WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over simple interest.
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Simple interest has to do with savings account.
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When you take money and you want to save it,
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you take it to the bank and you put it into a savings account.
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That money that you deposit, that you put into the bank, is the principal.
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The initial amount, the money that you have, that you give to the bank, is called the principal.
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Deposit just means you putting in.
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You are going to put it into the savings account.
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Because you are giving it to the bank, the bank uses that money.
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They try to make more money.
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Since they are using your money, it is like they are borrowing your money.
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They end up paying you what is called interest.
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Interest is the money the bank pays you based on the interest rate.
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Again you take your money.
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You put it in the bank, in a savings account to try to save the money.
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The bank pays you money just for putting your money into their bank.
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That is interest; interest is also money.
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It is the money earned; the money the bank paid you; the amount the bank paid you.
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Interest rate is the percent.
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They are going to give you a percent of that money.
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This is in percent; that is the interest rate.
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Simple interest is a type of interest; it is only based on the principal.
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Only based on the initial deposit, the amount that you first deposit.
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When they calculate the interest only based on that money, that is called simple interest.
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There is going to be different types of interest.
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We are only going to go over simple interest.
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Simple again is when the bank pays you interest based on just the principal amount.
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The formula for the simple interest is the principal, how much you deposit,
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times the rate, the percent the bank is going to pay you,
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and T for time, number of years that they are going to pay you.
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PRT means P times R times T; the principal times the rate times the time.
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You are going to multiply those three together.
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That is going to give you the amount that you earned in interest, how much you made from the bank.
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Interest again is in dollars because if you are making that money, then it is in dollars.
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The principal; again it is money; dollars.
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The rate; the rate is the percent; and T for time in years.
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If it is 2 years, then T is going to be 2.
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5 years, T is 5.
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Since the bank is paying you, the bank is paying you a percent, you would want a high percent.
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The higher the percent, the greater your interest, how much you are going to make.
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Just keep all that in mind; I equals PRT; P times R times T.
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Let's go through our examples; find the simple interest.
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P, the principal, is 200 dollars.
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The formula again is I, the interest, equals P times R times T.
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I, amount that you make, is in dollars; P is in dollars.
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Rate is in percent; T is in years.
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Principal, the amount that you deposit, is 200 dollars.
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I want to find the interest; I is what I am looking for.
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Equals; P which is 200; R... remember since R is in percent,
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anytime you use a percent to solve something out, you have to change it to decimal.
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We can't solve out any numbers that is in percent form.
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We have to change it to decimal form; 10 percent; remember percent to decimal.
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Think of it as the number has to get smaller because decimals are small.
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10 percent, I have to move the decimal point two spaces over to the left
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because that is going to make the number smaller.
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From here, I am going to go one, two; remember the decimal point.
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If you don't see one, it is always at the end of the number.
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You are going to go one space, two spaces.
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It is going to be 0.10 or 0.1.
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Remember when the 0 is at the end of a number behind the decimal point, then it is nothing.
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You can just drop; it will be 0.1 or 0.10; it is the same thing.
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I can write 0.10 times T; how many years?--12 years.
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I wrote these numbers in parentheses; that means multiply.
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If you have a bunch of parentheses together like that, that means multiply.
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The reason why I don't use the X symbol for times, since we are using variable,
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you don't want to use that little X to represent times because X can be a variable.
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Now you want to just it either in parentheses...
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Actually that is the only way you should do it if you are multiplying numbers together.
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How do I find the interest?--I have to just multiply these numbers together.
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200 times 0.10; 200 times 0.1; remember 0.1.
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I just want to make the number smaller.
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Again since 0 is at the end of a number behind the decimal point, I can just drop it.
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0.1; this is 0; 0; 2.
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How many numbers do I have behind the decimal points?
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One; I am going to start at the end here.
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I am going to go in one space; it will be 20.0.
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Again this 0 is at the end of a number behind the decimal point.
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I can just drop it; this is actually the same thing as 20.
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200 times 0.10 was 20; I have to now multiply the 12; 20 times 12.
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0 times 2 is 0; 2 times 2 is 4; put a 0 right here.
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1 times 0 is 0; 1 times 2 is 2; need to add.
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0 plus 2 is 2; 4 plus 0 is 4; 0 plus 0 is 0.
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The interest is going to be 240 dollars.
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Over 12 years, you are going to be making this much money.
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Find the simple interest earned over 5 years
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when the principal is 500 dollars and the interest rate is 5 percent.
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The time, we know that this is time because it is saying over 5 years.
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T equals 5 years.
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It makes it easier if you are just going to write down what each variable is.
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Principal is 500; P is 500 dollars.
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The interest rate is 5 percent; it is not I.
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I is the amount that you earned or amount that you have.
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Rate, the interest rate, is the percent; look for this number, rate.
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R equals 5 percent.
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Simple interest equals the principal, PRT, 500.
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Times R which is again 5 percent; change it to a decimal.
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It is going to go from here one, two; 0.05.
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Then time; how many years?--5 years.
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500 dollars times the rate 0.05; for 5 years; you just multiply those three out.
