Understanding Compound Interest: The What, Why, and How
Compound interest is growth on top of growth—returns earn returns. Over time, this feedback loop accelerates balances compared to simple interest.
Model scenarios instantly with the calculator at
/finance/compound-interest-calculator.
The Core Variables
- Principal: Your starting amount
- Rate of return (r): Annualized return you expect to earn
- Time (t): How long you’re invested
- Compounding frequency (n): Times per year returns are credited
- Contributions: Additional deposits (monthly, annually) that fuel growth
The Formula (No Derivation Needed)
For a single lump sum:
A = P × (1 + r/n)^(n×t)
For ongoing contributions, the calculator handles the math; the intuition remains: earlier and larger contributions compound longer.
Walk‑Through Example
Invest $100/month at a 7% annual return for 25 years.
- Total contributions: $30,000
- Ending balance: typically well over $60,000–$70,000 (market returns vary)
- Much of the ending balance is growth from compounding, not just deposits
How Frequency Fits In
- Monthly vs annual compounding creates a modest difference; daily adds only a small edge beyond monthly.
- Over decades, contribution size, time invested, and net return (after fees/taxes) matter most.
Effective Annual Rate (EAR)
Nominal 6% compounded monthly has EAR ≈ (1 + 0.06/12)^12 − 1 ≈ 6.17%. Use EAR to compare products with different frequencies.
Practical Levers for Better Outcomes
- Start early—even small amounts matter
- Automate contributions and reinvest dividends/interest
- Keep costs low so more of your return compounds
- Use tax‑advantaged accounts to reduce drag
- Stay diversified to remain invested through volatility
FAQs
What if I can’t invest much right now? Start small and be consistent; increase contributions as income grows.
Should I worry about market drops? Volatility is normal. Diversification and time horizon help compounding keep working.