Compound Interest Deep Dive

Algebra 2 · Axiom Academy

Compound your money more often and it grows faster — chase that frequency to its limit and you'll land on one of math's most famous constants. You invest 10,000 at 5% annual interest for 10 years — your bank lets you choose how often it compounds. Three ways to see what “more often” is really worth. Same 10,000 , same 5% rate, same 10 years — only how often it compounds changes. Set the frequency, hit Grow, and watch the balance climb toward the dashed ceiling above it. Strip the scenario to its simplest possible form — 1 at 100% for 1 year — and push the compounding frequency toward infinity. Watch what the gauge locks onto. Is chasing a better frequency worth it? Annual compounding grows it to 16,288.95 after 10 years. Slide toward continuous compounding and watch how much extra that actually buys — and how quickly the extra dries up. Push compounding to its limit and A = P(1 + r/n) nt becomes A = Pe rt — the same constant e ≈ 2.71828 that drives population growth, radioactive decay, and Euler's identity e iπ + 1 = 0 .

This is the written version of the interactive lesson above. See the full Algebra 2 course.