this, it's the 100

00:02:55.548 --> 00:02:59.853
times 1.1 which was
this number right there.

00:02:59.853 --> 00:03:03.187
Now we're going to multiply
that times 1.1 again.

00:03:03.187 --> 00:03:04.780
Remember, where does the 1.1 come from?

00:03:04.780 --> 00:03:13.254
1.1 is the same thing as
100% plus another 10%.

00:03:13.254 --> 00:03:15.851
That's what we're getting.
We have 100% of our

00:03:15.851 --> 00:03:19.188
original deposit plus another 10%,

00:03:19.188 --> 00:03:21.682
so we're multiplying by 1.1.

00:03:21.682 --> 00:03:22.707
Here, we're doing that twice.

00:03:22.707 --> 00:03:24.858
We multiply it by 1.1 twice.

00:03:24.858 --> 00:03:27.856
After three years, how
much money do we have?

00:03:27.856 --> 00:03:31.749
It's going to be, after
three years, we're going

00:03:31.749 --> 00:03:40.771
to have 100 times 1.1 to the
3rd power, after n years.

00:03:40.771 --> 00:03:42.520
We're getting a little abstract here.

00:03:42.520 --> 00:03:47.121
We're going to have 100
times 1.1 to the nth power.

00:03:47.121 --> 00:03:49.997
You can imagine this is
not easy to calculate.

00:03:49.997 --> 00:03:54.074
This was all the situation
where we're dealing with 10%.

00:03:54.074 --> 00:03:57.388
If we were dealing in a
world with let's say it's 7%.

00:03:57.388 --> 00:03:59.854
Let's say this is a
different reality here.

00:03:59.854 --> 00:04:03.395
We have 7% compounding annual interest.

00:04:03.395 --> 00:04:10.052
Then after one year we
would have 100 times,

00:04:10.052 --> 00:04:13.186
instead of 1.1, it would be 100% plus 7%,

00:04:13.186 --> 00:04:19.120
or 1.07. Let's go to 3 years.

00:04:19.120 --> 00:04:21.008
After 3 years, I could do 2 in between,

00:04:21.008 --> 00:04:26.785
it would be 100 times
1.07 to the 3rd power,

00:04:26.785 --> 00:04:29.352
or 1.07 times itself
3 times. After n years

00:04:29.352 --> 00:04:31.600
it would be 1.07 to the nth power.

00:04:31.600 --> 00:04:34.022
I think you get the
sense here that although

00:04:34.022 --> 00:04:36.678
the idea's reasonably
simple, to actually calculate

00:04:36.678 --> 00:04:39.121
compounding interest is
actually pretty difficult.

00:04:39.121 --> 00:04:41.919
Even more, let's say I were to ask you

00:04:41.919 --> 00:04:56.513
how long does it take
to double your money?

00:04:56.513 --> 00:04:59.652
If you were to just use
this math right here,

00:04:59.652 --> 00:05:02.340
you'd have to say, gee, to double my money

00:05:02.340 --> 00:05:05.763
I would have to start with
$100. I'm going to multiply

00:05:05.763 --> 00:05:07.590
that times, let's say whatever, let's say

00:05:07.590 --> 00:05:11.534
it's a 10% interest, 1.1
or 1.10 depending on how

00:05:11.534 --> 00:05:15.675
you want to view it, to
the x is equal to ...

00:05:15.675 --> 00:05:17.281
Well, I'm going to double my money so it's

00:05:17.281 --> 00:05:19.271
going to have to equal to $200.

00:05:19.271 --> 00:05:21.527
Now I'm going to have to solve for x

00:05:21.527 --> 00:05:23.722
and I'm going to have to
do some logarithms here.

00:05:23.722 --> 00:05:25.120
You can divide both sides by 100.

00:05:25.120 --> 00:05:28.924
You get 1.1 to the x is equal to 2.

00:05:28.924 --> 00:05:31.145
I just divided both sides by 100.

00:05:31.145 --> 00:05:33.523
Then you could take the
logarithm of both sides

00:05:33.523 --> 00:05:37.390
base 1.1, and you get x. I'm showing you

00:05:37.390 --> 00:05:39.353
that this is complicated on purpose.

00:05:39.353 --> 00:05:41.186
I know this is confusing. There's multiple

00:05:41.186 --> 00:05:43.118
videos on how to solve these.

