Compound interest and Euler's number

[@meyou4912]

Bro best visual explanation of why e shows up.

[@MiguelAngelLopezP]

I’m glad to say that it’s not a dream, the bank is currently paying me 13% I guess it just depends on the country. For reference inflation is currently at 6%

[@MathAndPhysics]

Yes, the world has definitely changed since I made this video.

[@anunuevesiete]

Same, I’m getting 15%, crazy isn’t it?

[@jackbauer8460]

Awesome video!

[@gern0tk]

Why do banks not compund continuously? I mean it's sounds complicated but all they really need to do is evaluate the Euler function once per year and pay me the interest I deserve.

[@firstkaransingh]

Where does that 1 come from ? could you explain. Excellent explanation 👏

[@bungus49]

Disclaimer, i'm not a big math guy, I can't explain the euler part lmfao. Just to add on: First, what is the given interest rate of 10% in decimal form? That would be .1 Now if you multiply the principal deposit of $100 by just .1, your product would be less than $100, so that's no good. This essentially tells you what 10% or .1% of $100 is, which is just $10. This is useful however, now we just need to use this info to see what a 10% increase of our principal would be, aka mo money! Thus this is where the 1 comes in, for if you add together the decimal form of the given .1 interest rate with 1: (1+r)=(1+.1)= 1.1, now try multiplying the principal by this value, bam, $110!

[@sushi2slushy]

nothing governs p/r both equals to 1, so this is hard fitted outcome?

[@MathAndPhysics]

I put them both to 1 at the end because I wanted to extract just the e from p*e^r. Also, I think the example of starting with 1€ and an interest rate of 100% is very intuitive, but you could of course run this with any numbers p and r and use the general formula. The point I wanted to make at the end is that this simple problem with nice integer numbers has a solution that contains an irrational number. It is just math but to me it surely feels like a bit of magic.

[@sushi2slushy]

@@MathAndPhysics hey thanks for the reply! i think what really got me to understand this is that for ANY interest_rate, the maximum interest approaches e^interest_rate (with regular -> ~infinite frequent payments)

[@HUGOPEREZ12345]

​@@MathAndPhysicswhy not I=P(1+r)^t ?