I must admit I still don't understand continual compounding

Imagine that instead of compounding the interest every day, you wanted to calculate it every nanosecond. And then, every billionth of a nanosecond. If you keep dividing that until it’s an infinite number of infinitely small compounding, you get a super simple equation:

  interest = e^(years*rate)

10% interest for 5 years?

  e^(5*.1) = 1.649

3% for 8 years?

  e^(8*.03) = 1.271

You can plug any numbers into that and get the end result in 1 step.

Sibling’s explanation is a great starting point! If you understand annual, weekly, and daily compounding, continuous compounding is the limit of what happens when the time you compound over becomes ever shorter. It’s not obvious without calculus, but it’s a well-defined function.

Explained in a terrible way, it's integrals for interest if "compound daily/monthly/yearly" was an estimation using discrete intervals

you didn't really improve by hiding behind "integrals"; this is why so many kids are afraid of calculus.

The explanation worked for me. I learned basic calculus but didn't know about continual compounding interest.

There's a reason I prefaced it with "explained in a terrible way". It clicks that way in my head, might for others

this isn’t kindergarten. if something is described concisely by analysis then that’s how I want it explained to me too.