00:00Hi guys, so in this
00:02lesson we are going to
00:03look at compound interest. Now,
00:06I'll save you the speech
00:08about how great compound interest
00:11is, but note Albert Einstein
00:15said it was the eighth
00:17wonder of the world. So
00:18it's very, very useful and
00:22important. And if you're not
00:24earning compound interest in some
00:26way right now,
00:28Then research it. You should
00:31have some kind of investment
00:33that is earning compound interest.
00:36Anyway, I'll leave it there.
00:37Let's look at this example.
00:39Mrs. Flynn invests 6 ,000
00:41euros with her bank at
00:424 .6 % per annum
00:45interest compounded quarterly. Right? So
00:47there's a lot of interest.
00:48Sorry, a lot of important
00:49things here. 4 .6 %
00:52per annum compounded
00:56quarterly. This is important. Now
00:59you are lucky that the
01:00IB have decided to give
01:02us the compound interest formula.
01:03They didn't do that in
01:05the past. So we have
01:05this component just form a
01:07great. A calculate the amount
01:09in her account after five
01:11years. So she's going to
01:12earn some interest here. So
01:14how do we do it?
01:16Well, we say the future
01:16value, the future value. So
01:19this is the formula. F
01:20is future value. PV is
01:22present value.
01:24n is the number of
01:25years k is the number
01:26of compounding periods per year.
01:28So in this case k
01:29will be 4 and or
01:31percent is the nominal annual
01:33rate of interest. So that's
01:34just going to be 4
01:35.6. That's quite straightforward. So
01:36let's write out those things.
01:39pv equals 6000. That's the
01:41present value. She's invested n
01:47equals n equals 5 because
01:51it's 5 years
01:52years, k is the number
01:55of compounding periods per year,
01:58which in this case is
01:594. And what was the
02:02last one? R, R equals
02:044 .6. So now it's
02:06just a case of subbing
02:08this in here. So what
02:10I'm going to do, um,
02:136000 multiplied by 1 plus
02:18R is 4 .6. So
02:204 .6 over 100 times
02:244 all to the power
02:27of kn which is 4
02:30times 5. Straight forward, get
02:35out your calculator and type
02:38it out. 6000 times 1
02:43plus fraction
02:484 .6 over 100 times
02:514, 100 times 4, all
02:56to the power of 4
02:58times 5. Let me move
03:02this over here a bit.
03:04Press Enter, and I get
03:067 ,541 .7. 7 ,541
03:11.70. Okay, so she has
03:16Mrs. Flynn has earned, well,
03:21she is, her amount is
03:23now up to 7 ,541
03:25.70 euros if you like.
03:28Now note a question might
03:29be calculate how much interest
03:31she earned and if that's
03:32the case you do this
03:32minus $6 ,000 obviously to
03:34give you 1 ,541. Okay,
03:37nice. Part B. In which
03:41year will it reach 10
03:43,000 euros? Okay, so now
03:44Now it's saying the future
03:46value is 10 ,000. The
03:49future value is 10 ,000,
03:51let's write this over here.
03:52Future value is now 10
03:55,000. What do we not
03:57know though? We don't know
03:58how long it's gonna take.
04:00So the present value is
04:02still 6 ,000. The n,
04:06the number of years, which
04:08we're trying to find, I
04:09don't know, k is still
04:11four and r is
04:12still 4 .6. Now this
04:16is 6000 times 1 plus
04:224 .6 over 100 times
04:304 all to the power
04:32of Kn which is 4n
04:35and I don't know what
04:36n is but I can
04:39find out with
04:40my wonderful GDC. Let's go
04:45to algebra numerical solve. So
04:49right out the equation, 10
04:51,000 equals 6 ,000 times
04:561 plus fraction 4 .6.
05:04I'm just going to write
05:05400 now guys, 400, 400,
05:07400.
05:08close brackets to the power
05:12of, so clearly the only
05:14way you can get this
05:15wrong is if you mess
05:16up the typing in and
05:17that's actually harder than you
05:18think. And then I have
05:20to do comma in to
05:22find in. So look, is
05:23that equation exactly the same
05:25as this equation? Yeah, I
05:28think it is press enter
05:29and I get 11 .168611
05:32.1686. Now,
05:36This is I find this
05:42very confusing because it doesn't
05:43say Find and it says
05:45in which year so when
05:47it says in which year
05:48it means is it in
05:492020 or 2021 or 2022?
05:52Whatever so we need to
05:56find the year now 11
05:57it's 11 .1686 so it's
06:00gonna be okay Let's let's
06:04think with this one
06:043. When n is 1,
06:08that is the end of
06:092020. When n is 2,
06:12that is the end of
06:132021. When n is 3,
06:16that's the end of 2022.
