[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.38,0:00:01.47,Default,,0000,0000,0000,,Male Voice: What I want\Nto do in this video
Dialogue: 0,0:00:01.47,0:00:06.94,Default,,0000,0000,0000,,is talk a little bit\Nabout compounding interest
Dialogue: 0,0:00:06.94,0:00:08.42,Default,,0000,0000,0000,,and then have a little bit of a discussion
Dialogue: 0,0:00:08.42,0:00:12.34,Default,,0000,0000,0000,,of a way to quickly, kind\Nof an approximate way,
Dialogue: 0,0:00:12.34,0:00:14.76,Default,,0000,0000,0000,,to figure out how quickly\Nsomething compounds.
Dialogue: 0,0:00:14.76,0:00:16.43,Default,,0000,0000,0000,,Then we'll actually see how good
Dialogue: 0,0:00:16.43,0:00:18.94,Default,,0000,0000,0000,,of an approximation this really is.
Dialogue: 0,0:00:18.94,0:00:20.68,Default,,0000,0000,0000,,Just as a review, let's say I'm running
Dialogue: 0,0:00:20.68,0:00:23.21,Default,,0000,0000,0000,,some type of a bank and I tell you that I
Dialogue: 0,0:00:23.21,0:00:33.40,Default,,0000,0000,0000,,am offering 10% interest\Nthat compounds annually.
Dialogue: 0,0:00:33.40,0:00:35.31,Default,,0000,0000,0000,,That's usually not the\Ncase in a real bank;
Dialogue: 0,0:00:35.31,0:00:37.68,Default,,0000,0000,0000,,you would probably compound continuously,
Dialogue: 0,0:00:37.68,0:00:39.41,Default,,0000,0000,0000,,but I'm just going to\Nkeep it a simple example,
Dialogue: 0,0:00:39.41,0:00:41.33,Default,,0000,0000,0000,,compounding annually.\NThere are other videos
Dialogue: 0,0:00:41.33,0:00:43.68,Default,,0000,0000,0000,,on compounding continuously.\NThis makes the math
Dialogue: 0,0:00:43.68,0:00:46.35,Default,,0000,0000,0000,,a little simpler. All that\Nmeans is that let's say
Dialogue: 0,0:00:46.35,0:00:53.01,Default,,0000,0000,0000,,today you deposit $100\Nin that bank account.
Dialogue: 0,0:00:53.01,0:00:56.14,Default,,0000,0000,0000,,If we wait one year,\Nand you just keep that
Dialogue: 0,0:00:56.14,0:01:01.47,Default,,0000,0000,0000,,in the bank account, then\Nyou'll have your $100
Dialogue: 0,0:01:01.47,0:01:04.70,Default,,0000,0000,0000,,plus 10% on your $100 deposit.
Dialogue: 0,0:01:04.70,0:01:08.97,Default,,0000,0000,0000,,10% of 100 is going to be another $10.
Dialogue: 0,0:01:08.97,0:01:14.92,Default,,0000,0000,0000,,After a year you're going to have $110.
Dialogue: 0,0:01:14.92,0:01:17.25,Default,,0000,0000,0000,,You can just say I added 10% to the 100.
Dialogue: 0,0:01:17.25,0:01:22.38,Default,,0000,0000,0000,,After two years, or a year\Nafter that first year,
Dialogue: 0,0:01:22.38,0:01:24.98,Default,,0000,0000,0000,,after two years, you're going to get 10%
Dialogue: 0,0:01:24.98,0:01:28.33,Default,,0000,0000,0000,,not just on the $100,\Nyou're going to get 10%
Dialogue: 0,0:01:28.33,0:01:32.61,Default,,0000,0000,0000,,on the $110. 10% on 110 is you're going
Dialogue: 0,0:01:32.61,0:01:36.18,Default,,0000,0000,0000,,to get another $11, so 10% on 110 is $11,
Dialogue: 0,0:01:36.18,0:01:39.86,Default,,0000,0000,0000,,so you're going to get 110 ...
