## Compound interest introduction | Interest and debt | Finance & Capital Markets | Khan Academy

Male Voice: What I want

to do in this video is talk a little bit

about compounding interest and then have a little bit of a discussion of a way to quickly, kind

of an approximate way, to figure out how quickly

something compounds. Then we’ll actually see how good of an approximation this really is. Just as a review, let’s say I’m running some type of a bank and I tell you that I am offering 10% interest

that compounds annually. That’s usually not the

case in a real bank; you would probably compound continuously, but I’m just going to

keep it a simple example, compounding annually.

There are other videos on compounding continuously.

This makes the math a little simpler. All that

means is that let’s say today you deposit $100

in that bank account. If we wait one year,

and you just keep that in the bank account, then

you’ll have your $100 plus 10% on your $100 deposit. 10% of 100 is going to be another $10. After a year you’re going to have $110. You can just say I added 10% to the 100. After two years, or a year

after that first year, after two years, you’re going to get 10% not just on the $100,

you’re going to get 10% on the $110. 10% on 110 is you’re going to get another $11, so 10% on 110 is $11, so you’re going to get 110 … That was, you can imagine,

your deposit entering your second year, then

you get plus 10% on that, not 10% on your initial deposit. That’s why we say it compounds. You get interest on the

interest from previous years. So 110 plus now $11. Every year the amount of interest we’re getting, if

we don’t withdraw anything, goes up. Now we have $121. I could just keep doing

that. The general way to figure out how much you

have after let’s say n years is you multiply it. I’ll use

a little bit of algebra here. Let’s say this is my original

deposit, or my principle, however you want to

view it. After x years, so after one year you

would just multiply it … To get to this number right

here you multiply it by 1.1. Actually, let me do it this way. I don’t want to be too abstract. Just to get the math here,

to get to this number right here, we just multiplied that number right there is 100 times 1

plus 10%, or you could say 1.1. This number right here is going to be, this 110 times 1.1 again.

It’s this, it’s the 100 times 1.1 which was

this number right there. Now we’re going to multiply

that times 1.1 again. Remember, where does the 1.1 come from? 1.1 is the same thing as

100% plus another 10%. That’s what we’re getting.

We have 100% of our original deposit plus another 10%, so we’re multiplying by 1.1. Here, we’re doing that twice. We multiply it by 1.1 twice. After three years, how

much money do we have? It’s going to be, after

three years, we’re going to have 100 times 1.1 to the

3rd power, after n years. We’re getting a little abstract here. We’re going to have 100

times 1.1 to the nth power. You can imagine this is

not easy to calculate. This was all the situation

where we’re dealing with 10%. If we were dealing in a

world with let’s say it’s 7%. Let’s say this is a

different reality here. We have 7% compounding annual interest. Then after one year we

would have 100 times, instead of 1.1, it would be 100% plus 7%, or 1.07. Let’s go to 3 years. After 3 years, I could do 2 in between, it would be 100 times

1.07 to the 3rd power, or 1.07 times itself

3 times. After n years it would be 1.07 to the nth power. I think you get the

sense here that although the idea’s reasonably

simple, to actually calculate compounding interest is

actually pretty difficult. Even more, let’s say I were to ask you how long does it take

to double your money? If you were to just use

this math right here, you’d have to say, gee, to double my money I would have to start with

$100. I’m going to multiply that times, let’s say whatever, let’s say it’s a 10% interest, 1.1

or 1.10 depending on how you want to view it, to

the x is equal to … Well, I’m going to double my money so it’s going to have to equal to $200. Now I’m going to have to solve for x and I’m going to have to

do some logarithms here. You can divide both sides by 100. You get 1.1 to the x is equal to 2. I just divided both sides by 100. Then you could take the

logarithm of both sides base 1.1, and you get x. I’m showing you that this is complicated on purpose. I know this is confusing. There’s multiple videos on how to solve these. You get x is equal to log base 1.1 of 2. Most of us cannot do this in our heads. Although the idea’s simple, how long will it take for me to double

my money, to actually solve it to get the exact answer, is not an easy thing to do. You

can just keep, if you have a simple calculator, you

can keep incrementing the number of years until you

get a number that’s close, but no straightforward way to do it. This is with 10%. If

we’re doing it with 9.3%, it just becomes even more difficult. What I’m going to do in the next video is I’m going to explain something called the Rule of 72, which

is an approximate way to figure out how long,

to answer this question, how long does it take

to double your money? We’ll see how good of

an approximation it is in that next video.

Wow, I did this JUST last term and I really wished there was a Khan video for it. I can't believe my bad luck…

Thanks sal! Great video as usual.

There is one on this certain topic that Mr. Khan did a long time ago in his finance playlist, I believe. You may not have been searching hard enough!

How about finding the total amount of the money is the interest rate per month and the deposited cash is compounded monthly

If*

Thanks

Thanks…Don't know why Pre-calc requires me to learn this…

Short,precise,simple,sweet…you make my short list for the Nobel

I like turtles

Hands down best video ever

Halona w/here

Hey,

I'm from Switzerland and I love Khan Academy and these maths videos! I learned a lot with these videos! So thanks to Khan Academy!

