Compound Growth

Algebra 2 · Axiom Academy

One relationship — B = P(1 + r) t — decides every compounding balance. Save on a schedule, and the deposits add up to a geometric series. You deposit 1,000 into an account paying 5% a year , compounded annually — one relationship decides the balance at any year, and what regular deposits build up to. Set a rate and press Grow — each year the balance is multiplied by the same factor, (1 + r), so year-to-year it's a geometric sequence. Now save 1,000 every year instead of once — drag the number of years and watch the running deposits add up to a geometric series. Is chasing a higher rate worth it? You're earning 5% on 1,000 for 20 years — drag the rate up and watch the extra dollars grow FASTER each point, not slower. The same (1 + r) engine runs every compounding balance — multiply, don't add , and the growth accelerates. A single 1,000 deposit at 5% clears 2,653 in 20 years; save 1,000 a year instead and you've built 12,578 — the running deposits summed as a geometric series. (Add a constant AMOUNT each step instead of a constant PERCENT — like extra seats per stadium row — and you get an arithmetic sequence, not geometric.)

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