WEBVTT
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Hey, this is Professor Perez from South of that college.
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Today, we're going to do some problems with simple interest.
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Of course, we've got to get Charlie out.
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He better be ready to go.
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Hey, Charlie, you ready to go?
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Yeah, your favorite subject.
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Simple interest problem.
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Oh, you think this is fun, huh?
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Remember, if you don't get it down now, you can always come back and do it.
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Next semester.
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Here we go.
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Right there.
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Simple interest.
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Yeah, some people call this formula PURT.
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That's because I equals PRT, where I is the interest.
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P is the principal.
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R is the interest rate and T is the time and years.
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Now, in some cases, we take out a loan for 90 days, in which case we have to convert days
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to years.
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And that conversion that's used with the simple interest formula is that one year is 360
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days.
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That's because the average of all of our 12 months is 30 days and 30 times 12 is the 360.
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Well, we all know that in a year, there's 365 days or actually 365 and a quarter days.
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That's why every fourth year, we have a leap your day.
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Anyway, let's get to work, Charlie.
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Right here.
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Yeah, a student takes out an emergency loan for $600 for school supplies.
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The interest rate is 6% annually.
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How much interest does a student have to pay after six months?
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Now, notice here our time is not a full year, it's six months.
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Okay, so keep that in mind.
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Now, our interest is what we're going to calculate, right?
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How much interest does a student have to pay?
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The principal is 600, the rate as a decimal is 0.06.
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And the time in years, Charlie, six months is how much a year?
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Huh, that's right.
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So 0.5 years.
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And now we use our formula i equals prt, our principal is 600, our rate as a decimal is
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0.06 and our time is 0.5 or a half.
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Okay, Charlie, what do you get for that product?
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18.
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That's right.
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So after six months, the student has to pay how much, Charlie?
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18.
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Six, that's right.
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$618 total to pay off that loan, right?
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Because the student has to pay $18 of interest.
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All right, that's what we just calculated.
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All right, Charlie, let's do another one.
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An investor deposits $2,000 into a savings account.
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The account pays 7% interest annually.
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What is a principal after two years?
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Now, be careful with this one.
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Now, notice Charlie, it's every two years, but the, there is 7% interest paid annually.
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That means every year we have to calculate the interest.
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And because we're putting the money into an account for two years, we have to do two calculations,
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one after the first year and then one after the second year.
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Watch, you'll see.
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We're going to have to figure out what our interest is, right?
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Our initial principal is 2,000.
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The rate as a decimal Charlie is what?
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0.07, that's right.
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And notice our time is two years, but we have one plus one because we got to do two calculations.
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So here we go for the first year, Charlie.
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I equals PRT.
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Our principal for the first year is 2,000.
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Our rate is 0.07 and the time is one year.
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This is for the first year.
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So what do you get for that product, Charlie?
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140.
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Very nice.
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So that $140 is the interest earned after the first year.
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So after the first year, Charlie, what is the principal?
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2,000, 140.
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Very nice there.
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So let's do the calculation for the second year.
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I equals PRT.
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Our new principal is what, Charlie?
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2,000, 140.
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Very nice.
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Our rate is 0.07 and our time is one year.
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This is for the second year.
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Okay, Charlie.
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So our earned interest is what?
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What's that product?
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149.
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80.
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Very nice there, Charlie.
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$149.80.
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So now, this is the interest earned for the second year.
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So Charlie, what is the total balance after the two years?
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Remember, it's got to be 2,140 plus the $149.80.
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And so what do you get?
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$20, 189.80.
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It's very nice there, Charlie.
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So for the two years, there's the principal.
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Now how much did the investor actually earn over the two years, Charlie?
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$2,89.80.
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And that's right.
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Okay, not bad.
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All right, Charlie.
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Let's do another one.
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A student needs a 90-day loan for $750.
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The annual interest rate is 18%.
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Careful with that.
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How much does a student pay the lender after 90 days?
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So the student is going to pay off a loan in 90 days, but let's figure out how much he
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has to pay.
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You've got to pay some interest plus the amount he borrowed.
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All right, so we're going to use our simple interest formula, eyes that we're going to try
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to calculate.
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The principal is $750.
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Now what's the rate, Charlie?
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Remember, it has to be a decimal.
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And so what is it?
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0.18.
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That's right.
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Remember, you've got to move the decimal.
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Two places to the left.
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And now the time and years, now here's where we have to be careful because the time we're
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given is 90 days.
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And that has to be converted into years.
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And so Charlie, we were told at the beginning of his lecture that one year is how many days?
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360.
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That's right.
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So to convert that 90 days to years, it's 90 divided by 360.
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Or it's that fraction of a year.
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That's another way of thinking about it.
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So we're going to do conversions in the next lecture, by the way.
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So we'll talk more about this conversion here.
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Now, so here's our formula.
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I equals our principal, which is 750, our interest rate, which is 0.18.
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And our time and years, now Charlie, what's this quotient?
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90 divided by 360.
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0.25.
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0.25.
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Very nice.
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And so now we get our product.
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And what is our product, Charlie?
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33.75.
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That's right.
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$33.75.
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So that's how much interest the student has to pay on top of the money that he already borrowed.
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And so Charlie, what's the total amount that the student has to pay after the 90 days?
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73.
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That's right.
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You just sum those up and that gives it to you right there.
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So that completes our simple interest lecture.
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That was so much fun.
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I think it's time for us to kick a break and relax.
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We'll see you all again soon.