Compound Interest Calculator — Future Value & Growth

The future value formula for compound interest is: FV = P × (1 + r/n)^(n×t), where P = principal, r = annual interest rate (as decimal), n = number of compounding periods per year, t = time in years. With monthly contributions (C): FV = P(1+r/n)^(nt) + C × [(1+r/n)^(nt) − 1] / (r/n). Example: $10,000 at 6% for 20 years, compounded monthly: FV = $10,000 × (1 + 0.06/12)^(12×20) = $33,102.

Compounding frequency has a measurable but not dramatic effect at typical rates. At 6% for $10,000 over 20 years: Annual compounding → $32,071; Monthly → $33,102; Daily → $33,198. The difference between monthly and daily is only $96 over 20 years. The bigger factor is the interest rate itself — a 1% higher rate makes a far larger difference than changing from annual to daily compounding.

EAR = (1 + r/n)^n − 1. It converts a nominal rate with a given compounding frequency into the equivalent simple annual rate. Example: 6% nominal rate compounded monthly → EAR = (1 + 0.06/12)^12 − 1 = 6.168%. Banks advertise savings account APY, which is the same as EAR. When comparing accounts with different compounding frequencies, always compare APY/EAR, not the nominal rate.

Simple interest: FV = P × (1 + r × t). For small t, the difference is minimal. For long periods, the gap is enormous. Example: $10,000 at 7% for 30 years: Simple = $31,000; Compound (annual) = $76,123 — 2.5× more. At 40 years: Simple = $38,000; Compound = $149,745 — nearly 4× more. This is why Einstein allegedly called compound interest the "eighth wonder of the world."

The Rule of 72 quickly estimates how long it takes to double your money: Doubling time (years) = 72 / annual interest rate. Examples: at 6% → 12 years; at 8% → 9 years; at 10% → 7.2 years; at 12% → 6 years. It also works in reverse: to double in 10 years, you need approximately 72/10 = 7.2% annual return. The rule is accurate within 1% for rates between 2% and 20%.