Basic Math Simple Interest

Welcome back to Educator.com.0000

For the next lesson, we are going to go over simple interest.0002

Simple interest has to do with savings account.0010

When you take money and you want to save it,0015

you take it to the bank and you put it into a savings account.0018

That money that you deposit, that you put into the bank, is the principal.0023

The initial amount, the money that you have, that you give to the bank, is called the principal.0026

Deposit just means you putting in.0037

You are going to put it into the savings account.0039

Because you are giving it to the bank, the bank uses that money.0042

They try to make more money.0049

Since they are using your money, it is like they are borrowing your money.0052

They end up paying you what is called interest.0055

Interest is the money the bank pays you based on the interest rate.0061

Again you take your money.0066

You put it in the bank, in a savings account to try to save the money.0067

The bank pays you money just for putting your money into their bank.0072

That is interest; interest is also money.0078

It is the money earned; the money the bank paid you; the amount the bank paid you.0082

Interest rate is the percent.0090

They are going to give you a percent of that money.0093

This is in percent; that is the interest rate.0097

Simple interest is a type of interest; it is only based on the principal.0104

Only based on the initial deposit, the amount that you first deposit.0113

When they calculate the interest only based on that money, that is called simple interest.0119

There is going to be different types of interest.0126

We are only going to go over simple interest.0129

Simple again is when the bank pays you interest based on just the principal amount.0132

The formula for the simple interest is the principal, how much you deposit,0144

times the rate, the percent the bank is going to pay you,0154

and T for time, number of years that they are going to pay you.0162

PRT means P times R times T; the principal times the rate times the time.0167

You are going to multiply those three together.0176

That is going to give you the amount that you earned in interest, how much you made from the bank.0178

Interest again is in dollars because if you are making that money, then it is in dollars.0188

The principal; again it is money; dollars.0193

The rate; the rate is the percent; and T for time in years.0197

If it is 2 years, then T is going to be 2.0208

5 years, T is 5.0211

Since the bank is paying you, the bank is paying you a percent, you would want a high percent.0215

The higher the percent, the greater your interest, how much you are going to make.0222

Just keep all that in mind; I equals PRT; P times R times T.0228

Let's go through our examples; find the simple interest.0235

P, the principal, is 200 dollars.0240

The formula again is I, the interest, equals P times R times T.0242

I, amount that you make, is in dollars; P is in dollars.0252

Rate is in percent; T is in years.0257

Principal, the amount that you deposit, is 200 dollars.0264

I want to find the interest; I is what I am looking for.0267

Equals; P which is 200; R... remember since R is in percent,0270

anytime you use a percent to solve something out, you have to change it to decimal.0282

We can't solve out any numbers that is in percent form.0287

We have to change it to decimal form; 10 percent; remember percent to decimal.0291

Think of it as the number has to get smaller because decimals are small.0303

10 percent, I have to move the decimal point two spaces over to the left0307

because that is going to make the number smaller.0313

From here, I am going to go one, two; remember the decimal point.0315

If you don't see one, it is always at the end of the number.0318

You are going to go one space, two spaces.0322

It is going to be 0.10 or 0.1.0325

Remember when the 0 is at the end of a number behind the decimal point, then it is nothing.0330

You can just drop; it will be 0.1 or 0.10; it is the same thing.0335

I can write 0.10 times T; how many years?--12 years.0340

I wrote these numbers in parentheses; that means multiply.0352

If you have a bunch of parentheses together like that, that means multiply.0358

The reason why I don't use the X symbol for times, since we are using variable,0362

you don't want to use that little X to represent times because X can be a variable.0370

Now you want to just it either in parentheses...0378

Actually that is the only way you should do it if you are multiplying numbers together.0382

How do I find the interest?--I have to just multiply these numbers together.0389

200 times 0.10; 200 times 0.1; remember 0.1.0393

I just want to make the number smaller.0401

Again since 0 is at the end of a number behind the decimal point, I can just drop it.0404

0.1; this is 0; 0; 2.0409

How many numbers do I have behind the decimal points?0416

One; I am going to start at the end here.0419

I am going to go in one space; it will be 20.0.0421

Again this 0 is at the end of a number behind the decimal point.0427

I can just drop it; this is actually the same thing as 20.0431

200 times 0.10 was 20; I have to now multiply the 12; 20 times 12.0435

0 times 2 is 0; 2 times 2 is 4; put a 0 right here.0444

1 times 0 is 0; 1 times 2 is 2; need to add.0451

0 plus 2 is 2; 4 plus 0 is 4; 0 plus 0 is 0.0458

The interest is going to be 240 dollars.0467

Over 12 years, you are going to be making this much money.0481

Find the simple interest earned over 5 years0491

when the principal is 500 dollars and the interest rate is 5 percent.0494

The time, we know that this is time because it is saying over 5 years.0502

T equals 5 years.0506

It makes it easier if you are just going to write down what each variable is.0510

