Compound Interest Explained: How It Works & Examples
Understand compound interest with clear examples, the Rule of 72, and how compounding frequency affects growth. The math behind wealth building explained simply.
Simple Interest vs Compound Interest
Simple interest is calculated only on the original principal. If you deposit $10,000 at 5% simple interest, you earn $500 every year — always calculated on the original $10,000. After 10 years, you'd have $15,000.
Compound interest is calculated on principal plus previously earned interest. That same $10,000 at 5% compounded annually grows to $16,288 after 10 years — $1,288 more than simple interest. The longer the time horizon, the more dramatic the difference becomes.
The Compound Interest Formula
The standard formula is: A = P(1 + r/n)^(nt)
- A = final amount
- P = principal (initial investment)
- r = annual interest rate (decimal form)
- n = number of times interest compounds per year
- t = time in years
Example: $10,000 at 7% compounded monthly for 20 years: A = 10,000 × (1 + 0.07/12)^(12×20) = $40,065. That's $30,065 of growth on a $10,000 investment — entirely from compounding.
Compounding Frequency Matters
The more frequently interest compounds, the more you earn. On $10,000 at 5% over 10 years:
- Annually: $16,288
- Monthly: $16,470
- Daily: $16,487
The difference between monthly and daily compounding is small. The big jump is between annual and monthly compounding. This is why high-yield savings accounts advertise APY (Annual Percentage Yield) — which reflects the actual return after compounding — rather than the stated APR.
The Rule of 72
The Rule of 72 is a mental math shortcut to estimate how long it takes money to double: divide 72 by the annual interest rate.
- At 4%: 72 ÷ 4 = 18 years to double
- At 6%: 72 ÷ 6 = 12 years to double
- At 9%: 72 ÷ 9 = 8 years to double
- At 12%: 72 ÷ 12 = 6 years to double
Why Starting Early Is So Powerful
Investor A invests $5,000/year from age 25 to 35 (10 years, $50,000 total) then stops. Investor B invests $5,000/year from age 35 to 65 (30 years, $150,000 total). At a 7% return, Investor A ends up with more money at 65 ($602,000 vs $472,000) despite investing one-third as much. This is the power of time in compounding — the early decade of growth compounds for 30+ additional years.