00:05:43.118 --> 00:05:47.258
You get x is equal to log base 1.1 of 2.

00:05:47.258 --> 00:05:49.680
Most of us cannot do this in our heads.

00:05:49.680 --> 00:05:51.523
Although the idea's simple, how long will

00:05:51.523 --> 00:05:54.387
it take for me to double
my money, to actually

00:05:54.387 --> 00:05:57.597
solve it to get the exact answer, is not

00:05:57.597 --> 00:06:00.718
an easy thing to do. You
can just keep, if you have

00:06:00.718 --> 00:06:03.459
a simple calculator, you
can keep incrementing

00:06:03.459 --> 00:06:05.797
the number of years until you
get a number that's close,

00:06:05.797 --> 00:06:07.874
but no straightforward way to do it.

00:06:07.874 --> 00:06:11.261
This is with 10%. If
we're doing it with 9.3%,

00:06:11.261 --> 00:06:14.662
it just becomes even more difficult.

00:06:14.662 --> 00:06:16.207
What I'm going to do in the next video

00:06:16.207 --> 00:06:18.065
is I'm going to explain something called

00:06:18.065 --> 00:06:21.292
the Rule of 72, which
is an approximate way

00:06:21.292 --> 00:06:24.128
to figure out how long,
to answer this question,

00:06:24.128 --> 00:06:32.258
how long does it take
to double your money?

00:06:32.258 --> 00:06:34.480
We'll see how good of
an approximation it is

00:06:34.480 --> 00:06:36.633
in that next video.


Basics of estate tax

WEBVTT
Kind: captions
Language: en

00:00:00.745 --> 00:00:01.778
Voiceover: What I want to do in this video

00:00:01.778 --> 00:00:05.697
is think a little bit
about the estate tax.

00:00:05.697 --> 00:00:07.200
Estate tax.

00:00:07.200 --> 00:00:09.281
As the name of the tax implies,

00:00:09.281 --> 00:00:11.609
it is a tax on someone's estate,

00:00:11.609 --> 00:00:13.805
or, when someone passes away,

00:00:13.805 --> 00:00:16.889
it is a tax on what they
want to leave behind

00:00:16.889 --> 00:00:19.072
to whoever they want to leave it to,

00:00:19.072 --> 00:00:20.809
either in their will or in their family,

00:00:20.809 --> 00:00:22.542
or whoever they want to
leave their stuff to.

00:00:22.542 --> 00:00:26.137
Sometimes it's referred
to as an inheritance tax.

00:00:26.137 --> 00:00:29.005
Inheritance tax.

00:00:29.005 --> 00:00:32.608
Sometimes you'll hear it
talked this ways on the news.

00:00:32.608 --> 00:00:34.337
Maybe it's a little bit derisive.

00:00:34.337 --> 00:00:36.602
It's called a death tax.

00:00:36.602 --> 00:00:39.167
A death tax.

00:00:39.167 --> 00:00:42.009
The general idea, let's
say that right now,

00:00:42.009 --> 00:00:46.423
my entire net worth,
I am worth $3,000,000.

00:00:46.423 --> 00:00:49.001
I am worth $3,000,000.

00:00:49.001 --> 00:00:51.079
Then I pass away,

00:00:51.079 --> 00:00:55.735
so this $3,000,000 goes into my estate.

00:00:55.735 --> 00:00:58.079
This is my estate.

00:00:58.079 --> 00:01:00.668
This $3,000,000 could
be all of my savings;

00:01:00.668 --> 00:01:01.872
could be my stock portfolio;

00:01:01.872 --> 00:01:03.672
could be the value of
my land, my real estate;

00:01:03.672 --> 00:01:05.279
everything I own; my car.

00:01:05.279 --> 00:01:07.211
Everything combined is worth $3,000,000.

00:01:07.211 --> 00:01:10.831
It goes into my estate after I pass.

00:01:10.831 --> 00:01:13.269
Let's say I leave everything in my estate

00:01:13.269 --> 00:01:17.244
to my daughter.

00:01:17.244 --> 00:01:20.262
I leave it to my daughter.

00:01:20.262 --> 00:01:24.272
It's at this point that the
estate tax comes into question,

00:01:24.272 --> 00:01:27.143
of how much money will my daughter get?