Principal is 500; P is 500 dollars.0514

The interest rate is 5 percent; it is not I.0524

I is the amount that you earned or amount that you have.0530

Rate, the interest rate, is the percent; look for this number, rate.0535

R equals 5 percent.0542

Simple interest equals the principal, PRT, 500.0550

Times R which is again 5 percent; change it to a decimal.0562

It is going to go from here one, two; 0.05.0578

Then time; how many years?--5 years.0587

500 dollars times the rate 0.05; for 5 years; you just multiply those three out.0593

500 times 0.05; 0 times 5, 0; 0; 25.0601

Here 0 times all these, it just all becomes 0s.0617

If you want, you can just write them in; it is not going to change.0621

It is going to be 2; 5; 0; 0.0626

From these two numbers, how many numbers do I have behind the decimal point?0631

I have two; I am going to go to this side.0635

I am going to go one, two; this is 25.0638

0s are at the end of a number behind the decimal point.0643

500 times 0.05 is 25; that is actually 25 dollars.0646

This is actually saying the principal, how much you deposit, how much you put in,0653

times the interest rate, this is how much they are going to pay you, 25 dollars per year0659

because when you multiply that, that just becomes 1 year.0665

But then since you have 5 years, you are going to take the 25 dollars.0669

You are going to multiply it by 5 because they are going to pay you for 5 years.0675

5 times 5 is 25; 5 times 2 is 10; plus 2 is 12.0680

No decimal points or numbers behind decimal points; 125 is my interest earned.0690

I, the amount that I make, is 125 dollars.0698

This is how much the bank is paying me.0707

For putting 500 dollars into the account for 5 years with 5 percent interest.0709

This is how much I make in those 5 years.0715

The next example, Samantha deposited 100 dollars into a savings account with an interest rate of 2 percent.0722

Find how much simple interest she earned over 8 years.0732

She took 100 dollars into the bank; that is 100.0739

The interest rate is 2 percent; the rate R.... it is not I even though it is interest rate.0747

It starts with an I, but it is the rate; it is 2 percent.0757

How many years?--the time is 8 years.0764

That means she put in 100 dollars into the savings account for 8 whole years.0771

She left it in there for 8 years.0775

That bank had to pay her for all 8 years.0776

Again I am solving for I; equals the principal, 100, times the rate, 2 percent.0782

Change it to decimal; start at the end; you are going to go one, two.0792

Be careful, 2 percent is not 0.2.0800

It is 0.02 because you have to fill in that space; 0.02 times 8 years.0802

If I multiply just the principal times the rate,0815

that is going to give me how much I am going to make in 1 year.0818

That is why I have to multiply it by 8 because they have to pay Samantha interest for all 8 years.0822

It is times 8.0831

100 times 0.02; 0; 0; 2; again 0 multiplying by all that is nothing.0833

It just becomes that; if you want, you can draw in all your 0s.0845

You add it; 200; see it is the same thing.0851

Whenever you have a 0 that you have to multiply to all the numbers, it is just nothing.0854

It is just 0s; it doesn't change anything.0858

How many numbers do I have behind decimal points?0863

I have two; I am going to start here and go one, two.0866

It is 2 dollars; 2.00.0871

These 0s you just drop because it is at the end of number and it is behind the decimal point.0875

There is a shortcut you can do.0881

Whenever you are multiplying by 100 or 10 or 1000, any multiple of 10,0882

10, 100, 1000, 10000, 100000, 1 with a bunch of 0s,0891

you can move the decimal point however many 0s there are.0897

Since there is two 0s here for 100, you can move this to make it bigger0904

because remember when you multiply, you tend to make the numbers bigger.0910

Then you just move this over one, two spaces.0913

Let's say you are multiplying this number by 10.0918

10 only has one 0; you would move the decimal point over once.0921

If you are multiplying it by 1000, you have three 0s.0926

You would have to move the decimal point over three times.0929

0; then you fill in that extra space with a 0; that is a shortcut.0932

This is going to be 2; this was 2; times the 8.0938

2 times 8 we know is 16; I equals 16.0949

Put the dollar sign in there; interest is always in money, how much you made.0957

That means the bank, by Samantha putting 100 dollars into the savings account at the bank,0963

and then paying her 2 percent of that 100 for 8 years,0970

she is going to end up making a total of 16 dollars.0978

Let's say we want to find out how much she has overall, she has total.0987

She left the money into the bank; the bank has her 100 dollars.0993

The bank also paid her 16 dollars.0999

How much is she going to have in all?1001

She is going to have that 100 of her money that she put in the bank1004

and that 16 dollars that the bank paid her.1009

In all, to find the total amount that she has, you can just do1013

principal, how much she deposited, plus the amount that she earned.1021

That is 100 dollars plus the 16 dollars.1029

How much is she going to have in all?--116.1034

That is just to see how much she has in all, how much total.1042

Amount that she deposited plus the amount that she made from the bank.1046

That will be her total.1051

It has to be greater than the principal amount if it is the savings account1052

because she made money so then her remaining balance has to be greater than how much she put in.1057

