Where e comes from: compounding more and more often
This animation tracks one dollar growing under 100% annual interest as the number of compounding periods increases: yearly, semiannual, quarterly, monthly, daily, and hourly. Each step evaluates (1 + 1/n)^n and plots the result, showing the sequence climbing toward but never exceeding 2.71828. The visualization connects a concrete finance question to the limit definition of e, making it useful for introducing exponential growth, limits, and the number e in algebra or precalculus classes.
16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
One dollar at 100% interest paid in n instalments: (1 + 1/n)^n for yearly, twice, quarterly, monthly, daily, hourly, then the curve approaching e = 2.71828..., and the limit definition of e.
Make the next one in this series
- Show the same limit using continuous compounding and derive A = Pe^{rt} visually.
- Compare compound interest curves for different annual rates converging to e^r.
- Animate the Taylor series expansion of e^x and show it summing to the same constant e.
