What Is Compound Interest? The Math of Exponential Wealth
A complete guide to compound interest: the compounding formula, compounding frequency (daily, monthly, annual), and how geometric growth builds long-term wealth.
Key Takeaway
Simple interest grows linearly by paying interest only on the principal. Compound interest grows geometrically by earning interest on prior interest, creating an accelerating curve of financial accumulation.
Simple Growth vs. Geometric Compounding
Simple interest pays a fixed return strictly on the original principal invested. If you invest $10,000 at 5% simple interest, you earn $500 every year—never more, never less. After 30 years, you have $25,000.
With compound interest, the $500 you earn in year one is added to your principal. In year two, you earn 5% on $10,500 ($525). By year 30, that same $10,000 has grown to $43,219 without adding a single extra dollar.
The Standard Compound Interest Formula
The future value (A) of an initial lump sum (P) compounding at an annual interest rate (r) compounded (n) times per year over (t) years is calculated as:
Compound Interest Formula
A = P · (1 + r ÷ n)ⁿᵗ
The Rule of 72: Quick Mental Math for Doubling Money
A classic personal finance heuristic is the Rule of 72. Divide 72 by your expected annual rate of return to estimate how many years it takes for your investment to double in value:
- At 3% annual return (High-Yield Savings): 72 ÷ 3 = 24 years to double.
- At 6% annual return (Conservative Portfolio): 72 ÷ 6 = 12 years to double.
- At 8% annual return (Historical Stock Market Average): 72 ÷ 8 = 9 years to double.
Run Your Numbers with the Compound Interest Calculator
Put these concepts into practice. Test different inputs, compare scenarios, and see your customized payment or savings breakdown.
Sources & Methodology
FinoQuick mathematical models are deterministic and adhere to statutory lending standards, Consumer Financial Protection Bureau regulations, and IRS publications.
Frequently Asked Questions
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