[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:08.22,Default,,0000,0000,0000,,
Dialogue: 0,0:00:08.22,0:00:11.39,Default,,0000,0000,0000,,In the last video, we talked a\Nlittle bit about compounding
Dialogue: 0,0:00:11.39,0:00:15.48,Default,,0000,0000,0000,,interest. Our example was\Ninterest that compounds
Dialogue: 0,0:00:15.48,0:00:17.83,Default,,0000,0000,0000,,annually, not continuously\Nlike we would
Dialogue: 0,0:00:17.83,0:00:18.79,Default,,0000,0000,0000,,see in a lot of banks.
Dialogue: 0,0:00:18.79,0:00:21.39,Default,,0000,0000,0000,,I'll really just wanted to let\Nyou understand that although
Dialogue: 0,0:00:21.39,0:00:22.29,Default,,0000,0000,0000,,the idea is simple.
Dialogue: 0,0:00:22.29,0:00:25.04,Default,,0000,0000,0000,,Every year you get 10% of the\Nmoney that you started off
Dialogue: 0,0:00:25.04,0:00:25.65,Default,,0000,0000,0000,,with that year.
Dialogue: 0,0:00:25.65,0:00:28.72,Default,,0000,0000,0000,,And it's called compounding\Nbecause the next year you get
Dialogue: 0,0:00:28.72,0:00:31.90,Default,,0000,0000,0000,,money not just on your initial\Ndeposit, but you also get
Dialogue: 0,0:00:31.90,0:00:35.30,Default,,0000,0000,0000,,money or interest on the\Ninterest from previous years.
Dialogue: 0,0:00:35.30,0:00:37.47,Default,,0000,0000,0000,,That's why it's called\Ncompounding interest. And
Dialogue: 0,0:00:37.47,0:00:40.29,Default,,0000,0000,0000,,although that idea is pretty\Nsimple, we saw that the math
Dialogue: 0,0:00:40.29,0:00:41.42,Default,,0000,0000,0000,,can get a little tricky.
Dialogue: 0,0:00:41.42,0:00:44.95,Default,,0000,0000,0000,,If you have a reasonable\Ncalculator, you can solve for
Dialogue: 0,0:00:44.95,0:00:46.87,Default,,0000,0000,0000,,some of these things if\Nyou know how to do it.
Dialogue: 0,0:00:46.87,0:00:50.55,Default,,0000,0000,0000,,But it's nearly impossible to\Nactually do it in your head.
Dialogue: 0,0:00:50.55,0:00:53.64,Default,,0000,0000,0000,,For example, at the end of the\Nlast video, we said if I have
Dialogue: 0,0:00:53.64,0:00:54.70,Default,,0000,0000,0000,,a hundred dollars.
Dialogue: 0,0:00:54.70,0:00:57.86,Default,,0000,0000,0000,,And if I'm compounding at 10%\Na year, that's where this 1
Dialogue: 0,0:00:57.86,0:01:01.35,Default,,0000,0000,0000,,comes from, how long does it\Ntake for me to double my money
Dialogue: 0,0:01:01.35,0:01:02.91,Default,,0000,0000,0000,,and end up with this equation?
Dialogue: 0,0:01:02.91,0:01:06.42,Default,,0000,0000,0000,,And to solve that equation, most\Ncalculators don't have at
Dialogue: 0,0:01:06.42,0:01:08.11,Default,,0000,0000,0000,,log base 1.1.
Dialogue: 0,0:01:08.11,0:01:09.97,Default,,0000,0000,0000,,And I've shown this\Nin other videos.
Dialogue: 0,0:01:09.97,0:01:15.05,Default,,0000,0000,0000,,This you could also say, x is\Nequal to log base 10 of 2,
Dialogue: 0,0:01:15.05,0:01:18.61,Default,,0000,0000,0000,,divided by log base 1.1 of 2.
Dialogue: 0,0:01:18.61,0:01:23.90,Default,,0000,0000,0000,,This is another way to calculate\Nlog base 1.1 of 2.
Dialogue: 0,0:01:23.90,0:01:27.62,Default,,0000,0000,0000,,This should be log\Nbase 10 of 1.1.