Let's go over one more example.1067

If the simple interest earned in 4 years is 10 dollars1070

and the interest rate is 3 percent, how much is the principal?1076

Look at what they are asking for.1084

They are asking how much is the principal?--they are asking for the P.1085

The simple interest earned in 4 years is 10 dollars.1092

Simple interest... that is I... is how much?--10 dollars.1096

The rate is 3 percent; how many years?--4 years.1105

This seems really difficult because you are used to solving for I.1121

The formula, it has you solving for I; I equals PRT.1126

They are asking for P.1134

They give you the I; they are asking you for the P.1135

Whenever they do this, it is OK.1139

Just all you have to do is follow the formula.1140

Just plug in the numbers according to where it is in the formula.1145

I, we have I; we know what I is; I is 10.1152

Write 10 instead of I; equals; P is what we are looking for.1156

Leave in P because we don't know what P is.1164

R; R is 3 percent; we can replace R; 3 percent becomes... one, two, 0.03.1168

T, time, is 4; this looks pretty difficult, right?1185

I know that I have this and this that I have to multiply because this is times.1197

Parentheses means times; P times this times this.1201

I can't multiply P times this number because it is a variable.1205

But I can multiply this and this together.1209

4 times... you know what, let me just do it the other way.1214

0.03 times the 4; 3 times 4 is 12; 0; plus 1 is 1.1222

How many numbers are there behind decimal points?--two.1231

You start here; you go one, two; there is my number, 0.12.1235

It is as if this whole thing right here, when I multiply these two numbers together, it gave me 0.12.1241

Let me just write it again and write 0.12 instead of that number.1248

It is still P times this number times this number.1255

But then because I can solve these two out, it is just multiplied together.1259

I can solve it out; that is 0.12; then how do I solve for P?1263

This is also 0.12 times P; how do I solve for P?--remember my example?1269

If I have 6 equal to P times 3, I know that P is 2 because 2 times 3 is 6.1277

I can also say that 6 divided by 3 is P.1291

I can take this number and divide it by this number.1296

I can take 10 and divide it by 0.12.1299

If I take 10 divided by 0.12, I can solve for P.1304

I can figure out what my P is.1309

To divide decimals, if you have a decimal on the outside,1312

you have numbers behind it besides 0, then you need to go one, two.1317

You moved it two spaces because we have to get rid of the decimal point.1322

Decimal point here is at the end; I have to go one, two.1327

Decimal point is right there; fill these in with 0s; bring it straight up.1332

12 goes into 10 zero times; 12 goes into 100... let's see.1340

I am going to try to say 8; let's do it over here.1350

Let's see; 12 times 8 is 16; 8 times 1 is 8; plus 1 is 9.1358

You can just guess and check; you can try guessing 5.1366

You can try guessing 10; then see what the best number would be.1369

12 times 8, it is over this 0, is 96; subtract it.1377

100 minus 96 is going to be 4; bring down the 0.1385

12 goes into 40 how many times?--12 times 3 is 6...36.1392

12 times 4 is 48; this one is too big.1403

Then I know it has to be the 3; plug in the 3 in here.1410

That is 36; subtract it; that is 4 if I subtract it.1416

I can bring down a 0; I can divide it again; that is also 3.1425

36; 4; look it is a repeating number; 0; 3; here I can stop.1439

I know I am going to probably keep getting the same number 3.1455

It is a repeating number.1459

But I can stop because I am dealing with money; I am looking for principal.1461

If I am looking principal, then it has to be in money.1468

Money, we know that there is only two numbers behind the decimal point1472

because that is how much cents there are or pennies there are.1476

83.33 would be the same thing as 83 dollars and 33 cents.1482

P, when I divide this number by this number, I get 83 dollars and 33 cents.1491

Let's go over what I just did.1507

This problem gave me time, gave me the simple interest; they gave me I.1510

They gave me the interest rate; they are asking for the principal.1520

I just list it out, what I am looking for and what was given to me.1526

Then I plug everything into the formula.1531

I substitute in these numbers for these variables.1534

I, the interest rate is 10 dollars.1541

I am going to put in 10 instead of I; equals.1542

P, I don't know; I am going to leave the P.1545

R, I know is 3 percent; I change it to a decimal; put it in as R.1548

T, I know as 4; I am going to put in 4 instead of the T.1555

There is my equation; again I am solving for P.1559

Here I can multiply because everything is multiplied together; P times R times T.1564

Since I can't multiply P times a number, I can do number times the number.1570

These two I can multiply together; that is what I did; multiply them; get 0.12.1574

Then to find what P is, remember if you have this example, I can do this number divided by the 3.1581

I am going to do 10 divided by 0.12; you just divide it.1589

When you divide it, make sure you move the decimal point over twice.1597

You have to move this decimal point over twice; bring it up; divide it.1600

You end up getting 83 dollars and 33 cents; that is the principal.1605

That is how much was deposited to make 10 dollars with a 3 percent interest over 4 years.1611

That is how much was put into the bank.1620

That is it for this lesson; thank you for watching Educator.com.1626