Placeholder Image

字幕表 動画を再生する

  • Well now you've learned what I think is quite possibly one of

  • the most useful concepts in life, and you might already be

  • familiar with it, but if you're not this will hopefully keep

  • you from one day filing for bankruptcy.

  • So anyway, I will talk about interest, and then simple

  • versus compound interest.

  • So what's interest?

  • We all have heard of it.

  • Interest rates, or interest on your mortgage, or how

  • much interest do I owe on my credit card.

  • So interest-- I don't know what the actual formal definition,

  • maybe I should look it up on Wikipedia-- but it's

  • essentially rent on money.

  • So it's money that you pay in order to keep money

  • for some period of time.

  • That's probably not the most obvious definition, but

  • let me put it this way.

  • Let's say that I want to borrow $100 from you.

  • So this is now.

  • And let's say that this is one year from now.

  • One year.

  • And this is you, and this is me.

  • So now you give me $100.

  • And then I have the $100 and a year goes by,

  • and I have $100 here.

  • And if I were to just give you that $100 back, you would

  • have collected no rent.

  • You would have just got your money back.

  • You would have collected no interest.

  • But if you said, Sal I'm willing to give you $100 now if

  • you give me $110 a year later.

  • So in this situation, how much did I pay you to keep

  • that $100 for a year?

  • Well I'm paying you $10 more, right?

  • I'm returning the $100, and I'm returning another $10.

  • And so this extra $10 that I'm returning to you is essentially

  • the fee that I paid to be able to keep that money and do

  • whatever I wanted with that money, and maybe save

  • it, maybe invest it, do whatever for a year.

  • And that $10 is essentially the interest.

  • And a way that it's often calculated is a percentage

  • of the original amount that I borrowed.

  • And the original amount that I borrowed in fancy banker or

  • finance terminology is just called principal.

  • So in this case the rent on the money or the interest was $10.

  • And if I wanted to do it as a percentage, I would say 10 over

  • the principal-- over 100-- which is equal to 10%.

  • So you might have said, hey Sal I'm willing to lend you $100 if

  • you pay me 10% interest on it.

  • So 10% of $100 was $10, so after a year I pay you

  • $100, plus the 10%.

  • And likewise.

  • So for any amount of money, say you're willing to lend me any

  • amount of money for a 10% interest.

  • Well then if you were to lend me $1,000, then the interest

  • would be 10% of that, which would be $100.

  • So then after a year I would owe you $1,000 plus 10% times

  • $1,000, and that's equal to $1,100.

  • All right, I just added a zero to everything.

  • In this case $100 would be the interest, but

  • it would still be 10%.

  • So let me now make a distinction between simple

  • interest and compound interest.

  • So we just did a fairly simple example where you lent money

  • for me for a year at 10% percent, right?

  • So let's say that someone were to say that my interest rate

  • that they charge-- or the interest rate they charge to

  • other people-- is-- well 10% is a good number-- 10% per year.

  • And let's say the principal that I'm going to borrow

  • from this person is $100.

  • So my question to you-- and maybe you want to pause it

  • after I pose it-- is how much do I owe in 10 years?

  • How much do I owe in 10 years?

  • So there's really two ways of thinking about it.

  • You could say, OK in years at times zero-- like if I just

  • borrowed the money, I just paid it back immediately,

  • it'd be $100, right?

  • I'm not going to do that, I'm going to keep it

  • for at least a year.

  • So after a year, just based on the example that we just did, I

  • could add 10% of that amount to the $100, and I would

  • then owe $110.

  • And then after two years, I could add another 10% of the

  • original principal, right?

  • So every year I'm just adding $10.

  • So in this case it would be $120, and in year three,

  • I would owe $130.

  • Essentially my rent per year to borrow this $100 is $10, right?

  • Because I'm always taking 10% of the original amount.

  • And after 10 years-- because each year I would have had to

  • pay an extra $10 in interest-- after 10 years I

  • would owe $200.

  • Right?

  • And that $200 is equal to $100 of principal, plus $100 of

  • interest, because I paid $10 a year of interest.

  • And this notion which I just did here, this is actually

  • called simple interest.

  • Which is essentially you take the original amount you

  • borrowed, the interest rate, the amount, the fee that you

  • pay every year is the interest rate times that original

  • amount, and you just incrementally pay

  • that every year.

  • But if you think about it, you're actually paying a

  • smaller and smaller percentage of what you owe going

  • into that year.

  • And maybe when I show you compound interest

  • that will make sense.

  • So this is one way to interpret 10% interest a year.

  • Another way to interpret it is, OK, so in year zero it's $100

  • that you're borrowing, or if they handed the money, you say

  • oh no, no, I don't want it and you just paid it back,

  • you'd owe $100.

  • After a year, you would essentially pay the

  • $100 plus 10% of $100, right, which is $110.

  • So that's $100, plus 10% of $100.

  • Let me switch colors, because it's monotonous.

  • Right, but I think this make sense to you.

  • And this is where simple and compound interest

  • starts to diverge.

  • In the last situation we just kept adding 10%

  • of the original $100.

  • In compound interest now, we don't take 10% of

  • the original amount.

  • We now take 10% of this amount.

  • So now we're going to take $110.

  • You can almost view it as our new principal.

  • This is how much we offer a year, and then we

  • would reborrow it.

  • So now we're going to owe $110 plus 10% times 110.

  • You could actually undistribute the 110 out, and that's

  • equal to 110 times 110.

  • Actually 110 times 1.1.

  • And actually I could rewrite it this way too.

  • I could rewrite it as 100 times 1.1 squared,

  • and that equals $121.

  • And then in year two, this is my new principal-- this is

  • $121-- this is my new principal.

  • And now I have to in year three-- so this is year two.

  • I'm taking more space, so this is year two.

  • And now in year three, I'm going to have to pay the $121

  • that I owed at the end of year two, plus 10% times the amount

  • of money I owed going into the year, $121.

  • And so that's the same thing-- we could put parentheses around

  • here-- so that's the same thing as 1 times 121 plus 0.1 times

  • 121, so that's the same thing as 1.1 times 121.

  • Or another way of viewing it, that's equal to our original

  • principal times 1.1 to the third power.

  • And if you keep doing this-- and I encourage you do it,

  • because it'll really give you a hands-on sense-- at the end of

  • 10 years, we will owe-- or you, I forgot who's borrowing from

  • whom-- $100 times 1.1 to the 10th power.

  • And what does that equal?

  • Let me get my spreadsheet out.

  • Let me just pick a random cell.

  • So plus 100 times 1.1 to the 10th power.

  • So $259 and some change.

  • So it might seem like a very subtle distinction, but it ends

  • up being a very big difference.

  • When I compounded it 10% for 10 years using compound

  • interest, I owe $259.

  • When I did it using simple interest, I only owe $200.

  • So that $59 was kind of the increment of how much more

  • compound interest cost me.

  • I'm about to run out of time, so I'll do a couple more

  • examples in the next video, just you really get a deep

  • understanding of how to do compound interest, how the

  • exponents work, and what really is the difference.

  • I'll see you in the next video.

Well now you've learned what I think is quite possibly one of

字幕と単語

動画の操作 ここで「動画」の調整と「字幕」の表示を設定することができます

A2 初級

興味のある方へのご紹介 (Introduction to interest)

  • 19 2
    kellylin007 に公開 2021 年 01 月 14 日
動画の中の単語