Learn about Interest - part 2 Video

Get it off your chest – be the first to comment on this video!

Learn about Interest - part 2

Learn about Interest - part 2 Well, let’s generalize a bit what we learned in the last presentation. Let say I'm borrowing a few dollars that’s what I’ve borrow, so that’s my initial principle. So that’s principle, principle and let the R is equal to the rate. The interest rate that I'm borrowing yet or we could also, write that as 100R%, right and I'm going to borrow it for, well I don’t know T years, T years. Let see if we can come up with equations to figure out how much I'm going to owe at the end T years using either simple or compound interest. So lets do a simple first because that’s simpler. So at times zero, so let’s make this the time axis. Time zero, how much is I'm going to owe? Well that’s right when I borrow it, so if I borrow and pay it back immediately. I would just owe P, right. At time one, I owe P plus the interest plus you can kind of view if there’s a rent on that money and that’s R×P and that previously, in the previous example in the previous video R was 10%, P was 100. So I have to pay 10 dollars to borrow that money for a year and I have to pay back 110 dollars, and we can, this is the same thing as P×1+R, right because you could use as 1P+RP. And then after two years, how much do we owe? Well every year we just pay another RP, right. In the previous example was another 10 dollars. So you know if this 10% every year we just pay 10% of our original principle. So in year two, we owe P+RP that’s what we owe in year one and then another RP, so that equals P+1+2R and just take the P out and you get a 1+R+R. so 1+2R. And then in year three we owe, what we owe in year two, so P+RP+RO and then we just pay another RP or another say you know, if R is 10% or 50% of our original principle plus RP and so that equals P×1+3R, so after T years, after T years. How much do we owe? What’s our original principle times 1+, it would be TR. So you can distribute this out because every year we pay PR and there’s going to be T years and so that’s why it makes sense. So if I were to say, I'm borrowing, let’s see to do some numbers and you could work out this way, and I recommend you just memorize formulas. If I were to borrow 50 dollars at 15% simple interest for 15, well let say for 20 years. At the end of the 20 years, I would owe $50×1+20×.15, right and that equals to $50×1+, what’s 20×.15? It is 3, right. So its 50×=200 dollars, to borrow it for 20 years. So 50 dollars at 15% for 20 years results in 200 dollar payment at the end. So this was simple interest and this was the formula for it. Let see if we can do the same thing with a compound interest. Let me erase all of this and that’s not how I wanted to erase it. There we go. Okay, so at compound interest in year one it’s the same thing really is simple interest and we saw that in the previous video. I owe P+ and now the rate times P and that equals P×1+R, fair enough. Now this is year two is where compound and simple interest of urge. In simple interest we would just pay another RP and becomes 1+2R. In compound interest, this becomes a new principle right. So if this is a new principle, we are going to pay 1+R×this, right. Our original principle was P after one year we paid 1+R× the original principle, right ×1+R rate. So to go into year two, we’re going to pay what we owed at the end of year one which is P×1+R and then we’re going to grow that by our percent. So we’re going to multiply that again ×1+R and so that equals P×1+R². So the way you could think about it in simple interest every year we added a PR, you know in every simple interest we added +PR every year. So this was you know 50 dollars and this is 15% every year we’re adding three dollar, we’re adding 50%, we’re adding 750 in interest right where is P is the principle R of rate. In compound interest, every year we’re multiplying the principle ×1+ the rate right. So if we go to year three, we’re going to multiply this ×1+R, so year three is P×1+R³. So year T is going to be principle ×1+R to the T power. And so let see that same example. This is the, we owed 200 dollars and this example with simple interest. Let see what we owe in compound interest. The principle is 50 dollars, its 50 dollars. 1+ and what’s the rate, .15 and we’re borrowing it for 20 years, so this is equal to 50×1.15 to the 20th power, I know you can’t read that but let me. Now let me see what I can do about the 20th power. So let me use my Excel. Let me clear all of this or actually I use just; use my mouse instead of the pen to. Let me clear everything. Okay so let me just pick at random points. So, I just want to— +1.15 to the 20th power and you could use of any calculator, 16.37. Let say, so this equals 50×16.37 and what’s 50× that plus, 50× that, 818 dollars. So you now realize that if someone is giving you a loan and they say, oh 0711 you need 20 year loan, I'm going to lend it to you at 15%. Its pretty important clarify whether they going to charge you 15% interest at simple interest or compound interest because with compound interest you’re going to end up paying, I mean look at this. You just to borrow 50 dollars; you’re going to paying 618 dollars more than if this was simple interest. Unfortunately, in the real world most of it is compound interest and not only it is compound but they don’t even just compound it every year and they don’t even just compound it every six months. They actually compound it continuously and so you should watch the next several videos and continuously compounding interest. And then you’ll actually start to learn about the magic of E. anyway, I'll see you all in the next video.

