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  • >> This is YourMathGal,

  • Julie Harland.

  • Please visit my website

  • at yourmathgal.com where all

  • of my videos were organized

  • by topic.

  • We're going

  • to do the following three

  • problems on this video.

  • They all involved

  • in investment

  • of 20,000 dollars

  • and a 12 percent interest

  • account and we're trying

  • to find out how much many

  • there is in the account

  • after 20 years,

  • but the conditions

  • are different.

  • The first one is just if it's

  • in the simple interest

  • account, the second problem is

  • if it's compounded yearly

  • so we'll be using the compound

  • interest formula,

  • and the third one will be

  • if it's compounded daily also

  • using the compound

  • interest formula.

  • So, here's the first problem.

  • You're investing 20,000

  • at 12 percent for 20 years.

  • So, you've got this formula,

  • I equals PRT

  • so the principal is 20,000,

  • the rate is 12 percent

  • which you could write

  • as 12/100 or 0.12

  • and the time is 20 years.

  • So, we simply put

  • that in the formula,

  • I equals 20,000 times

  • and I'm going to do it

  • as 12/100 so if I can do this

  • in my head just

  • as well times 20.

  • So, I can cancel that hundred

  • with two of those zeros

  • and what does that give me

  • in interest?

  • Well, I have 200 dollars,

  • right, times 12 times 20,

  • so I'm just going

  • to do 2 times 2 is 4 times 12

  • that's 48,

  • and then how many zeros do I

  • have here, 1, 2, 3 zeros,

  • so that's what you make an

  • interest, pretty amazing

  • isn't it?

  • In other words,

  • way more than you're

  • original investment.

  • Now, how much money is

  • in the account?

  • It says, how much money is

  • in the account,

  • that's a different question.

  • So, I have my 20,000 dollars

  • then I get to add on to that.

  • That's was already

  • in the account to begin with

  • and so my answer is

  • 68,000 dollars.

  • So if you--

  • now if you got an extra 20,000

  • dollars around which I don't,

  • but if you do

  • and you just let it sit

  • in an account earning simple

  • interest, that's how much

  • money would be in the account

  • after 20 years, of course,

  • 20 years is a long time

  • to wait.

  • So, we're going

  • to remember this.

  • We're going

  • to compare all these later.

  • Let's go on to the

  • next problem.

  • So, if 20,000 is invested

  • in an account earning 12

  • percent interest compounded

  • yearly, how much money is

  • in the account after 20 years?

  • We need this formula.

  • This is the compound interest

  • formula and remember,

  • these are what these variables

  • stand for in the compound

  • interest formula.

  • All right,

  • so my principal here is 20,000

  • and my rate is still 12

  • percent or 0.12 or 12/100.

  • My variable N,

  • okay that's how often--

  • how many times per year

  • it's compounded.

  • Well, it's only yearly,

  • so N is just one in this case,

  • once a year, and the time is

  • in years, it's 20 years.

  • So, T equals 20.

  • So, if we put

  • that in this formula,

  • we've got 20,000 times 1 plus,

  • now what's the rate,

  • 0.12 over 1 times N times T,

  • 1 times 20.

  • That's the exponent,

  • so I've got 20,000 times,

  • all right,

  • what's this going to be?

  • Well, 0.12 by 1 is just 0.12

  • and 1 plus that is 1.12

  • to the 20th.

  • So, of course

  • if you have a lot of time,

  • you could take 1.12

  • and multiply it,

  • finds itself 20 times

  • to get the answer,

  • that I'm going to suggest,

  • you put that on your

  • calculator

  • and there's different

  • calculators

  • on how you're going

  • to enter this, so go ahead

  • and try it.

  • I showed how I did it

  • in my calculator and I'm going

  • to just show the series

  • of keystrokes I use.

  • So, these are the keystrokes I

  • use on my calculator now

  • that's because I'm doing the

  • order of operation myself.

  • I'm just thinking well,

  • in order of operations,

  • I first have to do 1.12

  • and raise it to the power,

  • that's what this is,

  • 1.12 and I use the Y

  • to the X key

  • or you might have a little

  • caret, this is called a caret,

  • and then the number

  • for the exponent would be 20

  • then I put equals

  • and there will be a number

  • that comes up

  • and then I'll use

  • the multiplication.

  • I'm going to take that answer

  • and multiply it

  • by 20,000 dollars

  • and then I'm going

  • to put equal sign

  • and when I do that,

  • I get this number rounded

  • to the nearest cent,

  • 192,925.86 cents,

  • okay that is a huge difference

  • than when we did the simple

  • interest formula,

  • I'm going to remind you,

  • this is how much money is

  • in the account after 20 years.

  • So, you put in 20,000,

  • you let it sit there

  • for 20 years,

  • you've got a 192,925 dollars

  • in your account,

  • simple interest you'd only

  • had 68,000.

  • It's really amazing.

  • So, compounding interest is

  • great if you're putting money

  • an account and you want

  • to earn a lot of interest.

  • But if you're borrowing many,

  • you're hoping somebody is

  • going to give it to you

  • as simple interest

  • because you would pay a

  • lot less.