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500 times 0.05; 0 times 5, 0; 0; 25.
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Here 0 times all these, it just all becomes 0s.
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If you want, you can just write them in; it is not going to change.
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It is going to be 2; 5; 0; 0.
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From these two numbers, how many numbers do I have behind the decimal point?
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I have two; I am going to go to this side.
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I am going to go one, two; this is 25.
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0s are at the end of a number behind the decimal point.
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500 times 0.05 is 25; that is actually 25 dollars.
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This is actually saying the principal, how much you deposit, how much you put in,
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times the interest rate, this is how much they are going to pay you, 25 dollars per year
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because when you multiply that, that just becomes 1 year.
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But then since you have 5 years, you are going to take the 25 dollars.
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You are going to multiply it by 5 because they are going to pay you for 5 years.
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5 times 5 is 25; 5 times 2 is 10; plus 2 is 12.
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No decimal points or numbers behind decimal points; 125 is my interest earned.
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I, the amount that I make, is 125 dollars.
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This is how much the bank is paying me.
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For putting 500 dollars into the account for 5 years with 5 percent interest.
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This is how much I make in those 5 years.
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The next example, Samantha deposited 100 dollars into a savings account with an interest rate of 2 percent.
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Find how much simple interest she earned over 8 years.
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She took 100 dollars into the bank; that is 100.
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The interest rate is 2 percent; the rate R.... it is not I even though it is interest rate.
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It starts with an I, but it is the rate; it is 2 percent.
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How many years?--the time is 8 years.
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That means she put in 100 dollars into the savings account for 8 whole years.
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She left it in there for 8 years.
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That bank had to pay her for all 8 years.
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Again I am solving for I; equals the principal, 100, times the rate, 2 percent.
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Change it to decimal; start at the end; you are going to go one, two.
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Be careful, 2 percent is not 0.2.
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It is 0.02 because you have to fill in that space; 0.02 times 8 years.
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If I multiply just the principal times the rate,
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that is going to give me how much I am going to make in 1 year.
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That is why I have to multiply it by 8 because they have to pay Samantha interest for all 8 years.
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It is times 8.
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100 times 0.02; 0; 0; 2; again 0 multiplying by all that is nothing.
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It just becomes that; if you want, you can draw in all your 0s.
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You add it; 200; see it is the same thing.
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Whenever you have a 0 that you have to multiply to all the numbers, it is just nothing.
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It is just 0s; it doesn't change anything.
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How many numbers do I have behind decimal points?
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I have two; I am going to start here and go one, two.
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It is 2 dollars; 2.00.
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These 0s you just drop because it is at the end of number and it is behind the decimal point.
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There is a shortcut you can do.
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Whenever you are multiplying by 100 or 10 or 1000, any multiple of 10,
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10, 100, 1000, 10000, 100000, 1 with a bunch of 0s,
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you can move the decimal point however many 0s there are.
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Since there is two 0s here for 100, you can move this to make it bigger
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because remember when you multiply, you tend to make the numbers bigger.
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Then you just move this over one, two spaces.
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Let's say you are multiplying this number by 10.
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10 only has one 0; you would move the decimal point over once.
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If you are multiplying it by 1000, you have three 0s.
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You would have to move the decimal point over three times.
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0; then you fill in that extra space with a 0; that is a shortcut.
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This is going to be 2; this was 2; times the 8.
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2 times 8 we know is 16; I equals 16.
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Put the dollar sign in there; interest is always in money, how much you made.
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That means the bank, by Samantha putting 100 dollars into the savings account at the bank,
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and then paying her 2 percent of that 100 for 8 years,
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she is going to end up making a total of 16 dollars.
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Let's say we want to find out how much she has overall, she has total.
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She left the money into the bank; the bank has her 100 dollars.
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The bank also paid her 16 dollars.
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How much is she going to have in all?
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She is going to have that 100 of her money that she put in the bank
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and that 16 dollars that the bank paid her.
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In all, to find the total amount that she has, you can just do
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principal, how much she deposited, plus the amount that she earned.
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That is 100 dollars plus the 16 dollars.
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How much is she going to have in all?--116.
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That is just to see how much she has in all, how much total.
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Amount that she deposited plus the amount that she made from the bank.
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That will be her total.
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It has to be greater than the principal amount if it is the savings account
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because she made money so then her remaining balance has to be greater than how much she put in.
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Let's go over one more example.
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If the simple interest earned in 4 years is 10 dollars
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and the interest rate is 3 percent, how much is the principal?
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Look at what they are asking for.
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They are asking how much is the principal?--they are asking for the P.
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The simple interest earned in 4 years is 10 dollars.
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Simple interest... that is I... is how much?--10 dollars.
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The rate is 3 percent; how many years?--4 years.
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This seems really difficult because you are used to solving for I.
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The formula, it has you solving for I; I equals PRT.
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They are asking for P.
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They give you the I; they are asking you for the P.
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Whenever they do this, it is OK.
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Just all you have to do is follow the formula.
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Just plug in the numbers according to where it is in the formula.
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I, we have I; we know what I is; I is 10.
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Write 10 instead of I; equals; P is what we are looking for.
