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