For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Simple Interest

#### Related Links

- Principal: The money you deposit in a savings account
- Interest: The money the bank pays you based on the interest rate
- Simple interest: The interest paid only on the principal
- Simple Interest Formula: I = prt
- I = interest ($)
- p = principal (4)
- r = interest rate per year
- t = time in years

### Simple Interest

P = $300

Interest rate = 15%

Time = 10 years

- I = Prt

I = interest

P = principal

r = interest rate per year

t = time in years - 15% = .15
- I = (300)(.15)(10)

P = $150

Interest rate = 30%

Time = 5 years

- I = Prt
- I = interest

P = principal

r = interest rate per year

t = time in years - 30% = .30
- I = (150)(.30)(5)

- I = Prt
- I = interest

P = $600

r = 10%

t = 15

- 10% = .10
- I = (600)(.10)(15)

- I = Prt
- I = interest

P = $400

r = 5%

t = 30 - 5% = .05
- I = (400)(.05)(30)

- I = Prt
- I = interest

P = $120

r = 10%

t = 9 - 10% = .10
- I = (120)(.10)(9)

- I = Prt
- I = interest

P = $ 250

r = 20%

t = 15 - 20% = .20
- I = (250)(.20)(15)

- I = Prt
- I = interest

P = $ 600

r = 2%

t = 6 - 2% = .02
- I = (600)(.02)(6)

- I = Prt
- I = $ 250

P = principal

r = 5%

t = 10 - 5% = .05
- 250 = (P)(.05)(10)
- 250 = 0.5P
- P = [250/0.5]

- I = Prt
- I = $ 500

P = principal

r = 2%

t = 10 - 2% = .02
- 500 = (P)(.02)(10)
- 500 = 0.2P
- P = [500/0.2]

- I = Prt
- I = $120

P = principal

r = 2%

t = 1 - 2% = .02
- 120 = (P)(.02)(1)
- 120 = 0.02P
- P = [120/0.02]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Simple Interest

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Simple Interest 0:05
- Principal
- Interest & Interest Rate
- Simple Interest
- Simple Interest Formula 2:23
- Simple Interest Formula: I = prt
- Extra Example 1: Finding Simple Interest 3:53
- Extra Example 2: Finding Simple Interest 8:08
- Extra Example 3: Finding Simple Interest 12:02
- Extra Example 4: Finding Simple Interest 17:46

### Basic Math Online Course

### Transcription: 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 left*0307

*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 years*0491

*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 year*0659

*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 bigger*0904

*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 bank*1004

*and that 16 dollars that the bank paid her.*1009

*In all, to find the total amount that she has, you can just do*1013

*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 account*1052

*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 dollars*1070

*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 point*1472

*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

0 answers

Post by Han Jun Kim on March 22, 2013

And if these questions were in real life, is the actual money that the owner is given principle plus interest?

0 answers

Post by Han Jun Kim on March 22, 2013

Is there a difference between interest and simple interest?

1 answer

Last reply by: Professor Pyo

Sat Mar 2, 2013 1:37 AM

Post by Edward Hook on February 9, 2013

I hope you got rid of your cold quickly.

0 answers

Post by Ahmed Mahdi on October 4, 2012

where should i get good book for practicing all of these lessons.

Thank you.

1 answer

Last reply by: chad louis

Sat Sep 22, 2012 8:03 PM

Post by chad louis on September 22, 2012

shouldn't the interest be the difference between the principal and the total money earned over a certain period of time?