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# Introduction to interest | Interest and debt | Finance & Capital Markets | Khan Academy

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.

99 comments

the notion that you exist because a magical sky man pooffed you into existence isn't logic either..

Which is why we call it "faith" and not logic, unlike the big bang theory.

So faith.. because you just can not to too certain..lol

what? how about you just don't worry about what other people believe..

sadly it is slightly worrying when people confuse"real" numbers with God claims..look at OP

It's like money making kids. But money isn't alive. Money shouldn't be able to make kids… I think this is why our economic system goes wrong…

the annotation said you've

u mad bro

The notion that people think it's intelligent to argue about these things isn't even close to logical.

where did 1.1 come from? how did the equation 110 + 10%(110) turn into 100(1.1)2= $121 ? answer me

because every year you get 10% interest, meaning the final total of every year is 110/100 which 1.1.

So with your principal at 100, with 10% interest in mind it is 110/100 x 100 = 110. For the second year you can either calculate it by 110/100 x 110 or (110/100)^2 x 100

Is this whereI would start to learn about finance in general? I know there are several finance-related playlists.

nice man nicee fuck those god lovers lol

The concept of e and compound interest and he was reffering to previous videos.

He did say and now you've learned and he was referring to the compound interest and the number e series.

wow~ it's been 9 months already. Thanks!!

I hear clearly, and after watching all of his videos up to this point in order, it completely makes sense that he would say that. Watch the series on compound interest and the number e and you'll see as well that it's true. If you don't I don't expect you to be arguing anymore since you would be arguing with lack of knowledge.

I'm watching them in upload order I would have never known about that video if that were true. Like I said if you don't watch it, then keep your arguments to yourself. And don't make up lies to justify your argument.

If you are referring to 5:45 no. This is what you owe overall. 1st year- $110 2nd year- $120 etc. You do not pay that at the end of the year, that's how much you owe. Your principal is multiplied by .1 every year (which is the interest rate, 10%) until you pay the principal.

I'm sorry but I'm not interested in this

no, you add 10$ every year to your principal for ten years

Great video 🙂

atually it's not his fault, cause the sub wrote "you've" instead of "you'll"..

Thanks for clarifying what compound interest is exactly.

THX 🙂

can somebody pas this on to Obama ?

Where'd the 1.1 come from??

Yea I'm kind of unsure about the 1.1 also

where did he get 400 from at 8:35.

I thought the original principle was 100??? WTH?

STOP TREATING THE PEOPLE LIKE FIVE YEAR OLDS.

But very helpful.

Thank you so much! I owe you a big part of my studies! Whenever I do not understand economics, statistics, math of finance, you are the one who helps me understand. So I wanted to say thank you!! You are an amazing Professor! Again very very thankful! 🙂

Principle*

@Hanan Abdulaziz

very helpful

I think ur ok ut could afford to be better I guess

"Rent on money" This is the best definition I have ever heard about "interest"

YOU USE WIKIPEDIA O.O

I am thankful to Khan academy. keep up your great work.

Cool

the title made this scary but the video made this very easy

did anyone realize that he spelled principle wrong

great explanation

where did he get 1.1 from??????????

Hello I stumbled upon this video when I was looking for your Share market and Stock and Options related videos, I could not find them anywhere on the channel . Can you help me locate the course or playlist. Thanks,

Follow me on Instagram @livebiebah

Really? Why don't you teach it to the person who filed for bankruptcy four times then? And still thinks he's a "winner" because other people who work with money manage it for him.

You could also teach it to people at Wells Fargo. I had a friend who dropped them cold over 5 years ago because she thought they were "the worst financial institution ever." She withdrew everything and told everyone who would listen about how they were the worst financial institution ever.

Thank you so much khan now I understand compound and simple interest

thanks youre awesome

This guy is an idiot.

There's a formula for simple interest: A=P(1+it) You learn this for the Actuarial FM Exam. A is amount value, P is the principal, i is the interest rate, and t is time. Compound would be A=P(1+i)^t

240р((((((!!!!!!!!!

Funny everyone programmed to accept this interest idea the way it is. You see how the loan shark got $200 from $100 loan? He made $100 for doing nothing. No one else is benefiting 200% from this transaction. If the loan was to buy a bike, the bike manufacture got paid for just 1 bike. The owner received 1 bike. Yet the loan shark get paid for 2 bikes……hmmmm ok great system that no one dares to question.

im a sexual trex lol

isnt 10 percent equal to 0.1 so that each year it would be 100.1

Whos watching this in 2017

Yup

Lol actually hes one of the OG youtubers

They call it interest because people have no interest in loaning money for nothing. But the idea of receiving money on top of the money that they loaned makes the offer much more interesting.

Well done;

Is there any tutorial about Project Feasibility Test Analysis?

i am watching this in 2017

Is there a quicker way to learn this.

I wished sal would have used a new car loan as an example. Most car loans use simple interest thus making the illustration more practical. In his example sal is assuming the principle doesnt change, someone borrows $100 @ 10% interest and waiting x number of years to pay it back. No one does this most people will make subsequent payments over time thus reducing the principle.

but why am i taught to use i=prt instead? with that formula we would jist compute the actual money with the interest… then we wouldnt really be getting the interest unless we subtract it to the principal money, right? but if we really want to get the interest asap we should just use i=prt. then again when looking for the actual money with its interest, we can use p(1+tr).

Is my answers true in number 1. I= 11.0111

Interest is interesting

There shouldn't be a "$" sign when calculating the interest rate. It should just be 10% instead of $10%

Bad bad handwriting…

thanks a lot

_ _

–

Um only 240p come on make them HD

Interest is a bitch

Can we express interest in terms of month or day ,if yes how can ? +khanacademy

in simple interest rate, after each year it should be 110 dollars. same because principle is same and interest is also same

2018: wohoo

@3:28 IM BLIND!!!!

6,000.

货币的时间价值。单利与复利。

How 10/100 = 10???

Hey bogus it's principle

What is the first sentence he said when he begins talking??

Didn't understand anything after 7:38

2018

2018??????? September

This video is AINCIENT! LOL

i swear this is how i had explained to myself, 'rent on money'! im 32 years old noob in finance…thats why sal hits the mark for even the uninitiated!

Learning this in class….yay

I have two questions, can somebody give me an idea please? suppose we have two companies in an industry i.e. 1) ABC 2) DEF. Let's say we have financial reports of both companies for 5 years. For each company i can find all the ratios for every year separately. suppose we are going to find a specific ratio i.e. liquidity ratio of both companies.

Now my questions are: 1) How to find combined liquidity ratio for company ABC for 5 years?

2) How we can calculate combined liquidity ratio of both (industry) companies (ABC and DEF)?

Six minutes of content, four of commercials. No, thanks.

hi

Thank you so much! 👏🏻👏🏻👏🏻 it’s really good lessons you are providing here without putting fees and that’s such a huge thing these days ☹️ many thanks 🙏🏻 even big professors can’t do what you’re doing. Really grateful ✨

2019 👐

Wow eleven years ago.. good ol' 240p

How can you know so much Mr. Khan, thank you for the great explanations

I'm watching this because of the negative interest rates floating around which after watching this video, I am more certain that our financial lenders have gone mad.

This video is a bit chaotic when you get into compounding. Maybe a re-do necessary?

this is very informative but the way it is shown is extremely untidy, unclear and confusing. please can the display be neater?