📖 How Compound Interest Works
Compound interest is often called the "eighth wonder of the world." Unlike simple interest, which is calculated only on the principal, compound interest is calculated on the principal and the accumulated interest. This means your money earns interest on its interest — creating an exponential growth effect over time.
The Compound Interest Formula
Where A = Final amount, P = Principal, r = Annual interest rate (decimal), n = Compounding periods per year, t = Time in years.
How Compounding Frequency Affects Growth
The more frequently interest compounds, the faster your money grows. Daily compounding yields slightly more than monthly, which beats quarterly or annual compounding. For a $10,000 investment at 7% over 10 years: annually yields ~$19,672, while daily compounding yields ~$20,137 — a meaningful difference at scale.
The Rule of 72
A mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 7% interest, your money doubles approximately every 10.3 years (72 ÷ 7 = 10.3). At 10%, it doubles every 7.2 years.
❓ What is APY vs. APR?
APR (Annual Percentage Rate) is the stated interest rate without accounting for compounding. APY (Annual Percentage Yield) reflects the actual rate of return after compounding. APY is always equal to or greater than APR — this is the number to compare when shopping for savings accounts.
❓ How does inflation affect compound interest?
To find your "real" return after inflation, use the Fisher equation: Real Rate ≈ Nominal Rate − Inflation Rate. If your investment earns 7% and inflation is 3%, your real purchasing-power growth is approximately 4% per year.