06:17So when n is 11,
06:18that's the end of 2030.
06:22So when n is 11,
06:24it's the end of 2030.
06:27But it hasn't quite reached
06:2910 ,000 when n is
06:3011. It needs 11 .16,
06:32so it needs a bit
06:32of
06:33next year. So the year
06:35is going to be 2031.
06:43Okay, and I want to
06:44show you another way we
06:45can kind of, I want
06:49to show you another way
06:49to visualize that. So if
06:52I if I graph this
06:53and I did this in
06:54the arithmetic sequence lesson as
06:57well, if I graph the
07:00function
07:016 ,000 times 1 plus
07:094 .6 over 400 to
07:16the power of 4. Now,
07:22X, I have to put
07:23remember X when you're graphing.
07:25I get this, but if
07:26I do menu table splits
07:29screen here is actually what's
07:31happening. This is, this is
07:36my, my sequence. So this
07:39is, this is what she
07:40has at the end of
07:41year one. She'll have this.
07:44This is what are at
07:45the end of 2020, when
07:47N is one, end of
07:482020, end of 2021, 22,
07:5223, 24, 25, 26, 27,
07:5328, 29, 30, end of
07:562030.
07:57This is end of 2030
07:59one, which is more than
08:0010 ,000. So the it'll
08:02grow in the year 2030
08:06one. Yes, that is absolutely
08:08confusing. Okay, this is fine.
08:14Absolutely correct. This is how
08:15I want you to do
08:16it. No problem. But I
08:17want you also to understand
08:20how to use finance solver.
08:24Now, if I
08:25If I go to Finance
08:27here and Finance solver, I
08:30have this. Now this looks
08:32a bit scary when it
08:33makes your life quite easy.
08:36So for compound interest, if
08:39I do, it says down
08:43here what's going on. And
08:46is the number of payments.
08:48Now it's all happening quarterly
08:50and there's five years.
08:53number of payments if you
08:54like is 5 times 4
08:56which is 20. The interest
08:59rate is 4 .6. The
09:02present value is 6 ,000
09:04but because the money is
09:09you're investing it so you
09:10actually I like to think
09:12of it as if it's
09:13moving away from you you
09:14make it negative. If you
09:16were taking out a loan
09:17and those of you doing
09:19applications will use this for
09:21loans, you make a positive.
09:24But seeing as we're investing
09:25it just moving away from
09:26us, we make it negative.
09:28The payment is zero because
09:29we're not making any more
09:30payments, we're just leaving it
09:31there. The future value, leave
09:34that. I don't know what
09:35that is yet. I'm going
09:36to press enter and calculate
09:37that. The payments per year
09:41is for because it's happening
09:43quarterly and the compounding periods
09:49is also 4 because it's
09:51happening quarterly. Now if I
09:52go to Future Value and
09:55press Enter, there I go.
09:57I get 7 ,541 .69.
10:03Now what you can also
10:05do is put in the
10:08Future Value. If I put
10:09in the Future Value of
10:1010 ,000 and I want
10:13to define n, I then
10:15go to n and
10:17I press enter. And because
10:20this it's like 44 .6
10:21quarters, so I need to
10:23divide by four to get
10:2411 .168. What I can
10:27also do is imagine it
10:29said, so imagine part a
10:32again, but this time it
10:33didn't give me the interest
10:34rate. And it said the
10:37future value is 7 ,541
10:41.7. What was the interest
10:44rate? Well,
10:45You go to the you
10:46put in all the other
10:47values and then you go
10:48to the interest rate press
10:50enter there and you get
10:524 .60 oh, oh, now
10:54obviously this has happened because
10:56this future value is rounded
10:57but you get it 4
10:59.6 so finance solver actually
11:02I It's really really useful.
11:04It makes complicated questions really
11:07really easy Those of you
11:09studying applications. We're absolutely 100
11:11% going to use it
11:12for loans and annuities
11:13and it's going to be
11:14really, really useful for that.
11:16But for compound interest, what
11:18I recommend is you use
11:20the formula and then use
11:21fine unsolver just to check
11:23your answer or to just
11:24kind of do it twice
11:25to make sure you're correct.
11:27Okay, that's compound interest. Yeah,
11:33invest your money wisely and
11:35invest it now. I waited
11:36too long in my life
11:39before I started investing my
11:41money.
11:41I should have started when
11:44I was much younger so
11:46I recommend you start as
11:48soon as you can as
11:49soon as you have some
11:50money.