 This video will talk about simple interest applications. So this is a simple interest, probably the simplest ones we can have. I is equal to P times R times T. I is the interest, P is the principal, and the R is your rate, and you have to be sure that you write your rate as a decimal. And then we have T, which is going to be time, and it's usually in years. So we have a finance company that offers a payday loan, a small $75 loan, to help people get it by a payday, usually no longer than two weeks, but we're going to do time in years, so that's going to be important right here. If the cost of this service is $18.75, determine the annual interest rate of interest charged by this company. So let's see what we have. We have a small loan of $75, and this is going to be RP. That's how much we're putting in. And then we have this two weeks, which is going to be our T, but we've got to think about the weeks. And then they tell us this $18.75, and that's going to be our I. They want us to find R. Determine R. So let's write our formula. I, we said was $18.75, is equal to the principal, which is $75, times the rate, which we don't know, times the time, which is two weeks. We know that there's 52 weeks in a year, so since we're going into years, we can write it with respect to weeks. So we have two over 52, so two per our 52 weeks, or it's 126 a year. So it's really going to be times 1 over 26. So what do we have here? Simply make it look a little nicer now. 75 times 1 over 26 would be 75 over 26 times R, which we're trying to solve for. This is our unknown. So we would want to multiply both sides by 26 over 75. When you divide by a fraction, remember, you multiply by its reciprocal. And if we take that, I have not done that in my calculator, so I'll have to pull that up. And I'm just going to literally, I can have a decimal answer, I want a decimal answer. But I'm literally just going to say 26 divided by 75 in parentheses, times my 18.75. And we find out that that answer is 6.5. So R is 6.5. But remember, we have to move the decimal two places to be able to figure out what the percentage is, so that is actually 650%. What does that tell you about getting a payday loan? So now we're going to talk about the total amount accumulated, that's this A, accumulated value. And to do that, you take your principal. But then you add to that the principal times the rate times the time. So this is our interest, okay? This is the principal plus our interest, if you think about it. But we wrote it this way so that you could see that we have a common factor of P. So we wrote P out here, and then we were left with 1, P times 1, and RT. So that's, we're going to use it as A is equal to P times 1 plus the rate times the time. So our problem. Business in strip mall, MS Custom Card Shop borrows $50,000. So that's the principal of this, in this account. From a group of investors at 4.55%, that's our rate, although we have to make it a decimal. And the business booms and blossoms enabling Emma to repay the loan fairly quickly. If she pays $62,500, which is the accumulated amount, how long will it take? How long was she using this loan? So we have, let's write it again, A is equal to P times 1 plus RT. It's simple interest, so it's just RT. So A is the $62,500, and we said we were investing $50,000 times 1 plus. And then we've got our rate over here, 4.55%. Remember you have to divide by 100 or move the decimal 2 to the left. So here's tens, there's hundreds. So we're going to have 0.0455 for our rate. And then for our time, we're going to have a T, because we don't know how long that is. That's what they're asking us for. This is a pretty straightforward problem. We have something in parentheses where our T is. So we have to clear everything away from the parentheses. So we're going to end up with $62,500 divided by our $50,000. And that's going to be equal to 1 plus 0.0455T. Now we have a linear equation, and I'm just going to leave it like this. Because I only want to get my calculator at once. So $62,500 divided by $50,000, and I'm subtracting my 1. Well, AB equal to 0.0455T. And if I move to where I have more space, the last thing I'm going to do is take my $62,500 divided by my $50,000, subtracting 1. And all of that, I will divide by 0.0455. And now I'm ready to look at my calculator, because I need to know that as a time. That doesn't really mean anything to me. Literally, like I see it, parentheses $62,500 divided by $50,000, and then minus 1. Order of operations will divide before I subtract. So I'm okay there. Close my parentheses divided by 0.0455. When I press Enter, I find out that it's going to take about five and a half years.