Compound Interest (Periodic)

With periodic compounding, each period's rate r is split into n slices and applied n times, so past interest starts earning interest of its own. $5,000 at 4% per year compounded monthly (n = 12) for 10 years grows to A = 5000 × (1 + 0.04/12)¹²⁰ ≈ $7,454.16: about $50 more than yearly compounding would give, because 120 small boosts beat 10 large ones.

Solving for r recovers the rate a savings product actually paid between two statements, and solving for t answers "how long until my balance reaches A?" Enter r as a decimal (4% → 0.04), and note that pushing n toward infinity lands on the continuous-compounding formula $A = Pe^{rt}$.