Dialogue: 0,0:01:39.86,0:01:42.06,Default,,0000,0000,0000,,That was, you can imagine,\Nyour deposit entering
Dialogue: 0,0:01:42.06,0:01:45.53,Default,,0000,0000,0000,,your second year, then\Nyou get plus 10% on that,
Dialogue: 0,0:01:45.53,0:01:47.43,Default,,0000,0000,0000,,not 10% on your initial deposit.
Dialogue: 0,0:01:47.43,0:01:49.46,Default,,0000,0000,0000,,That's why we say it compounds.
Dialogue: 0,0:01:49.46,0:01:53.40,Default,,0000,0000,0000,,You get interest on the\Ninterest from previous years.
Dialogue: 0,0:01:53.40,0:01:57.87,Default,,0000,0000,0000,,So 110 plus now $11. Every year the amount
Dialogue: 0,0:01:57.87,0:01:59.52,Default,,0000,0000,0000,,of interest we're getting, if\Nwe don't withdraw anything,
Dialogue: 0,0:01:59.52,0:02:04.53,Default,,0000,0000,0000,,goes up. Now we have $121.
Dialogue: 0,0:02:04.53,0:02:06.94,Default,,0000,0000,0000,,I could just keep doing\Nthat. The general way
Dialogue: 0,0:02:06.94,0:02:11.32,Default,,0000,0000,0000,,to figure out how much you\Nhave after let's say n years
Dialogue: 0,0:02:11.32,0:02:17.33,Default,,0000,0000,0000,,is you multiply it. I'll use\Na little bit of algebra here.
Dialogue: 0,0:02:17.33,0:02:21.73,Default,,0000,0000,0000,,Let's say this is my original\Ndeposit, or my principle,
Dialogue: 0,0:02:21.73,0:02:25.28,Default,,0000,0000,0000,,however you want to\Nview it. After x years,
Dialogue: 0,0:02:25.28,0:02:27.32,Default,,0000,0000,0000,,so after one year you\Nwould just multiply it ...
Dialogue: 0,0:02:27.32,0:02:31.54,Default,,0000,0000,0000,,To get to this number right\Nhere you multiply it by 1.1.
Dialogue: 0,0:02:31.54,0:02:32.69,Default,,0000,0000,0000,,Actually, let me do it this way.
Dialogue: 0,0:02:32.69,0:02:34.44,Default,,0000,0000,0000,,I don't want to be too abstract.
Dialogue: 0,0:02:34.44,0:02:37.79,Default,,0000,0000,0000,,Just to get the math here,\Nto get to this number
Dialogue: 0,0:02:37.79,0:02:40.26,Default,,0000,0000,0000,,right here, we just multiplied that number
Dialogue: 0,0:02:40.26,0:02:48.10,Default,,0000,0000,0000,,right there is 100 times 1\Nplus 10%, or you could say 1.1.
Dialogue: 0,0:02:48.10,0:02:50.12,Default,,0000,0000,0000,,This number right here is going to be,
Dialogue: 0,0:02:50.12,0:02:55.55,Default,,0000,0000,0000,,this 110 times 1.1 again.\NIt's this, it's the 100
Dialogue: 0,0:02:55.55,0:02:59.85,Default,,0000,0000,0000,,times 1.1 which was\Nthis number right there.
Dialogue: 0,0:02:59.85,0:03:03.19,Default,,0000,0000,0000,,Now we're going to multiply\Nthat times 1.1 again.
Dialogue: 0,0:03:03.19,0:03:04.78,Default,,0000,0000,0000,,Remember, where does the 1.1 come from?
Dialogue: 0,0:03:04.78,0:03:13.25,Default,,0000,0000,0000,,1.1 is the same thing as\N100% plus another 10%.
Dialogue: 0,0:03:13.25,0:03:15.85,Default,,0000,0000,0000,,That's what we're getting.\NWe have 100% of our
Dialogue: 0,0:03:15.85,0:03:19.19,Default,,0000,0000,0000,,original deposit plus another 10%,
Dialogue: 0,0:03:19.19,0:03:21.68,Default,,0000,0000,0000,,so we're multiplying by 1.1.
Dialogue: 0,0:03:21.68,0:03:22.71,Default,,0000,0000,0000,,Here, we're doing that twice.
