Compound Interest Explained
How compound interest works, the Rule of 72, and why starting early matters.
What Is Compound Interest
Compound interest is interest earned on both your initial principal and the accumulated interest from previous periods.
While simple interest earns returns only on the principal, compound interest creates exponential growth because your interest starts earning its own interest.
Simple vs Compound
$10,000 at 7% over 30 years
Input
Simple interest
Result
$31,000
Same investment
$10,000 at 7% over 30 years
Input
Compound interest (monthly)
Result
~$81,000
The Rule of 72
The Rule of 72 is a simple way to estimate how long it will take to double your money: divide 72 by your annual interest rate.
- At 6%: 72 ÷ 6 = 12 years to double
- At 8%: 72 ÷ 8 = 9 years to double
- At 10%: 72 ÷ 10 = 7.2 years to double
Compounding Frequency Matters
More frequent compounding (daily vs annual) generates slightly higher returns. The difference grows with larger amounts and longer timeframes, but the biggest factor by far is time in the market.
A practical method
Compound interest applies each period's rate to the current balance, including prior interest. The general single-deposit formula is A = P(1 + r/n)^(nt), where P is principal, r the annual nominal rate, n compounding periods per year, and t years. Regular deposits need an additional cash-flow calculation.
- Match rate and periods: Use the annual rate as a decimal and the correct compounding frequency.
- Apply the single-balance formula: Calculate growth of the existing principal across all periods.
- Add contributions by timing: Beginning-of-period deposits receive one more period of growth than end-of-period deposits.
- Separate components: Show principal, total contributions, and estimated growth so the result is auditable.
Worked example
$5,000 at a constant 4% annual rate compounded monthly for three years grows to about $5,636 before fees and taxes. Adding monthly deposits changes both the final balance and the share attributable to contributions.
Checks, edge cases, and common mistakes
- Do not mix annual and monthly rates in the same formula or contribution schedule.
- Confirm whether the quoted rate is nominal or effective before comparing products.
- Include fees, taxes, and inflation when relevant to the real outcome.
- Projected returns can vary materially over time and are not guaranteed.
Compound Interest Calculator
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Desmarto Editorial Team
The Desmarto team creates accurate, well-researched content about time, date, and work-hour calculations. Every guide is reviewed for precision and clarity.