Math Playground
Money

Compound interest derivation

Why A = P(1 + r/n)^(nt) — and where every letter comes from.

If P is the principal, r is the annual rate, n is the number of times compounded per year, and t is years:

Compound interest
A = P(1 + r/n)^(nt)

Why?

Each compounding period multiplies by (1 + r/n). After n·t periods, you've multiplied that many times.

As n → ∞ (continuous compounding), A → P·e^(rt).