How compound interest works
Simple interest only pays on your original deposit. Compound interest pays on your interest too — each period's earnings are added to the balance, and the next period earns on the whole thing. Over years, that feedback loop produces the snowball curve you see in the table above.
Where P is your initial deposit, r the annual rate, n the number of compounding periods per year and t the time in years. When you add regular contributions, the math extends to a growing annuity — the calculator above handles it by simulating month by month with the effective monthly rate, which stays accurate for every compounding frequency.
The Rule of 72 — mental math for investors
Want to know how fast your money doubles without a calculator? Divide 72 by the annual rate:
| Annual return | Years to double |
|---|---|
| 3% (savings account) | ≈ 24 years |
| 6% (conservative portfolio) | ≈ 12 years |
| 8% (S&P 500 long-term average) | ≈ 9 years |
| 9% | ≈ 8 years |
| 12% | ≈ 6 years |
At 7%, money doubles roughly every 10.3 years — so 30 years is almost exactly three doublings: ×2, ×4, ×8. That's the $81,165 in the example above.
Growth of $10,000 by rate and time
Monthly compounding, no additional deposits:
| Rate | 10 years | 20 years | 30 years |
|---|---|---|---|
| 5% | $16,470 | $27,126 | $44,677 |
| 7% | $20,096 | $40,387 | $81,165 |
| 9% | $24,514 | $60,092 | $147,306 |
| 10% | $27,070 | $73,281 | $198,374 |
Notice the pattern: going from 20 to 30 years often doubles the outcome. The last decade of compounding is worth more than the first two — the strongest argument for starting early.
Does compounding frequency matter?
$10,000 at 7% for 30 years, different frequencies:
| Frequency | Final balance |
|---|---|
| Annually | $76,123 |
| Quarterly | $80,194 |
| Monthly | $81,165 |
| Daily | $81,645 |
A ~6.6% edge from monthly vs annual — real, but modest. Rate and time dominate frequency. Don't pick an investment for its compounding schedule; pick it for its net return.
The real superpower: regular contributions
Same $10,000 at 7% for 30 years — but now add just $200 per month: the final balance jumps from $81,165 to about $325,000. You only contributed $82,000 of your own money; compounding added roughly $243,000. Monthly deposits feed the snowball every single month, which is why consistent, boring contributions beat lucky timing over any long horizon.
Frequently asked questions
What is the compound interest formula?
For a lump sum: A = P × (1 + r/n)n·t. With regular contributions, the future value of the deposits adds an annuity term — the calculator simulates month by month using the effective monthly rate for full accuracy.
What is the Rule of 72?
Divide 72 by your annual rate: that's roughly how many years it takes to double your money. 72 ÷ 7 ≈ 10.3 years at 7%.
Does compounding frequency matter much?
Modestly — see the table above (~6.6% spread between annual and monthly on a 30-year horizon). Rate and time matter far more.
Can compound interest work against me?
Yes. Credit card debt compounds daily — an unpaid balance grows exactly like a great investment, but in the lender's pocket. Always attack high-interest debt before investing.
Is this calculator free?
Yes — 100% free, unlimited, no sign-up. CalculUnits is funded by non-intrusive ads, never by paywalls.