The Mathematics of Compound Interest — A Developer's Deep Dive By Jessica Arnwine, CAER Financial Group | caergroup.com The Formula The compound interest formula: A = P(1 + r/n)^(nt) Where: A = Final amount P = Principal (initial deposit) r = Annual interest rate (decimal) n = Compounding periods per year t = Time in years The Rule of 72 — A Logarithmic Approximation The precise doubling time formula: T = ln(2) / ln(1 + r) ≈ 0.693 / r The Rule of 72 approximates this as: T ≈ 72 / (r × 100) Why 72 and not 69.3? Because 72 is divisible by 2, 3, 4, 6, 8, 9, and 12 — making mental arithmetic dramatically easier with ~1-2% error for rates between 2-20%.…