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Understanding Compound Interest
5 min read
Compound interest means earning (or paying) interest on both the original principal and any interest already accumulated. Over time this creates exponential growth—a small difference in rate or time horizon can produce dramatically different outcomes. Understanding it is one of the most useful things you can learn about personal finance.
The Formula
A = P × (1 + r/n)^(n×t)
• A = Final amount
• P = Principal
• r = Annual interest rate (decimal)
• n = Compounding periods per year (monthly = 12, daily = 365)
• t = Years
Example: $5,000 at 6% compounded monthly for 10 years.
A = 5000 × (1 + 0.06/12)^(12×10) = 5000 × (1.005)^120 ≈ $9,096
Why Frequency Matters
The more frequently interest compounds, the faster the balance grows. On $10,000 at 5% for 10 years:
• Annual compounding → $16,288
• Monthly compounding → $16,470
• Daily compounding → $16,487
The difference between annual and daily compounding is modest at this rate, but it grows with higher rates and longer time horizons.
Compounding Works Against You Too
Credit card debt often compounds daily. If you carry a $3,000 balance at 22% APR and only make minimum payments, compound interest means you pay far more than the original $3,000. This is the same force that grows wealth in savings accounts—just working against you.
The Rule of 72
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in roughly 72 ÷ 6 = 12 years. At 8%, it doubles in about 9 years.
Try the Compound Interest Calculator.
Frequently Asked Questions
Is APY the same as APR?
No. APR (Annual Percentage Rate) is the stated rate. APY (Annual Percentage Yield) reflects compounding and shows the true annual return. When comparing savings accounts or loans, use APY for accurate comparisons.
How does starting early affect compound growth?
Enormously. Investing $5,000 at age 25 at 7% grows to roughly $74,800 by age 65. Waiting until 35 gives you only 30 years and about $38,000—about half as much, for a delay of just 10 years.