Formula for continuously compounding interest | Finance & Capital Markets | Khan Academy

Created by Sal Khan.
Watch the next lesson:
www.khanacadem...
Missed the previous lesson? Watch here: www.khanacadem...
Finance and capital markets on Khan Academy: This is an older tutorial (notice the low-res, bad handwriting) about one of the coolest numbers in reality and how it falls out of our innate desire to compound interest continuously.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Finance and Capital Markets channel: / channel
Subscribe to Khan Academy: www.youtube.co...

[@sudipachakravarty2332]

everybody stop. he's talking the language of the gods

[@Ygnez]

Thanks, really helpful to understand where the formula comes from rather than just typing it in at the exams :D

[@Ash-ii4hg]

I know this is really late, but thank you Sal so much for this video. Really helped me out understand this in 8 minutes when I couldn’t in a whole hour.

[@Playxen69]

Man i have been in trouble understanding this easy notion eventhough i have a bachelor in economics. Grateful for your videos !

[@jeremytay273]

Hahaha! I was just watching Futurama's older episodes... 93 cents at 2.25 interest for 1000 years was about 4.28 billion... Searced it and saw all these different arguments for compounding interest. Khan's tha mannnn!

[@gabrielherzog2462]

I don't get how my math book didn't include such a simple helpful equation.

[@gabrielgan2971]

Ikr, same here, if they included this explanation, I wouldn't have been so confused

[@chocomalk9801]

Loansharking 101

[@carlossanchez340]

Sal: Writes seriously confusing expressions Also Sal: "oh, by the way, these expressions can be written in 4 letters"

[@evanwong7463]

Thank you very much. This is the only channel clearly explained how the formula comes from

[@dianafarhat9479]

Thank you so much for sharing the mathematical derivation as well!

[@marsCubed]

KhanAcademy probably mentions this in another video. However, for a quick way to get doubling time (useful for checking results). Doubling time = 72 divided by rate of increase. (plz note, it introduces some inaccuracy) ie, 6% interest per year = 72/6 = 12 = doubling time of 12 years. ie, the initial quantity will double in 12 years with a 6% rate of increase. This shortcut might be good as a the subject of a video.. ie, why is it that 72 works like this? I get it intuitively, imagining a function curve, but have never seen it explored/described properly.

[@deweizhang9054]

khan literally knows everything

[@Dawwe9505]

Very simple when laid out like this, thank you!

[@masonjohnson6159]

You guys: *explain stuff in a very good way* Me, being dumb: I don’t get it anyways I love this channel and would be forever stuck without it

[@ryanio123]

This is great Sal. Thank you very much - very well explained.

[@sumeiahaltareb15]

watching this and being able to understand it just makes me feel so much love. thank you

[@thomasbrown336]

Great video, and explanation.

[@1986svs05]

@4:32 the whole goal is fuckin to get ... lol

[@iosonoi.7132]

Wow you made me wait 8 minutes and 40 seconds to tell me compound interest =Pe^(rt)

[@Ash-ii4hg]

True, but he explained how it works. I mean, you really can just do a Google search if you really want to know, but you can’t fully get it just by that. Here it instead shows how the equation is made and why it works out, a lot more important in my opinion.

[@swarnim7745]

So we can use either formulas right? The one we started with in the beginning and the one we derived by the end?

[@mwerensteijn]

Thanks a lot!

[@sudipachakravarty2332]

imma put this formula as my wi-fi password

[@emmabrembah774]

it very interesting working it

[@Daniel-gf5id]

how do you make this an exponential function so that I can graph it?

[@janetaylor8055]

@MathMars Using the formula A=Pe^rt for continuously compounding interest, when you solve to see how long it takes P to double, you always end up with ln(2) divided by the interest rate. ln(2)=.693, so ln(2)/.06 is approximately equal to 72/6

[@Majagarbulinska]

How can you know so much!

[@Majagarbulinska]

I mean, whatever I need to know I search for it in Khan Academy and you are almost always the tutor

[@sridellahife5486]

Is this on the app?? I don't see it!

[@alex.yorkeu2563]

Thank you!

[@Alock94]

How do you input this into a financial calculator comment section?

[@sachinladha1111]

Infinity is magical

[@satishmohite7718]

sir, which platform/software is used for demonstration; its very attractive!!

[@sudipachakravarty2332]

7:48 "all of that is equal to E" yes, guys, even Sal Khan agrees that whatever happens, everything comes back to the E (you know what time it is...)It's meme review time

[@milindbebarta2226]

But if 0.05 is the annual compounded rate, isn't the continuously compounded rate = ln(1+0.05) and not 0.05?

[@harsha2874]

I think you forgot to add 1 50(1+0.10)^3 =66.55

[@minnieanimals9646]

He is too smart

[@BhagwatMarg471]

Thanks sir

[@MrMarkgyuro]

wow. i got the aha moment

[@abhivish2017]

Nice...

[@heyitsmeh8465]

is this the same thing as in engineering economics?

[@warcatbattalion]

skip to 8:00 for what actually matters

[@turnwell9530]

ecksdee Thank you

[@francisraemdonck1703]

I do that aprox on the top of my head. Maybe that explains the hair loss.

[@PetStuBa]

the fun starts when the interest rate depends on time :p

[@sudipachakravarty2332]

oh no. we don't do that here

[@RitsuOuO]

I need an answer now. How do you do this problem? What interest rate is required for an investment subject to continuous compounding to double in 10 years? I am so confused because this problem only has T=10years.

[@RitsuOuO]

***** It's correct, I figured it out a while ago though, thanks.

[@carlouienievera2307]

I like how used up the calculator looks

[@jligon3]

Inter arresting

[@alexbenfield3374]

Subscribed.

[@stylistfashionboo]

does anyone know how to work out 't', if a question does not state a number for it?

[@cierraropp7789]

I had the same question. I am trying to figure out what "t" is.

[@user-im8kd4ey5n]

HELP ME!!! PLEASE!!!!! MY BRAAAAIIIN!!!!

[@jasontan6184]

t is the number of years. u can figure it out by using logarithm.t will be: [ln(FV/PV)]/r

[@vedantvohra3949]

I don’t get it!

[@jobertescoreal9532]

Escoreal, Jobert L.

[@matildawillcox1693]

What a vid

[@1971SuperLead]

That made no sense to me.

[@alexlenskii]

Cause you're stupid

[@willardnyambalo934]

you are funny

[@RedSauce1]

My brain :(

[@GermanSnipe14]

#Khan2016

[@sachinsingh1469]

*E*

[@prateekkundra5019]

RIP

[@CarolinaKid_]

Stop at 4:30, after that its nonsense

[@Dawwe9505]

That's literally the where the point of the video is lol

[@Ash-ii4hg]

idk, i understood it...

[@bobby1113]

Stutter Stutter