Dialogue: 0,0:01:27.62,0:01:29.29,Default,,0000,0000,0000,,I say this because most\Ncalculators have
Dialogue: 0,0:01:29.29,0:01:30.70,Default,,0000,0000,0000,,a log base 10 function.
Dialogue: 0,0:01:30.70,0:01:32.62,Default,,0000,0000,0000,,And this and this\Nare equivalent.
Dialogue: 0,0:01:32.62,0:01:34.32,Default,,0000,0000,0000,,I've proven it in\Nother videos.
Dialogue: 0,0:01:34.32,0:01:36.40,Default,,0000,0000,0000,,So in order to say how long\Ndoes it take to double my
Dialogue: 0,0:01:36.40,0:01:38.02,Default,,0000,0000,0000,,money at 10% a year?
Dialogue: 0,0:01:38.02,0:01:39.69,Default,,0000,0000,0000,,You'd have to put that\Nin your calculator.
Dialogue: 0,0:01:39.69,0:01:41.86,Default,,0000,0000,0000,,And let's try it out.
Dialogue: 0,0:01:41.86,0:01:43.21,Default,,0000,0000,0000,,Let's try it out right here.
Dialogue: 0,0:01:43.21,0:01:46.03,Default,,0000,0000,0000,,We're going to have, 2, and\Nwe're going to take the
Dialogue: 0,0:01:46.03,0:01:56.09,Default,,0000,0000,0000,,logarithm of that, 0.3, divided\Nby 1.1, and the
Dialogue: 0,0:01:56.09,0:01:57.95,Default,,0000,0000,0000,,logarithm of that.
Dialogue: 0,0:01:57.95,0:02:00.44,Default,,0000,0000,0000,,We close the parentheses.
Dialogue: 0,0:02:00.44,0:02:03.71,Default,,0000,0000,0000,,Is equal to 7.27 years.
Dialogue: 0,0:02:03.71,0:02:06.35,Default,,0000,0000,0000,,Roughly 7.3 years.
Dialogue: 0,0:02:06.35,0:02:10.41,Default,,0000,0000,0000,,So this is roughly equal\Nto 7.3 years.
Dialogue: 0,0:02:10.41,0:02:13.28,Default,,0000,0000,0000,,As we saw in the last video,\Nthis is not necessarily
Dialogue: 0,0:02:13.28,0:02:16.22,Default,,0000,0000,0000,,trivial to set up, but even if\Nyou understand the math here,
Dialogue: 0,0:02:16.22,0:02:18.59,Default,,0000,0000,0000,,it's not easy to do\Nthis in your head.
Dialogue: 0,0:02:18.59,0:02:20.72,Default,,0000,0000,0000,,It's literally almost impossible\Nto do in your head.
Dialogue: 0,0:02:20.72,0:02:23.64,Default,,0000,0000,0000,,So what I want to show\Nyou is a rule to
Dialogue: 0,0:02:23.64,0:02:25.40,Default,,0000,0000,0000,,approximate this question.
Dialogue: 0,0:02:25.40,0:02:29.00,Default,,0000,0000,0000,,How long does it take for you\Nto doubles your money?
Dialogue: 0,0:02:29.00,0:02:34.06,Default,,0000,0000,0000,,And that rule is called\Nthe rule of 72.
Dialogue: 0,0:02:34.06,0:02:37.38,Default,,0000,0000,0000,,Sometimes it's the rule of\N70 or the rule of 69.
Dialogue: 0,0:02:37.38,0:02:41.35,Default,,0000,0000,0000,,But rule of 72 tends to be the\Nmost typical one, especially
Dialogue: 0,0:02:41.35,0:02:43.90,Default,,0000,0000,0000,,when you're talking about\Ncompounding over
Dialogue: 0,0:02:43.90,0:02:45.00,Default,,0000,0000,0000,,set periods of time.
Dialogue: 0,0:02:45.00,0:02:46.59,Default,,0000,0000,0000,,Maybe not continuous\Ncompounding.
Dialogue: 0,0:02:46.59,0:02:49.67,Default,,0000,0000,0000,,Continuous compounding you'll\Nget closer to 69 or 70.
