Compound interest is often called the "eighth wonder of the world" — and for good reason. Unlike simple interest, which only earns interest on the original principal, compound interest earns interest on both the principal and all previously accumulated interest. This snowball effect makes money grow exponentially over time and is the engine behind long-term wealth building.
The compound interest formula
Where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years.
Worked examples
- Savings account: $10,000 at 5% compounded monthly for 10 years. A = $10,000 × (1 + 0.05/12)^(12×10) = $16,470.09. You earned $6,470 in interest.
- Daily compounding: Same $10,000 at 5% for 10 years, but compounded daily. A = $10,000 × (1 + 0.05/365)^(365×10) = $16,486.65. Daily vs. monthly compounding adds only $16.56 — the difference shrinks as frequency increases.
- 20-year horizon: $10,000 at 7% compounded annually for 20 years. A = $10,000 × (1.07)^20 = $38,696.84. The original investment nearly quadrupled.
Compounding frequency matters
The more frequently interest compounds, the more you earn — but with diminishing returns:
- Annual: Once per year — the simplest form.
- Semi-annual: Twice per year — common for bonds.
- Quarterly: Four times per year — common for savings accounts.
- Monthly: 12 times per year — the most common frequency for consumer accounts.
- Daily: 365 times per year — often advertised by high-yield savings accounts.
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%: 72 ÷ 6 = 12 years. At 8%: 72 ÷ 8 = 9 years. At 10%: 72 ÷ 10 = 7.2 years. This approximation works well for rates between 2% and 15%.
Compound interest vs. simple interest
On a $10,000 deposit at 5% for 20 years: simple interest earns $10,000 (total: $20,000). Compound interest (annual) earns $16,533 (total: $26,533). The $6,533 difference is pure compounding effect — interest earning interest. The longer the time horizon, the bigger the gap.