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

Created by Sal Khan.

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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.

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[sudipachakravarty]

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

[Ash-iihg]

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.

[Ygnez]

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

[Playxen]

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

[jeremytay]

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!

[gabrielherzog]

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

[sumeiahaltareb]

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

[carlossanchez]

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

[evanwong]

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

[dianafarhat]

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

[Dawwe]

Very simple when laid out like this, thank you!

[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.

[swarnim]

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

[ryanio]

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

[princxssluci]

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

[warcatbattalion]

skip to 8:00 for what actually matters

[iosonoi.]

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

[Daniel-gfid]

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

[sridellahife]

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

[Alock]

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