Dialogue: 0,0:02:49.67,0:02:51.69,Default,,0000,0000,0000,,But I'll show you what\NI mean in a second.
Dialogue: 0,0:02:51.69,0:02:57.25,Default,,0000,0000,0000,,So to answer that same question,\Nlet's say I have 10%
Dialogue: 0,0:02:57.25,0:02:58.50,Default,,0000,0000,0000,,compounding annually.
Dialogue: 0,0:02:58.50,0:03:06.99,Default,,0000,0000,0000,,
Dialogue: 0,0:03:06.99,0:03:10.47,Default,,0000,0000,0000,,Using the rule of 72, I say how\Nlong does it take for me
Dialogue: 0,0:03:10.47,0:03:11.74,Default,,0000,0000,0000,,to double my money?
Dialogue: 0,0:03:11.74,0:03:16.50,Default,,0000,0000,0000,,I literally take 72, that's why\Nit's called the rule of
Dialogue: 0,0:03:16.50,0:03:18.57,Default,,0000,0000,0000,,72, I divide it by\Nthe percentage.
Dialogue: 0,0:03:18.57,0:03:20.78,Default,,0000,0000,0000,,So the percentage is 10.
Dialogue: 0,0:03:20.78,0:03:22.78,Default,,0000,0000,0000,,It's decimal representation\Nis 0.1.
Dialogue: 0,0:03:22.78,0:03:25.46,Default,,0000,0000,0000,,But it's 10 per 100\Npercentage.
Dialogue: 0,0:03:25.46,0:03:27.49,Default,,0000,0000,0000,,So 72 two divided by 10.
Dialogue: 0,0:03:27.49,0:03:33.38,Default,,0000,0000,0000,,And I get 7.2, it was annual,\Nso 7.2 years.
Dialogue: 0,0:03:33.38,0:03:35.68,Default,,0000,0000,0000,,If this was 10% compounding\Nmonthly, it
Dialogue: 0,0:03:35.68,0:03:37.32,Default,,0000,0000,0000,,would be 7.2 months.
Dialogue: 0,0:03:37.32,0:03:42.21,Default,,0000,0000,0000,,So I got 7.2 years, which is\Npretty darn close to what we
Dialogue: 0,0:03:42.21,0:03:44.91,Default,,0000,0000,0000,,got by doing all that\Nfancy math.
Dialogue: 0,0:03:44.91,0:03:47.46,Default,,0000,0000,0000,,Similarly, let's say that\NI'm compounding--
Dialogue: 0,0:03:47.46,0:03:49.23,Default,,0000,0000,0000,,let's do another problem.
Dialogue: 0,0:03:49.23,0:03:55.42,Default,,0000,0000,0000,,Let's say I have 6% compounding\Nannually.
Dialogue: 0,0:03:55.42,0:04:04.37,Default,,0000,0000,0000,,
Dialogue: 0,0:04:04.37,0:04:11.02,Default,,0000,0000,0000,,Using the rule of 72, I just\Ntake 72 divided by the 6.
Dialogue: 0,0:04:11.02,0:04:14.46,Default,,0000,0000,0000,,And I get 6 goes into\N72, 12 times.
Dialogue: 0,0:04:14.46,0:04:19.06,Default,,0000,0000,0000,,So it'll take 12 years for me\Nto double my money, if I'm
Dialogue: 0,0:04:19.06,0:04:22.35,Default,,0000,0000,0000,,getting 6% on my money\Ncompounding annually.
Dialogue: 0,0:04:22.35,0:04:23.57,Default,,0000,0000,0000,,Let's see if that works out.
Dialogue: 0,0:04:23.57,0:04:26.53,Default,,0000,0000,0000,,So we learned last time, the\Nother way to solve this would
Dialogue: 0,0:04:26.53,0:04:30.49,Default,,0000,0000,0000,,literally be, we would say x,\Nthe answer to this, should be
Dialogue: 0,0:04:30.49,0:04:38.31,Default,,0000,0000,0000,,close to log base anything of\N2 divided by-- this is where
Dialogue: 0,0:04:38.31,0:04:41.15,Default,,0000,0000,0000,,we get the doubling our money\Nfrom, the 2 means 2 times our
Dialogue: 0,0:04:41.15,0:04:45.88,Default,,0000,0000,0000,,money-- divided by log base\Nwhatever this is 10 of.