Currently we have this topic in school and my teacher can't explain that as good as you 😀

Little question, are you also going to add English grammar explanation videos on Khan Academy? That would be really nice!

why does it become $11? can someone explain it to me, that'd be nice. 🙂

Why are you multiplying it by 1.1… What does that stand for? Is that the interest then why is not just written as 10%?

can some one explain something to me in simple plain English

if i have a term deposit account which pays monthly 2% does that mean i get 2% interest every single month of the year equating to 24% a year

im having a hard time understanding the fact sheets banks have given me they say things like this

Term at maturity monthly quarterly

1 month 2%

2 months 3.10%

3 months 3.15%

12 months 3.35% 3.25% 3.30%

so what does all this mean so say for example with the 12 months does that mean if i start of with $5000 each month i get $162.5 from interest?

"Calculating compounding interest is pretty difficult"? a few exponentials or logarithms! Let's define difficult, aren't kids supposed to learn all this before hitting high school?

This video is very helpful. Could you please also do a video on decreasing compounds? I don't know what it's called but when say for example a car decreases by 10% of its value at that point every year? Sorry if this isn't very clear!

if u guys dont get this i feel bad cause its easy peasy

You are awsome! Even though it is simple, you explain it very well for those who forgot 🙂 Thank you!

So how do i find out how to start getting compound interest ? What type of investment do I have to make to take advantage of compound interest ?

I love you man, thanks!

where is that next video to ease the difficult calculation??

have an exam on Wednesday I have tried to understand compound interest for 2 month know but I just still don't understand it after all this hard studying paying hard attention in class I still don't get it (grade 11 essential exam) guest my parents are going to send me back to Africa because I have a 87% chance of failing

Great Video

thank you

Guess I have to start learning proper ways to retire in 8th grade.

should've given the formula first

why cant i freakin understand!?!?!?!?!?!?

This is what he meant A=P(1+R/T)NT

A =total amount

P=principal

R=rate

N=compounding period

T=time

because I could not understand what he was saying.

(p.s. don't forget B.E.D.M.A.S)

Just give me the formula that's y I came here. To for the stupid jiberish

Terrible teaching

Thanks a lot for the video, it simplified things a lot for me (compared to how my teacher explained it).

I used to hate math ,but now numbers are my best friend

Thanks this helped so much

What if for example, 65000 is depreciating by 16% each year?

frustrating. So how long does it take ……..already. Apparently a long time if you

are writing it out and then not telling us. ahhhhhhhhhhhhhhh!

So if we just knew how long it took $100 to double — then we would have a good idea of how this works. So how long does it take $100 to double at 10% interest??? You don't tell us — why not? Then I would get compound interest at work.

If it did not compound then I would get $10 each year – and I need another $100 to double the amount. So the answer is 10 years to wait for it to double without compounding. since it does compound—- probably takes about 9 years. It is that simple.

Thank you for this video! In school I was only given the compounding interest formula, which I never understood how it worked, and then told to just plug numbers into the formula and get my answer . After this explanation I see how the formula works. Can't believe I never realized what the (1 +r) part was doing this entire time!

Thanks, this was pretty helpful.

Helped a lot Thanks!!!

What app is he using

SIKTIRGIT OROSPUCOCUGU

I could not understand it well

Your amazing dude.

when i grow up i wanna be a calculator

I really really really wish he would have solved this. I was following and then realized he wasn't going to solve. Aarrggg! C'mon!!

Very Helpful Thanks For The Video

Thank u man really helpful vid

Nice

mr.khan

no offence but its kinda confusing…

I k ow your trying to help, bit I cNt see anything on the screen behind you.

great vid! btw you sound like dj vlad…hehe

i got 8ish years–anyone else?

omg this saved my life. thank you so much! 😀

This really helped me with my homework

Im in fifth grade and i could understand pretty well…

Thank you so much I finally understand this!!

very well don

Hi Mr. Khan. Very good video. the POWER of Compounding Interest Annually, Monthly, Weekly, or event BETTER Daily. Julia

👎🏻

good video

Thank you. Great video.

when i grow up i wanna be a calculator

x = 7.27 years btw in case you were wondering

Now I understand why I can't balance a checkbook

Start with the equation and don't write all over the place it's hard to follow

BITCONNEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEECT

thanks! great video and I understood instantly

Uhhh I don’t get this 🙄

Think you could have dragged that on any further? Your videos drag on so long I often loose focus during your constant elementary examples as to what is going on. I doubt anyone searching how to calculate compound interest needs a elementary math lesson (1+10%) about what is going on. If they cant figure it out then watching this video is pointless either way.

yee

Should’ve told us the formula and also I didn’t understand the question at the end

thank you so much your video really helped me, liked and subscribed

100 x ( 1.1 ) n is all u need to know lmfao

The answer is 100 x 1.1 to the 7.27254089735 power = 200

i am in 4th grade and i sorta understand

THANK YOU. GOD BLESS YOUR SOUL

This helped me more than my teacher did

I am 3rd grade and I am a math teacher of 6 grade now I need to teach them compound interest in 8th grade. My whole life is math.

Can any math genius here answer this question?

If Joe invests $1,000 in his portfolio every month into a ETF that grows 10% a year. how long will it take Joe to grow his portfolio to $1M? $10M? 100M? If that ETF grows 10% every year does that mean it grows 0.00833 every month?

SHIFT SOLVE

Excuse me sir but, why do you keep on repeating your words always, just after some sentences?

You write better on a computer that I do in real life

we want something different

When I grow up, I wanna invent my own math formula for middle school kids

how does this guy remember all of these maths topics

I was absent for a week, and this fella made me catch up on probably all of what we did.

I still don’t get it man.

goddd koa

Thanks Sal 🙂

Awesome video! Compound interest is so important for achieving long term wealth!