00:01:27.143 --> 00:01:29.269
It turns out for $3,000,000

00:01:29.269 --> 00:01:33.871
my daughter is exempt for inheritance.

00:01:33.871 --> 00:01:37.875
From an individual, the
first $5,000,000 are exempt.

00:01:37.875 --> 00:01:39.423
In this situation,

00:01:39.423 --> 00:01:42.336
where I'm leaving
$3,000,000 for my daughter,

00:01:42.336 --> 00:01:48.425
she actually will get
the entire $3,000,000.

00:01:48.425 --> 00:01:51.003
If, let's say, I'm even richer than that.

00:01:51.003 --> 00:01:53.925
Let's say that I have $6,000,000.

00:01:53.925 --> 00:01:56.079
Let's say the scenario,
where I have $6,000,000.

00:01:56.079 --> 00:01:59.002
It all goes to my estate.

00:01:59.002 --> 00:02:01.753
It all goes into the
estate after my death,

00:02:01.753 --> 00:02:05.604
and now the first $5,000,000 is exempt.

00:02:05.604 --> 00:02:08.004
Let me write my daughter over here.

00:02:09.188 --> 00:02:12.804
My daughter will get the
first 5,000,000 tax free.

00:02:12.804 --> 00:02:15.136
5,000,000 tax free,

00:02:15.136 --> 00:02:18.672
and then the increment
above that exemption,

00:02:18.672 --> 00:02:21.603
the increment above
what has been excluded,

00:02:21.603 --> 00:02:24.073
will then be taxed at a certain rate,

00:02:24.073 --> 00:02:26.070
and that rate is constantly changing,

00:02:26.070 --> 00:02:27.342
but for the sake of simplicity

00:02:27.342 --> 00:02:29.218
I'm going to go with 35%,

00:02:29.218 --> 00:02:32.803
and that's actually the rate in 2011.

00:02:32.803 --> 00:02:34.754
The rest of the 1,000,000,

00:02:34.754 --> 00:02:41.712
the 1,000,000 taxed at 35%.

00:02:41.712 --> 00:02:45.333
The Federal Government will
tax 35% of the 1,000,000,

00:02:45.333 --> 00:02:50.475
so they will essentially
take 350,000 for themselves.

00:02:50.475 --> 00:02:52.800
350,000 for themselves,

00:02:52.800 --> 00:02:57.291
and my daughter will
be left with 5,650,000,

00:02:57.291 --> 00:02:59.802
because of this 1,000,000
you take out 350,000.

00:02:59.802 --> 00:03:02.739
You have 650,000 left.

00:03:02.739 --> 00:03:04.468
My daughter, in this situation,

00:03:04.468 --> 00:03:06.207
will be left with ...

00:03:09.006 --> 00:03:15.017
Maybe I can write "$5.65 million."

00:03:15.017 --> 00:03:17.517
The Federal Government took 350,000.

00:03:17.517 --> 00:03:19.591
If I am super-rich,

00:03:19.591 --> 00:03:21.991
let's say that I am worth ...

00:03:23.729 --> 00:03:25.078
let me make a number
to make the math easy,

00:03:25.078 --> 00:03:27.207
so I don't have to get a calculator out.

00:03:27.207 --> 00:03:33.909
Let's say that I am worth $1,005,000,000.

00:03:33.909 --> 00:03:35.999
This is my net worth.

00:03:35.999 --> 00:03:40.575
In this situation, the first
5,000,000 will be excluded,

00:03:40.575 --> 00:03:44.142
so my daughter will get the 5,000,000.

00:03:44.142 --> 00:03:45.938
Will get the 5,000,000 directly.

00:03:45.938 --> 00:03:46.999
That will be excluded.

00:03:46.999 --> 00:03:51.268
Then everything above that
will be taxed at the 35%.

00:03:51.268 --> 00:03:55.793
In this situation, you have
$1,000,000,000 taxed at 35%.

00:03:55.793 --> 00:04:01.913
1,000,000,000 at 35%.

00:04:01.913 --> 00:04:05.999
In this scenario, the Federal Government

00:04:05.999 --> 00:04:10.943
will take $350,000,000.

00:04:10.943 --> 00:04:14.000
Would take $350,000,000,
and so that would leave,

00:04:14.000 --> 00:04:18.413
of this billion, $650,000,000
left for my daughter.

