How Compound Interest Works
Compound interest pays you interest on your principal plus all previously earned interest. A $10,000 investment at 8% annual return earns $800 in year one. In year two, you earn 8% on $10,800—that's $864. By year ten, a single $10,000 deposit becomes $21,589 without adding another dollar. By year thirty, it's $100,627.
The formula: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]. P is your starting principal, r is the annual interest rate as a decimal, n is how many times per year interest compounds, t is years, and PMT is your periodic contribution. This calculator runs the full computation for each year so you can see exactly when interest overtakes contributions.
The Rule of 72
Divide 72 by your annual return rate to estimate how many years it takes to double your money. At 6%, your money doubles in 12 years. At 8%, it doubles in 9 years. At 10%, just 7.2 years. This mental shortcut works because compound growth is exponential—the first doubling takes the longest, but each subsequent doubling happens on a larger base.
Example: $50,000 at 8% doubles to $100,000 in 9 years, then to $200,000 in 18 years, then to $400,000 in 27 years. That's an 8x return with zero additional contributions. Add $500/month and you'd have over $1 million in the same period.
Compounding Frequency Comparison
| Frequency | Periods/Year | $10K at 5% (10 yr) | $10K at 8% (20 yr) |
|---|---|---|---|
| Annually | 1 | $16,289 | $46,610 |
| Quarterly | 4 | $16,386 | $47,754 |
| Monthly | 12 | $16,470 | $48,218 |
| Daily | 365 | $16,487 | $48,955 |
Daily vs. monthly compounding adds only $17 on $10,000 over 10 years—negligible for most people. The real difference is between annual and monthly: $181 over 10 years, $1,608 over 20. Most savings accounts and bonds compound daily or monthly. Stock market returns effectively compound continuously since prices change every second.
Monthly Contributions: The Power of Consistency
Starting amount matters less than consistent contributions. Someone who invests $200/month at 7% for 30 years ends up with $226,706. Someone who starts with $20,000 but never adds another dollar ends up with $152,245. The monthly contributor wins by $74,461—despite investing $52,000 less out-of-pocket than the lump-sum investor.
Every year you delay costs you disproportionately. Starting at 25 instead of 35 with $300/month at 7% means $567,000 at age 65 vs. $227,000. That 10-year head start is worth $340,000 in extra growth. The money you invest in your 20s has the most doubling periods ahead of it and generates the highest returns per dollar invested.
Dollar-cost averaging—investing the same amount on a fixed schedule—also smooths out market volatility. You automatically buy more shares when prices are low and fewer when prices are high, lowering your average cost per share over time.
To plan how much to save each month toward a specific target, use the savings goal calculator. If you're buying a home and want to see total cost with interest, try the mortgage calculator. To keep your investment allocations on track as your portfolio grows, use the portfolio rebalance calculator.