Khan Academy

The Khan Academy is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere.

http://www.khanacademy.org/

Learn about Interest - part 2

Well, let’s generalize a bit what we learned in the last presentation. Let say I'm borrowing a few dollars that’s what I’ve borrow, so that’s my initial principle. So that’s principle, principle and let the R is equal to the rate. The interest rate that I'm borrowing yet or we could also, write that as 100R%, right and I'm going to borrow it for, well I don’t know T years, T years. Let see if we can come up with equations to figure out how much I'm going to owe at the end T years using either simple or compound interest. So lets do a simple first because that’s simpler. So at times zero, so let’s make this the time axis. Time zero, how much is I'm going to owe? Well that’s right when I borrow it, so if I borrow and pay it back immediately. I would just owe P, right.

At time one, I owe P plus the interest plus you can kind of view if there’s a rent on that money and that’s R×P and that previously, in the previous example in the previous video R was 10%, P was 100. So I have to pay 10 dollars to borrow that money for a year and I have to pay back 110 dollars, and we can, this is the same thing as P×1+R, right because you could use as 1P+RP. And then after two years, how much do we owe? Well every year we just pay another RP, right. In the previous example was another 10 dollars. So you know if this 10% every year we just pay 10% of our original principle. So in year two, we owe P+RP that’s what we owe in year one and then another RP, so that equals P+1+2R and just take the P out and you get a 1+R+R. so 1+2R.

And then in year three we owe, what we owe in year two, so P+RP+RO and then we just pay another RP or another say you know, if R is 10% or 50% of our original principle plus RP and so that equals P×1+3R, so after T years, after T years. How much do we owe? What’s our original principle times 1+, it would be TR. So you can distribute this out because every year we pay PR and there’s going to be T years and so that’s why it makes sense. So if I were to say, I'm borrowing, let’s see to do some numbers and you could work out this way, and I recommend you just memorize formulas. If I were to borrow 50 dollars at 15% simple interest for 15, well let say for 20 years. At the end of the 20 years, I would owe $50×1+20×.15, right and that equals to $50×1+, what’s 20×.15? It is 3, right.

So its 50×=200 dollars, to borrow it for 20 years. So 50 dollars at 15% for 20 years results in 200 dollar payment at the end. So this was simple interest and this was the formula for it. Let see if we can do the same thing with a compound interest. Let me erase all of this and that’s not how I wanted to erase it. There we go. Okay, so at compound interest in year one it’s the same thing really is simple interest and we saw that in the previous video. I owe P+ and now the rate times P and that equals P×1+R, fair enough. Now this is year two is where compound and simple interest of urge. In simple interest we would just pay another RP and becomes 1+2R.

In compound interest, this becomes a new principle right. So if this is a new principle, we are going to pay 1+R×this, right. Our original principle was P after one year we paid 1+R× the original principle, right ×1+R rate. So to go into year two, we’re going to pay what we owed at the end of year one which is P×1+R and then we’re going to grow that by our percent. So we’re going to multiply that again ×1+R and so that equals P×1+R². So the way you could think about it in simple interest every year we added a PR, you know in every simple interest we added +PR every year. So this was you know 50 dollars and this is 15% every year we’re adding three dollar, we’re adding 50%, we’re adding 750 in interest right where is P is the principle R of rate.

In compound interest, every year we’re multiplying the principle ×1+ the rate right. So if we go to year three, we’re going to multiply this ×1+R, so year three is P×1+R³. So year T is going to be principle ×1+R to the T power. And so let see that same example. This is the, we owed 200 dollars and this example with simple interest. Let see what we owe in compound interest. The principle is 50 dollars, its 50 dollars. 1+ and what’s the rate, .15 and we’re borrowing it for 20 years, so this is equal to 50×1.15 to the 20th power, I know you can’t read that but let me. Now let me see what I can do about the 20th power. So let me use my Excel. Let me clear all of this or actually I use just; use my mouse instead of the pen to. Let me clear everything. Okay so let me just pick at random points.

So, I just want to— +1.15 to the 20th power and you could use of any calculator, 16.37. Let say, so this equals 50×16.37 and what’s 50× that plus, 50× that, 818 dollars. So you now realize that if someone is giving you a loan and they say, oh 0711 you need 20 year loan, I'm going to lend it to you at 15%. Its pretty important clarify whether they going to charge you 15% interest at simple interest or compound interest because with compound interest you’re going to end up paying, I mean look at this. You just to borrow 50 dollars; you’re going to paying 618 dollars more than if this was simple interest. Unfortunately, in the real world most of it is compound interest and not only it is compound but they don’t even just compound it every year and they don’t even just compound it every six months.

They actually compound it continuously and so you should watch the next several videos and continuously compounding interest. And then you’ll actually start to learn about the magic of E. anyway, I'll see you all in the next video.

Transcription by: Scribe4you Transcription Services