00:04:18.413 --> 00:04:21.331
In total, she would get this 650,000,000,

00:04:21.331 --> 00:04:23.809
plus the 5,000,000 that was excluded.

00:04:23.809 --> 00:04:29.201
She would end up with a
total of $655,000,000.

00:04:29.201 --> 00:04:30.803
I wouldn't feel too bad for her.

00:04:30.803 --> 00:04:32.928
She should be pretty okay.

00:04:32.928 --> 00:04:34.834
That's just how the estate tax works.

00:04:34.834 --> 00:04:36.997
These examples I gave,

00:04:36.997 --> 00:04:38.877
the 5,000,000 that is excluded,

00:04:38.877 --> 00:04:42.534
this is for an individual
when they pass away.

00:04:42.534 --> 00:04:44.269
If it's being done as a couple,

00:04:44.269 --> 00:04:46.266
this exemption is actually 10,000,000.

00:04:46.266 --> 00:04:48.751
If, between my wife and I,

00:04:48.751 --> 00:04:52.207
we have $1,005,000,000,

00:04:52.207 --> 00:04:53.664
and let's say I pass away,

00:04:53.664 --> 00:04:55.197
and we own everything collectively,

00:04:55.197 --> 00:04:59.539
she actually gets the extra
joint exemption passed onto her,

00:04:59.539 --> 00:05:01.919
and then if and when she passes away,

00:05:01.919 --> 00:05:05.468
this would be $10,000,000
that will be tax-free.

00:05:05.468 --> 00:05:08.138
In this scenario, if this
is being done as a couple,

00:05:08.138 --> 00:05:10.956
my daughter would get
the entire $6,000,000.


Basics of US income tax rate schedule

WEBVTT
Kind: captions
Language: en

00:00:00.140 --> 00:00:01.556
What I want to do
in this video is

00:00:01.556 --> 00:00:04.270
try to get a good understanding
of how the US federal income

00:00:04.270 --> 00:00:05.950
tax rate schedule
works, and also

00:00:05.950 --> 00:00:08.610
what people mean when
they say tax brackets,

00:00:08.610 --> 00:00:11.190
or what does it mean
to be in a tax bracket.

00:00:11.190 --> 00:00:14.869
So let's say that I make
$100,000, and I'm single,

00:00:14.869 --> 00:00:17.410
and I'm not going to go into
the deductions or anything fancy

00:00:17.410 --> 00:00:17.950
like that.

00:00:17.950 --> 00:00:23.100
So let's say I make
$100,000 in a given year.

00:00:23.100 --> 00:00:25.640
And these numbers will change
as the tax code changes,

00:00:25.640 --> 00:00:28.080
but the general idea
is the same thing,

00:00:28.080 --> 00:00:30.310
although the details
might change.

00:00:30.310 --> 00:00:32.509
So the way the
rate schedule works

00:00:32.509 --> 00:00:39.850
is that the first $8,350 of my
$100,000 will be taxed at 10%.

00:00:39.850 --> 00:00:43.860
So the first $8,350
will be taxed at 10%.

00:00:43.860 --> 00:00:46.430
So I'll be paying, what, that's
pretty easy to calculate--

00:00:46.430 --> 00:00:53.910
I'll pay $835 on
that first $8,350.

00:00:53.910 --> 00:01:02.810
Now, the next $25,600, or
from $8,350 to $33,950,

00:01:02.810 --> 00:01:04.659
that will be taxed at 15%.

00:01:08.070 --> 00:01:12.850
So this amount right over here,
I will have to pay 15% on that.

00:01:12.850 --> 00:01:17.800
And so that the difference
between $33,950 and $8,350

00:01:17.800 --> 00:01:26.250
is $25,600 times 15%.

00:01:26.250 --> 00:01:29.470
I'll calculate it all at
the end using a calculator.

00:01:29.470 --> 00:01:35.930
Now, the next $48,300 is
going to be taxed at 25%.

00:01:35.930 --> 00:01:38.630
So let me draw that over here.

00:01:38.630 --> 00:01:42.210
So the next-- this next
slug right over here

00:01:42.210 --> 00:01:44.990
is going to be taxed at 25%.

00:01:44.990 --> 00:01:50.090
So this is the difference
between $82,250 and $33,950.

00:01:50.090 --> 00:01:52.270
That's $48,300.

00:01:52.270 --> 00:01:57.510
So it's going to be
$48,300 times 25%.