Dialogue: 0,0:04:45.88,0:04:49.78,Default,,0000,0000,0000,,In this case instead of 1.1\Nit's going to be 1.06.
Dialogue: 0,0:04:49.78,0:04:52.27,Default,,0000,0000,0000,,So you can already see it's a\Nlittle bit more difficult.
Dialogue: 0,0:04:52.27,0:04:54.46,Default,,0000,0000,0000,,Get our calculator out.
Dialogue: 0,0:04:54.46,0:05:04.77,Default,,0000,0000,0000,,So we have 2, log of that,\Ndivided by 1.06, log of that,
Dialogue: 0,0:05:04.77,0:05:08.68,Default,,0000,0000,0000,,is equal to 11.89.
Dialogue: 0,0:05:08.68,0:05:10.50,Default,,0000,0000,0000,,So about 11.9.
Dialogue: 0,0:05:10.50,0:05:14.54,Default,,0000,0000,0000,,So when you do all the fancy\Nmath, we got 11.9.
Dialogue: 0,0:05:14.54,0:05:17.33,Default,,0000,0000,0000,,So once again you see this is\Na pretty good approximation,
Dialogue: 0,0:05:17.33,0:05:22.72,Default,,0000,0000,0000,,and this math is much simpler\Nthan this math.
Dialogue: 0,0:05:22.72,0:05:25.30,Default,,0000,0000,0000,,And I think most of us can\Ndo this in our heads.
Dialogue: 0,0:05:25.30,0:05:27.96,Default,,0000,0000,0000,,So this is actually a good\Nway to impress people.
Dialogue: 0,0:05:27.96,0:05:31.89,Default,,0000,0000,0000,,And just to get a better sense\Nof how good this number 72 is,
Dialogue: 0,0:05:31.89,0:05:35.69,Default,,0000,0000,0000,,what I did is I plotted\Non a spreadsheet.
Dialogue: 0,0:05:35.69,0:05:38.76,Default,,0000,0000,0000,,I said, OK, here's the different\Ninterest rates.
Dialogue: 0,0:05:38.76,0:05:41.18,Default,,0000,0000,0000,,This is the actual time it\Nwould take to double.
Dialogue: 0,0:05:41.18,0:05:45.34,Default,,0000,0000,0000,,So I'm actually using this\Nformula right here to figure
Dialogue: 0,0:05:45.34,0:05:48.90,Default,,0000,0000,0000,,out the precise amount of time\Nit'll take to double.
Dialogue: 0,0:05:48.90,0:05:52.79,Default,,0000,0000,0000,,Let's say this is in years if\Nwe're compounding annually.
Dialogue: 0,0:05:52.79,0:05:55.19,Default,,0000,0000,0000,,So if you're at 1%, it'll\Ntake you 70 years
Dialogue: 0,0:05:55.19,0:05:55.98,Default,,0000,0000,0000,,to double your money.
Dialogue: 0,0:05:55.98,0:05:59.46,Default,,0000,0000,0000,,At 25% it'll only take you a\Nlittle over 3 years to double
Dialogue: 0,0:05:59.46,0:06:00.71,Default,,0000,0000,0000,,your money.
Dialogue: 0,0:06:00.71,0:06:02.96,Default,,0000,0000,0000,,
Dialogue: 0,0:06:02.96,0:06:10.87,Default,,0000,0000,0000,,This is the correct-- and\NI'll do this in blue--
Dialogue: 0,0:06:10.87,0:06:11.97,Default,,0000,0000,0000,,number right here.
Dialogue: 0,0:06:11.97,0:06:13.22,Default,,0000,0000,0000,,So this is actual.
Dialogue: 0,0:06:13.22,0:06:19.57,Default,,0000,0000,0000,,
Dialogue: 0,0:06:19.57,0:06:21.31,Default,,0000,0000,0000,,And I plotted it here, too.
