How Compound Interest Really Works: Formulas, Frequency & Rule of 72
Understand how interest on interest accelerates your savings and why compounding frequency matters over long horizons.
Simple Interest vs. Compound Interest
Simple interest is calculated solely on your initial principal amount. If you invest $1,000 at 5% simple interest, you earn exactly $50 every year, forever.
Compound interest, by contrast, is interest calculated on the initial principal plus all accumulated interest from previous periods. As your balance grows, each subsequent interest payment is larger than the previous one, generating an exponential curve.
Where A = final amount, P = principal, r = annual interest rate (decimal), n = compounding periods per year, and t = number of years.
The Impact of Compounding Frequency
How often interest is compounded makes a measurable difference. Common compounding intervals include annually (n = 1), quarterly (n = 4), monthly (n = 12), and daily (n = 365).
Comparing different compounding frequencies on an identical initial deposit:
• Simple Interest: $10,000 + ($600 × 20) = $22,000.00
• Compounded Annually (n=1): $10,000 × (1.06)^20 = $32,071.35
• Compounded Monthly (n=12): $10,000 × (1 + 0.06/12)^240 = $33,102.04
• Compounded Daily (n=365): $10,000 × (1 + 0.06/365)^7300 = $33,197.91
Compound interest added over $11,100 of pure growth beyond simple interest!
APY vs. APR: What Banks Don't Always Clarify
APR (Annual Percentage Rate) is the stated annual interest rate without taking compounding into account. APY (Annual Percentage Yield) reflects the actual total interest you earn over a full year including compounding effects. For savings accounts and CDs, always compare APY, not APR.
The Rule of 72: Quick Mental Math for Doubling Money
To estimate how many years it will take an investment to double at a fixed annual rate of return, divide 72 by the annual percentage rate:
For example, an investment returning 8% annually will double in approximately 72 ÷ 8 = 9 years. At 6%, it doubles in approximately 12 years.