00:01:57.510 --> 00:02:00.990
And then finally, the remainder,
the amount above $82,250,

00:02:00.990 --> 00:02:03.770
since I don't get into the
next bracket above that,

00:02:03.770 --> 00:02:06.240
this part right here is
going to be taxed at 28%.

00:02:11.419 --> 00:02:14.060
And let me get my
trusty calculator out

00:02:14.060 --> 00:02:16.580
to figure out what that is.

00:02:16.580 --> 00:02:18.910
So, if that's going to be
taxed at-- so the difference

00:02:18.910 --> 00:02:22.470
between $100,000 and $82,250.

00:02:22.470 --> 00:02:35.170
So $100,000 minus
$82,250 is $17,750.

00:02:35.170 --> 00:02:43.104
So it is $17,750 times 28%.

00:02:43.104 --> 00:02:44.520
And now I could
use the calculator

00:02:44.520 --> 00:02:46.552
to calculate all of these.

00:02:46.552 --> 00:02:48.510
So it's going to be--
let's do it all at once--

00:02:48.510 --> 00:02:57.910
17,750 times 28%-- so
I'll say that its 0.28--

00:02:57.910 --> 00:03:17.030
plus 48,300 times 25%, 0.25,
plus $25,600 times 15%, 0.15.

00:03:17.030 --> 00:03:22.460
Finally, plus $835.

00:03:22.460 --> 00:03:26.790
I'm going to pay $21,720.

00:03:26.790 --> 00:03:30.230
So the sum of all
of these, in total,

00:03:30.230 --> 00:03:36.694
I'm going to pay-- I already
forgot the number-- $21,720.

00:03:36.694 --> 00:03:39.110
And I want to make sure you
don't have the misconception--

00:03:39.110 --> 00:03:42.960
notice, you only pay the 28%
on the incremental amount

00:03:42.960 --> 00:03:44.310
when you enter that bracket.

00:03:44.310 --> 00:03:48.420
You don't pay this 28%
on the entire $100,000,

00:03:48.420 --> 00:03:51.160
just on the increment
above $80,250.

00:03:51.160 --> 00:03:53.540
You don't pay the 25%
on the entire amount,

00:03:53.540 --> 00:03:57.260
just on the increment
between $33,000 and $82,000.


Annual Percentage Rate (APR) and effective APR

WEBVTT
Kind: captions
Language: en

00:00:00.525 --> 00:00:02.605
Voiceover: Easily the most quoted number

00:00:02.605 --> 00:00:04.691
people give you when they're
publicizing information

00:00:04.691 --> 00:00:07.738
about their credit cards is the APR.

00:00:07.738 --> 00:00:09.691
I think you might guess
or you might already know

00:00:09.691 --> 00:00:12.941
that it stands for annual percentage rate.

00:00:17.971 --> 00:00:19.797
What I want to do in this
video is to understand

00:00:19.797 --> 00:00:22.197
a little bit more detail
in what they actually mean

00:00:22.197 --> 00:00:24.997
by the annual percentage
rate and do a little bit math

00:00:24.997 --> 00:00:28.329
to get the real or the
mathematically or the effective

00:00:28.329 --> 00:00:29.437
annual percentage rate.

00:00:29.437 --> 00:00:31.269
I was actually just
browsing the web and I saw

00:00:31.269 --> 00:00:34.104
some credit card that had
an annual percentage rate

00:00:34.104 --> 00:00:39.771
of 22.9% annual percentage rate,

00:00:39.771 --> 00:00:41.936
but then right next to it, they say

00:00:41.936 --> 00:00:53.098
that we have 0.06274% daily periodic rate,

00:00:54.936 --> 00:01:00.269
which, to me, this right here
tells me that they compound

00:01:00.269 --> 00:01:03.995
the interest on your credit
card balance on a daily basis

00:01:03.995 --> 00:01:06.688
and this is the amount that they compound.

00:01:06.688 --> 00:01:08.197
Where do they get these numbers from?

00:01:08.197 --> 00:01:17.197
If you just take .06274
and multiply by 365 days

00:01:17.197 --> 00:01:21.397
in a year, you should get this 22.9.

00:01:21.397 --> 00:01:22.861
Let's see if we get that.

00:01:22.861 --> 00:01:23.946
Of course this is percentage,

00:01:23.946 --> 00:01:27.352
so this is a percentage here
and this is a percent here.