  • Now, let's see what would

  • happen if we actually

  • compounded it daily instead

  • of yearly.

  • How much more

  • of a difference could that be

  • and most banks do

  • compound daily.

  • All right,

  • so here's the next part.

  • What about if you invested it

  • and you compounded it daily?

  • So, we're going

  • to have the same

  • variables here.

  • At the beginning,

  • you've got the principal is

  • still 20,000, right?

  • And the rate is still 12%,

  • but N is different.

  • How many times per year is

  • that if it's done daily.

  • And I know

  • that we don't have the same

  • number of days per year,

  • but usually its 365

  • and that's what for years.

  • So N is 365 and then

  • for how many years, 20.

  • So, the only thing different

  • from the previous problem is

  • that N is 365 as opposed to 1.

  • So, we're going

  • to plug those numbers in,

  • A equals 20,000 times 1 plus

  • 0.12, right?

  • That's the rate over,

  • right now, what was the N

  • in this case,

  • 365 and then you're going

  • to raise that to the N times

  • T, so, 365 times 20.

  • [ Pause ]

  • Now again,

  • the trick is entering this.

  • You could, you know,

  • enter it just like it--

  • you see it right here

  • if you've got a calculator

  • that allow--

  • I would say

  • if you had a graphing

  • calculator

  • and for sure can make--

  • make sure you enter

  • everything correctly.

  • I tend to like

  • to simplify it just a little

  • bit and there is an easy way

  • to always simplify this,

  • that's inside the parenthesis,

  • because whatever this

  • denominator is, 365,

  • you just think of--

  • that would be the whole

  • number, the number 1

  • over here, I could rewrite

  • that always as this number

  • over itself,

  • 365 over 365 right,

  • which means this ends

  • up being the whole number part

  • in front of the 12

  • and that ends

  • up being the denominator.

  • So, imagine if you change

  • that to 365

  • over 365 then you'd a common

  • denominator

  • and you'd have 365 plus 0.12.

  • So, I do that

  • and then I also do the 365

  • times 20, but

  • it's unnecessary.

  • You could leave it like this

  • and use parenthesis and,

  • you know, work it

  • in your calculator however

  • you like.

  • So, I'm going

  • to do just a little bit

  • of simplification before I put

  • it in the calculator,

  • and so like I said,

  • this will be 365.12

  • over 365 so, it's a--

  • and so I'm going to do--

  • I'm not going to actually do

  • that division.

  • I'm going to enter it just

  • like that in my calculator

  • and then 365 times 20,

  • let's see what is that,

  • that's 7,300, all right.

  • So, again,

  • you could just enter it

  • like it is at this point or at

  • that point

  • and my keystrokes again,

  • I'm going to start with what's

  • in the parenthesis here

  • so I'm actually going

  • to use a parenthesis.

  • So, I would do 365.12 divided

  • by 365 first

  • and then I would raised it

  • so you'd use the Y

  • to the X button

  • or the little caret

  • to the 7,300

  • and then you would equal

  • and then you would times

  • up by 20,000.

  • So, again here are

  • my keystrokes.

  • So, these are my keystrokes

  • down here.

  • I do what's in parenthesis,

  • 365.12 divided by 365,

  • I write what

  • that equals then I'm going

  • to raise that to the 7,300.

  • So, on my calculator,

  • that's the Y to the X button,

  • 7,300 then I'm going

  • to say what that equal so far

  • and I'm going to multiply

  • that answer by 20,000

  • and write equals.

  • And when you do that,

  • this is the number you

  • should get.

  • You see, I got 220,

  • 376 dollars and 58 cents

  • so that's how much many she

  • gets an account

  • and I didn't double

  • check this.

  • I probably will do that

  • but I always suggest you enter

  • your numbers more than once.

  • Okay, so now let's compare

  • this 3.

  • All right,

  • here are our results

  • if we invest 20,000 dollars

  • at 12% for 20 years,

  • you can see the amount

  • of the account at the end

  • of the 20 years

  • if you simply use

  • simple interest.

  • You'd only have 68,000 dollars

  • in the account.

  • If you compounded interest

  • yearly, you would have a

  • 192,925 huge difference

  • and if you compounded daily,

  • you have more but it's not

  • as huge of a difference

  • 220,376 dollars still I'll

  • take 28,000 dollars more

  • approximately,

  • that would be fine

  • and I prefer the

  • compounded daily.

  • The reason that com--

  • when you compound interest

  • by so much more money is your

  • getting interest

  • on your interest

  • and it just grows

  • very quickly.

  • Now of course

  • if this was 6 percent instead

  • of 12 percent it wouldn't be

  • as much of a difference.

  • Of course the higher

  • percentage is going

  • to make the bigger difference,

  • but it's compounding it or not

  • that makes a very

  • big difference.

  • So, I think that's a pretty

  • interesting to think about,

  • especially if you're borrowing

  • on your credit cards

  • and it's being compounded

  • like crazy

  • and you have a high

  • percentage rate.

  • So, think about that.

  • This is YourMathGal,

  • Julie Harland.

  • Please visit my website

  • at yourmathgal.com where all

  • of my videos were organized

  • by topic.

>> This is YourMathGal,

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