Dialogue: 0,0:03:22.71,0:03:24.86,Default,,0000,0000,0000,,We multiply it by 1.1 twice.
Dialogue: 0,0:03:24.86,0:03:27.86,Default,,0000,0000,0000,,After three years, how\Nmuch money do we have?
Dialogue: 0,0:03:27.86,0:03:31.75,Default,,0000,0000,0000,,It's going to be, after\Nthree years, we're going
Dialogue: 0,0:03:31.75,0:03:40.77,Default,,0000,0000,0000,,to have 100 times 1.1 to the\N3rd power, after n years.
Dialogue: 0,0:03:40.77,0:03:42.52,Default,,0000,0000,0000,,We're getting a little abstract here.
Dialogue: 0,0:03:42.52,0:03:47.12,Default,,0000,0000,0000,,We're going to have 100\Ntimes 1.1 to the nth power.
Dialogue: 0,0:03:47.12,0:03:49.100,Default,,0000,0000,0000,,You can imagine this is\Nnot easy to calculate.
Dialogue: 0,0:03:49.100,0:03:54.07,Default,,0000,0000,0000,,This was all the situation\Nwhere we're dealing with 10%.
Dialogue: 0,0:03:54.07,0:03:57.39,Default,,0000,0000,0000,,If we were dealing in a\Nworld with let's say it's 7%.
Dialogue: 0,0:03:57.39,0:03:59.85,Default,,0000,0000,0000,,Let's say this is a\Ndifferent reality here.
Dialogue: 0,0:03:59.85,0:04:03.40,Default,,0000,0000,0000,,We have 7% compounding annual interest.
Dialogue: 0,0:04:03.40,0:04:10.05,Default,,0000,0000,0000,,Then after one year we\Nwould have 100 times,
Dialogue: 0,0:04:10.05,0:04:13.19,Default,,0000,0000,0000,,instead of 1.1, it would be 100% plus 7%,
Dialogue: 0,0:04:13.19,0:04:19.12,Default,,0000,0000,0000,,or 1.07. Let's go to 3 years.
Dialogue: 0,0:04:19.12,0:04:21.01,Default,,0000,0000,0000,,After 3 years, I could do 2 in between,
Dialogue: 0,0:04:21.01,0:04:26.78,Default,,0000,0000,0000,,it would be 100 times\N1.07 to the 3rd power,
Dialogue: 0,0:04:26.78,0:04:29.35,Default,,0000,0000,0000,,or 1.07 times itself\N3 times. After n years
Dialogue: 0,0:04:29.35,0:04:31.60,Default,,0000,0000,0000,,it would be 1.07 to the nth power.
Dialogue: 0,0:04:31.60,0:04:34.02,Default,,0000,0000,0000,,I think you get the\Nsense here that although
Dialogue: 0,0:04:34.02,0:04:36.68,Default,,0000,0000,0000,,the idea's reasonably\Nsimple, to actually calculate
Dialogue: 0,0:04:36.68,0:04:39.12,Default,,0000,0000,0000,,compounding interest is\Nactually pretty difficult.
Dialogue: 0,0:04:39.12,0:04:41.92,Default,,0000,0000,0000,,Even more, let's say I were to ask you
Dialogue: 0,0:04:41.92,0:04:56.51,Default,,0000,0000,0000,,how long does it take\Nto double your money?
Dialogue: 0,0:04:56.51,0:04:59.65,Default,,0000,0000,0000,,If you were to just use\Nthis math right here,
Dialogue: 0,0:04:59.65,0:05:02.34,Default,,0000,0000,0000,,you'd have to say, gee, to double my money
Dialogue: 0,0:05:02.34,0:05:05.76,Default,,0000,0000,0000,,I would have to start with\N$100. I'm going to multiply
Dialogue: 0,0:05:05.76,0:05:07.59,Default,,0000,0000,0000,,that times, let's say whatever, let's say
Dialogue: 0,0:05:07.59,0:05:11.53,Default,,0000,0000,0000,,it's a 10% interest, 1.1\Nor 1.10 depending on how
Dialogue: 0,0:05:11.53,0:05:15.68,Default,,0000,0000,0000,,you want to view it, to\Nthe x is equal to ...