00:01:27.352 --> 00:01:30.125
Let me get out my trusty
calculator and see if that

00:01:30.125 --> 00:01:31.353
is what they get.

00:01:31.353 --> 00:01:37.991
If I take .06274 -

00:01:37.991 --> 00:01:39.727
Remember, this is a percent,
but I'll just ignore

00:01:39.727 --> 00:01:41.858
the percent sign, so as a
decimal, I would actually add

00:01:41.858 --> 00:01:49.602
two more zeros here, but
.06274 x 365 is equal to,

00:01:49.602 --> 00:01:53.102
right on the money, 22.9%.

00:01:53.102 --> 00:01:54.726
You say, "Hey, Sal,
what's wrong with that?

00:01:54.726 --> 00:01:58.851
"They're charging me .06274% per day,

00:01:58.851 --> 00:02:01.269
"they're going to do
that for 365 days a year,

00:02:01.269 --> 00:02:06.058
"so that gives me 22.9%."

00:02:06.058 --> 00:02:08.858
My reply to you is that
they're compounding

00:02:08.858 --> 00:02:10.125
on a daily basis.

00:02:10.125 --> 00:02:13.858
They're compounding this
number on a daily basis,

00:02:13.858 --> 00:02:16.267
so if you were to give them
$100 and if you didn't have

00:02:16.267 --> 00:02:18.269
to pay some type of a minimum
balance and you just let

00:02:18.269 --> 00:02:22.193
that $100 ride for a year,
you wouldn't just owe them

00:02:22.193 --> 00:02:24.391
$122.9.

00:02:24.391 --> 00:02:26.392
They're compounding this much every day,

00:02:26.392 --> 00:02:29.019
so if I were to write
this as a decimal ...

00:02:29.019 --> 00:02:31.660
Let me just write that as a decimal.

00:02:31.660 --> 00:02:36.993
0.06274%.

00:02:36.993 --> 00:02:44.410
As a decimal this is the
same thing as 0.0006274.

00:02:44.410 --> 00:02:45.854
These are the same thing, right?

00:02:45.854 --> 00:02:54.826
1% is .01, so .06% is .0006 as a decimal.

00:02:54.826 --> 00:02:56.918
This is how much they're
charging every day.

00:02:56.918 --> 00:03:00.326
If you watch the
compounding interest video,

00:03:00.326 --> 00:03:02.076
you know that if you wanted
to figure out how much

00:03:02.076 --> 00:03:06.118
total interest you would be
paying over a total year,

00:03:06.118 --> 00:03:09.293
you would take this number, add it to 1,

00:03:09.993 --> 00:03:19.410
so we have 1., this thing
over here, .0006274.

00:03:19.410 --> 00:03:23.993
Instead of just taking this
and multiplying it by 365,

00:03:23.993 --> 00:03:30.412
you take this number and you
take it to the 365th power.

00:03:30.412 --> 00:03:33.855
You multiply it by itself 365 times.

00:03:33.855 --> 00:03:36.584
That's because if I have $1 in my balance,

00:03:36.584 --> 00:03:39.669
on day 2, I'm going to
have to pay this much x $1.

00:03:39.669 --> 00:03:43.169
1.0006274 x $1.

00:03:43.169 --> 00:03:44.870
On day 2, I'm going to have to pay

00:03:44.870 --> 00:03:48.837
this much x this number again x $1.

00:03:48.837 --> 00:03:49.836
Let me write that down.

00:03:49.836 --> 00:03:58.072
On day 1, maybe I have $1 that I owe them.

00:03:58.072 --> 00:04:06.835
On day 2, it'll be $1 x
this thing, 1.0006274.

00:04:06.835 --> 00:04:14.934
On day 3, I'm going to have to pay 1.00 -

00:04:14.934 --> 00:04:16.066
Actually I forgot a 0.

00:04:16.066 --> 00:04:18.731
06274 x this whole thing.

00:04:18.731 --> 00:04:21.462
On day 3, it'll be $1,
which is the initial amount

00:04:21.462 --> 00:04:27.378
I borrowed, x 1.000, this number, 6274,

00:04:27.378 --> 00:04:29.046
that's just that there and
then I'm going to have to pay

00:04:29.046 --> 00:04:30.712
that much interest on
this whole thing again.

