WEBVTT

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 --> 00:01:04.703
plus 10% on your $100 deposit.

00:01:04.703 --> 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 --> 00:04:21.007
After 3 years, I could do 2 in between,

00:04:21.007 --> 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.