Dialogue: 0,0:05:15.68,0:05:17.28,Default,,0000,0000,0000,,Well, I'm going to double my money so it's
Dialogue: 0,0:05:17.28,0:05:19.27,Default,,0000,0000,0000,,going to have to equal to $200.
Dialogue: 0,0:05:19.27,0:05:21.53,Default,,0000,0000,0000,,Now I'm going to have to solve for x
Dialogue: 0,0:05:21.53,0:05:23.72,Default,,0000,0000,0000,,and I'm going to have to\Ndo some logarithms here.
Dialogue: 0,0:05:23.72,0:05:25.12,Default,,0000,0000,0000,,You can divide both sides by 100.
Dialogue: 0,0:05:25.12,0:05:28.92,Default,,0000,0000,0000,,You get 1.1 to the x is equal to 2.
Dialogue: 0,0:05:28.92,0:05:31.14,Default,,0000,0000,0000,,I just divided both sides by 100.
Dialogue: 0,0:05:31.14,0:05:33.52,Default,,0000,0000,0000,,Then you could take the\Nlogarithm of both sides
Dialogue: 0,0:05:33.52,0:05:37.39,Default,,0000,0000,0000,,base 1.1, and you get x. I'm showing you
Dialogue: 0,0:05:37.39,0:05:39.35,Default,,0000,0000,0000,,that this is complicated on purpose.
Dialogue: 0,0:05:39.35,0:05:41.19,Default,,0000,0000,0000,,I know this is confusing. There's multiple
Dialogue: 0,0:05:41.19,0:05:43.12,Default,,0000,0000,0000,,videos on how to solve these.
Dialogue: 0,0:05:43.12,0:05:47.26,Default,,0000,0000,0000,,You get x is equal to log base 1.1 of 2.
Dialogue: 0,0:05:47.26,0:05:49.68,Default,,0000,0000,0000,,Most of us cannot do this in our heads.
Dialogue: 0,0:05:49.68,0:05:51.52,Default,,0000,0000,0000,,Although the idea's simple, how long will
Dialogue: 0,0:05:51.52,0:05:54.39,Default,,0000,0000,0000,,it take for me to double\Nmy money, to actually
Dialogue: 0,0:05:54.39,0:05:57.60,Default,,0000,0000,0000,,solve it to get the exact answer, is not
Dialogue: 0,0:05:57.60,0:06:00.72,Default,,0000,0000,0000,,an easy thing to do. You\Ncan just keep, if you have
Dialogue: 0,0:06:00.72,0:06:03.46,Default,,0000,0000,0000,,a simple calculator, you\Ncan keep incrementing
Dialogue: 0,0:06:03.46,0:06:05.80,Default,,0000,0000,0000,,the number of years until you\Nget a number that's close,
Dialogue: 0,0:06:05.80,0:06:07.87,Default,,0000,0000,0000,,but no straightforward way to do it.
Dialogue: 0,0:06:07.87,0:06:11.26,Default,,0000,0000,0000,,This is with 10%. If\Nwe're doing it with 9.3%,
Dialogue: 0,0:06:11.26,0:06:14.66,Default,,0000,0000,0000,,it just becomes even more difficult.
Dialogue: 0,0:06:14.66,0:06:16.21,Default,,0000,0000,0000,,What I'm going to do in the next video
Dialogue: 0,0:06:16.21,0:06:18.06,Default,,0000,0000,0000,,is I'm going to explain something called
Dialogue: 0,0:06:18.06,0:06:21.29,Default,,0000,0000,0000,,the Rule of 72, which\Nis an approximate way
Dialogue: 0,0:06:21.29,0:06:24.13,Default,,0000,0000,0000,,to figure out how long,\Nto answer this question,
Dialogue: 0,0:06:24.13,0:06:32.26,Default,,0000,0000,0000,,how long does it take\Nto double your money?
Dialogue: 0,0:06:32.26,0:06:34.48,Default,,0000,0000,0000,,We'll see how good of\Nan approximation it is
Dialogue: 0,0:06:34.48,0:06:36.63,Default,,0000,0000,0000,,in that next video.