00:04:30.712 --> 00:04:35.732
I'm compounding 1.0006274.

00:04:35.732 --> 00:04:38.879
As you can see, we've kept
the balance for two days.

00:04:38.879 --> 00:04:42.398
I'm raising this to the second
power, by multiplying it

00:04:42.398 --> 00:04:42.999
by itself.

00:04:42.999 --> 00:04:44.378
I'm squaring it.

00:04:44.378 --> 00:04:47.600
If I keep that balance for
365 days, I have to raise it

00:04:47.600 --> 00:04:50.463
to the 365th power and
this is counting any kind

00:04:50.463 --> 00:04:53.332
of extra penalties or
fees, so let's figure out -

00:04:53.332 --> 00:04:56.462
This right here, this number,
whatever it is, this is -

00:04:56.462 --> 00:04:58.734
Once I get this and I subtract 1 from it,

00:04:58.734 --> 00:05:01.932
that is the mathematically
true, that is the effective

00:05:01.932 --> 00:05:02.878
annual percentage rate.

00:05:02.878 --> 00:05:04.878
Let's figure out what that is.

00:05:04.878 --> 00:05:22.598
If I take 1.0006274 and I
raise it to the 365 power,

00:05:22.598 --> 00:05:25.128
I get 1.257.

00:05:25.128 --> 00:05:30.045
If I were to compound
this much interest, .06%

00:05:30.045 --> 00:05:35.992
for 365 days, at the end
of a year or 365 days,

00:05:35.992 --> 00:05:40.655
I would owe 1.257 x my
original principle amount.

00:05:40.655 --> 00:05:47.138
This right here is equal to 1.257.

00:05:47.138 --> 00:05:49.989
I would owe 1.257 x my
original principle amount,

00:05:49.989 --> 00:05:53.138
or the effective interest rate.

00:05:53.138 --> 00:05:55.222
Do it in purple.

00:05:55.222 --> 00:06:01.304
The effective APR, annual percentage rate,

00:06:01.304 --> 00:06:04.121
or the mathematically correct
annual percentage rate

00:06:04.121 --> 00:06:08.388
here is 25.7%.

00:06:08.388 --> 00:06:11.520
You might say, "Hey, Sal,
that's still not too far off

00:06:11.520 --> 00:06:14.470
"from the reported APR,
where they just take

00:06:14.470 --> 00:06:18.720
"this number and multiply
by 365, instead of taking

00:06:18.720 --> 00:06:21.123
"this number and taking
it to the 365 power."

00:06:21.123 --> 00:06:23.722
You're saying, "Hey, this is roughly 23%,

00:06:23.722 --> 00:06:27.321
"this is roughly 26%, it's
only a 3% difference."

00:06:27.321 --> 00:06:30.388
If you look at that
compounding interest video,

00:06:30.388 --> 00:06:32.522
even the most basic one
that I put out there,

00:06:32.522 --> 00:06:34.804
you'll see that every
percentage point really, really,

00:06:34.804 --> 00:06:36.722
really matters, especially
if you're going to carry

00:06:36.722 --> 00:06:38.855
these balances for a long period of time.

00:06:38.855 --> 00:06:39.888
Be very careful.

00:06:39.888 --> 00:06:41.655
In general, you shouldn't
carry any balances

00:06:41.655 --> 00:06:43.272
on your credit cards,
because these are very high

00:06:43.272 --> 00:06:45.522
interest rates and you'll
end up just paying interest

00:06:45.522 --> 00:06:47.994
on purchases you made many, many years ago

00:06:47.994 --> 00:06:51.524
and you've long ago lost all
of the joy of that purchase.

00:06:51.524 --> 00:06:53.355
I encourage you to not even keep balances,

00:06:53.355 --> 00:06:54.855
but if you do keep any balances,

00:06:54.855 --> 00:06:56.926
pay very close attention to this.

00:06:56.926 --> 00:07:00.438
That 22.9% APR is still probably not

00:07:00.438 --> 00:07:02.996
the full effective interest
rate, which might be closer

00:07:02.996 --> 00:07:05.128
to 26% in this example.

00:07:05.128 --> 00:07:07.059
That's before they even
count the penalties

00:07:07.059 --> 00:07:09.438
and the other types of
fees that they might throw

00:07:09.438 --> 00:07:11.533
on top of everything.