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Leave in P because we don't know what P is.
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R; R is 3 percent; we can replace R; 3 percent becomes... one, two, 0.03.
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T, time, is 4; this looks pretty difficult, right?
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I know that I have this and this that I have to multiply because this is times.
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Parentheses means times; P times this times this.
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I can't multiply P times this number because it is a variable.
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But I can multiply this and this together.
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4 times... you know what, let me just do it the other way.
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0.03 times the 4; 3 times 4 is 12; 0; plus 1 is 1.
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How many numbers are there behind decimal points?--two.
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You start here; you go one, two; there is my number, 0.12.
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It is as if this whole thing right here, when I multiply these two numbers together, it gave me 0.12.
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Let me just write it again and write 0.12 instead of that number.
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It is still P times this number times this number.
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But then because I can solve these two out, it is just multiplied together.
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I can solve it out; that is 0.12; then how do I solve for P?
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This is also 0.12 times P; how do I solve for P?--remember my example?
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If I have 6 equal to P times 3, I know that P is 2 because 2 times 3 is 6.
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I can also say that 6 divided by 3 is P.
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I can take this number and divide it by this number.
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I can take 10 and divide it by 0.12.
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If I take 10 divided by 0.12, I can solve for P.
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I can figure out what my P is.
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To divide decimals, if you have a decimal on the outside,
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you have numbers behind it besides 0, then you need to go one, two.
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You moved it two spaces because we have to get rid of the decimal point.
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Decimal point here is at the end; I have to go one, two.
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Decimal point is right there; fill these in with 0s; bring it straight up.
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12 goes into 10 zero times; 12 goes into 100... let's see.
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I am going to try to say 8; let's do it over here.
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Let's see; 12 times 8 is 16; 8 times 1 is 8; plus 1 is 9.
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You can just guess and check; you can try guessing 5.
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You can try guessing 10; then see what the best number would be.
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12 times 8, it is over this 0, is 96; subtract it.
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100 minus 96 is going to be 4; bring down the 0.
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12 goes into 40 how many times?--12 times 3 is 6...36.
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12 times 4 is 48; this one is too big.
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Then I know it has to be the 3; plug in the 3 in here.
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That is 36; subtract it; that is 4 if I subtract it.
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I can bring down a 0; I can divide it again; that is also 3.
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36; 4; look it is a repeating number; 0; 3; here I can stop.
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I know I am going to probably keep getting the same number 3.
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It is a repeating number.
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But I can stop because I am dealing with money; I am looking for principal.
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If I am looking principal, then it has to be in money.
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Money, we know that there is only two numbers behind the decimal point
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because that is how much cents there are or pennies there are.
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83.33 would be the same thing as 83 dollars and 33 cents.
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P, when I divide this number by this number, I get 83 dollars and 33 cents.
00:25:07.200 --> 00:25:09.800
Let's go over what I just did.
00:25:09.800 --> 00:25:20.000
This problem gave me time, gave me the simple interest; they gave me I.
00:25:20.000 --> 00:25:25.700
They gave me the interest rate; they are asking for the principal.
00:25:25.700 --> 00:25:31.300
I just list it out, what I am looking for and what was given to me.
00:25:31.300 --> 00:25:33.700
Then I plug everything into the formula.
00:25:33.700 --> 00:25:40.900
I substitute in these numbers for these variables.
00:25:40.900 --> 00:25:42.500
I, the interest rate is 10 dollars.
00:25:42.500 --> 00:25:45.600
I am going to put in 10 instead of I; equals.
00:25:45.600 --> 00:25:48.500
P, I don't know; I am going to leave the P.
00:25:48.500 --> 00:25:55.300
R, I know is 3 percent; I change it to a decimal; put it in as R.
00:25:55.300 --> 00:25:59.000
T, I know as 4; I am going to put in 4 instead of the T.
00:25:59.000 --> 00:26:03.900
There is my equation; again I am solving for P.
00:26:03.900 --> 00:26:09.800
Here I can multiply because everything is multiplied together; P times R times T.
00:26:09.800 --> 00:26:14.600
Since I can't multiply P times a number, I can do number times the number.
00:26:14.600 --> 00:26:20.700
These two I can multiply together; that is what I did; multiply them; get 0.12.
00:26:20.700 --> 00:26:28.900
Then to find what P is, remember if you have this example, I can do this number divided by the 3.
00:26:28.900 --> 00:26:37.300
I am going to do 10 divided by 0.12; you just divide it.
00:26:37.300 --> 00:26:40.500
When you divide it, make sure you move the decimal point over twice.
00:26:40.500 --> 00:26:45.100
You have to move this decimal point over twice; bring it up; divide it.
00:26:45.100 --> 00:26:51.500
You end up getting 83 dollars and 33 cents; that is the principal.
00:26:51.500 --> 00:27:00.100
That is how much was deposited to make 10 dollars with a 3 percent interest over 4 years.
00:27:00.100 --> 00:27:06.400
That is how much was put into the bank.
00:27:06.400 --> 00:27:09.000
That is it for this lesson; thank you for watching Educator.com.