Dialogue: 0,0:06:21.31,0:06:24.45,Default,,0000,0000,0000,,If you look at the blue line,\Nthat's the actual.
Dialogue: 0,0:06:24.45,0:06:26.14,Default,,0000,0000,0000,,I didn't plot all of them.
Dialogue: 0,0:06:26.14,0:06:28.60,Default,,0000,0000,0000,,I think I started at maybe 4%.
Dialogue: 0,0:06:28.60,0:06:32.56,Default,,0000,0000,0000,,So if you look at 4%, it\Ntakes you 17.6 years
Dialogue: 0,0:06:32.56,0:06:33.37,Default,,0000,0000,0000,,to double your money.
Dialogue: 0,0:06:33.37,0:06:37.36,Default,,0000,0000,0000,,So 4%, it takes 17.6 years\Nto double your money.
Dialogue: 0,0:06:37.36,0:06:39.45,Default,,0000,0000,0000,,So that's that dot right\Nthere on the blue.
Dialogue: 0,0:06:39.45,0:06:46.27,Default,,0000,0000,0000,,At 5% percent, it takes you 14\Nyears to double your money.
Dialogue: 0,0:06:46.27,0:06:48.20,Default,,0000,0000,0000,,And so this should also give you\Nan appreciation that every
Dialogue: 0,0:06:48.20,0:06:50.78,Default,,0000,0000,0000,,percentage really does matter\Nwhen you're talking about
Dialogue: 0,0:06:50.78,0:06:54.49,Default,,0000,0000,0000,,compounding interest. When it\Ntakes 2%, it takes you 35
Dialogue: 0,0:06:54.49,0:06:55.31,Default,,0000,0000,0000,,years to double your money.
Dialogue: 0,0:06:55.31,0:06:57.49,Default,,0000,0000,0000,,1% takes you 70 years.
Dialogue: 0,0:06:57.49,0:07:00.90,Default,,0000,0000,0000,,You double your money twice\Nas fast. It it really is
Dialogue: 0,0:07:00.90,0:07:02.68,Default,,0000,0000,0000,,important, especially if you\Nthink about doubling your
Dialogue: 0,0:07:02.68,0:07:05.23,Default,,0000,0000,0000,,money, or even tripling your\Nmoney for that matter.
Dialogue: 0,0:07:05.23,0:07:13.20,Default,,0000,0000,0000,,Now in red, I said what does\Nthe rule of 72 predict?
Dialogue: 0,0:07:13.20,0:07:17.28,Default,,0000,0000,0000,,So if you just take 72 and\Ndivided it by 1%, you get 72.
Dialogue: 0,0:07:17.28,0:07:21.73,Default,,0000,0000,0000,,If you take 72 divided\Nby 4, you get 18.
Dialogue: 0,0:07:21.73,0:07:25.10,Default,,0000,0000,0000,,Rule of 72 says it'll take you\N18 years to double your money
Dialogue: 0,0:07:25.10,0:07:27.58,Default,,0000,0000,0000,,at a 4% interest rate,\Nwhen the actual
Dialogue: 0,0:07:27.58,0:07:30.52,Default,,0000,0000,0000,,answer is 17.7 years.
Dialogue: 0,0:07:30.52,0:07:31.42,Default,,0000,0000,0000,,So it's pretty close.
Dialogue: 0,0:07:31.42,0:07:34.46,Default,,0000,0000,0000,,So that's what's in\Nred right there.
Dialogue: 0,0:07:34.46,0:07:37.49,Default,,0000,0000,0000,,
Dialogue: 0,0:07:37.49,0:07:38.82,Default,,0000,0000,0000,,So I've plotted it here.
Dialogue: 0,0:07:38.82,0:07:40.68,Default,,0000,0000,0000,,The curves are pretty close.
Dialogue: 0,0:07:40.68,0:07:45.51,Default,,0000,0000,0000,,For low interest rates, so\Nthat's these interest rates
Dialogue: 0,0:07:45.51,0:07:53.14,Default,,0000,0000,0000,,over here, the rule of 72\Nslightly over estimates how
Dialogue: 0,0:07:53.14,0:07:54.88,Default,,0000,0000,0000,,long it'll take to double\Nyour money.
Dialogue: 0,0:07:54.88,0:07:57.61,Default,,0000,0000,0000,,And as you get to higher\Ninterest rates, it slightly
Dialogue: 0,0:07:57.61,0:08:01.34,Default,,0000,0000,0000,,underestimates how long it'll\Ntake you to double your money.
Dialogue: 0,0:08:01.34,0:08:05.09,Default,,0000,0000,0000,,If you had to think about is\N72 really the best number?
Dialogue: 0,0:08:05.09,0:08:06.84,Default,,0000,0000,0000,,Well this is kind\Nof what I did.
Dialogue: 0,0:08:06.84,0:08:09.34,Default,,0000,0000,0000,,If you just take the interest\Nrate and you multiply it by
Dialogue: 0,0:08:09.34,0:08:11.27,Default,,0000,0000,0000,,the actual doubling time.
Dialogue: 0,0:08:11.27,0:08:12.79,Default,,0000,0000,0000,,And here you get a\Nbunch of numbers.
Dialogue: 0,0:08:12.79,0:08:14.94,Default,,0000,0000,0000,,For low interest rate\N69 works good.
Dialogue: 0,0:08:14.94,0:08:17.36,Default,,0000,0000,0000,,For very high interest\Nrates 78 works good.
Dialogue: 0,0:08:17.36,0:08:20.47,Default,,0000,0000,0000,,But if you look at this, 72\Nlooks like a pretty good
Dialogue: 0,0:08:20.47,0:08:21.29,Default,,0000,0000,0000,,approximation.
Dialogue: 0,0:08:21.29,0:08:26.15,Default,,0000,0000,0000,,You can see it took us pretty\Nwell all the way from 4% all
Dialogue: 0,0:08:26.15,0:08:27.62,Default,,0000,0000,0000,,the way to 25%.
Dialogue: 0,0:08:27.62,0:08:30.31,Default,,0000,0000,0000,,Which is most of the interest\Nrates most of us are going to
Dialogue: 0,0:08:30.31,0:08:32.41,Default,,0000,0000,0000,,deal with for most\Nof our lives.
Dialogue: 0,0:08:32.41,0:08:34.30,Default,,0000,0000,0000,,So hopefully you found\Nthat useful.
Dialogue: 0,0:08:34.30,0:08:36.75,Default,,0000,0000,0000,,It's a very easy way to figure\Nout how fast it's going to
Dialogue: 0,0:08:36.75,0:08:37.53,Default,,0000,0000,0000,,take you to double your money.
Dialogue: 0,0:08:37.53,0:08:39.02,Default,,0000,0000,0000,,Let's do one more,\Njust for fun.
Dialogue: 0,0:08:39.02,0:08:44.68,Default,,0000,0000,0000,,
Dialogue: 0,0:08:44.68,0:08:50.48,Default,,0000,0000,0000,,Let's say I have a 9% percent\Nannual compounding.
Dialogue: 0,0:08:50.48,0:08:53.50,Default,,0000,0000,0000,,And how long does it take for\Nme to double my money?
Dialogue: 0,0:08:53.50,0:08:59.61,Default,,0000,0000,0000,,Well 72 divided by 9 is\Nequal to 8 years.
Dialogue: 0,0:08:59.61,0:09:02.81,Default,,0000,0000,0000,,It'll take me 8 years\Nto double my money.
Dialogue: 0,0:09:02.81,0:09:06.20,Default,,0000,0000,0000,,And the actual answer-- this\Nis the approximate answer
Dialogue: 0,0:09:06.20,0:09:12.19,Default,,0000,0000,0000,,using the rule of 72--\N9% is 8.04 years.
Dialogue: 0,0:09:12.19,0:09:15.94,Default,,0000,0000,0000,,So once again, in our head we\Nwere able to do a very good
Dialogue: 0,0:09:15.94,0:09:17.19,Default,,0000,0000,0000,,approximation.
Dialogue: 0,0:09:17.19,0:09:27.86,Default,,0000,0000,0000,,