Compound Interest Calculator
Lump sum + monthly contributions, computed together. See your future value at a glance.
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⚠️ Pre-tax estimate, ignoring inflation. Real-world returns are reduced by taxes (capital gains, dividends), inflation, and market volatility. Equity/ETF investments carry risk.
The Compound Interest Formula
- Lump sum:
FV = P × (1 + r)n - Monthly contributions:
FV = M × ((1 + r)n − 1) ÷ r - P = principal, M = monthly contribution, r = monthly rate (annual ÷ 12), n = total months
Equivalent to Excel's FV function. Both annual and monthly compounding are unified by converting to a monthly rate.
$500/month at 7% — Growth by Period
| Period | Total Invested | Future Value | Net Profit | Multiple |
|---|---|---|---|---|
| 5 years | $30,000 | $35,797 | $5,797 | ×1.19 |
| 10 years | $60,000 | $86,541 | $26,541 | ×1.44 |
| 15 years | $90,000 | $158,481 | $68,481 | ×1.76 |
| 20 years | $120,000 | $260,463 | $140,463 | ×2.17 |
| 25 years | $150,000 | $405,036 | $255,036 | ×2.70 |
| 30 years | $180,000 | $609,985 | $429,985 | ×3.39 |
| 40 years | $240,000 | $1,312,407 | $1,072,407 | ×5.47 |
From 5 to 30 years, principal grows 6× but future value grows 17×. Compound interest eats time.
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Return rate comparison ($1,000/month, 30 years)
| Annual Return | Total Invested | Future Value | Net Profit |
|---|---|---|---|
| 3% | $360,000 | $582,737 | $222,737 |
| 5% | $360,000 | $832,259 | $472,259 |
| 7% | $360,000 | $1,219,971 | $859,971 |
| 10% | $360,000 | $2,260,488 | $1,900,488 |
A 1 percentage point difference compounds into $150K–$400K over 30 years. Even a 0.5% ETF expense ratio matters significantly long-term.
$100,000 lump sum at 7%
| Period | Future Value | Multiple |
|---|---|---|
| 5 years | $140,255 | ×1.40 |
| 10 years | $196,715 | ×1.97 |
| 15 years | $275,903 | ×2.76 |
| 20 years | $386,968 | ×3.87 |
| 25 years | $542,743 | ×5.43 |
| 30 years | $761,226 | ×7.61 |
At 7% compound, money roughly doubles every 10 years; over 30 years it grows ~8×. (Reference: S&P 500 long-term average ~7–10%.)
Rule of 72 (years to double)
Estimate quickly with «72 ÷ annual return rate». Matches the exact formula ln(2) ÷ ln(1 + r) within fractions of a year.
| Annual Return | Rule of 72 | Exact Value |
|---|---|---|
| 3% | 24 years | 23.45 years |
| 5% | 14.4 years | 14.21 years |
| 6% | 12 years | 11.90 years |
| 7% | 10.3 years | 10.24 years |
| 9% | 8 years | 8.04 years |
| 12% | 6 years | 6.12 years |
For rates ≥10%, the Rule of 70 is slightly more accurate; for rates ≤5%, the Rule of 69 is best. But 72 has more divisors, making it easier for mental math.
Simple vs Compound ($100K, 7%, 30 years)
| Type | After 30 Years | Difference |
|---|---|---|
| Simple (principal + 7% × 30) | $310,000 | — |
| Compound (1.0730) | $761,226 | +$451,226 |
The gap grows exponentially with time. Under 5 years, simple and compound differ little; over 20 years, the difference is decisive.
Real return after inflation and taxes
InflationLong-term US average ~2–3%. Nominal 7% return − 2.5% inflation = real return ~4.5%.
Taxable accountsDividends and realized capital gains are taxed annually, reducing effective return. Long-term capital gains rates (US): 0%, 15%, or 20%.
Tax-deferred (401(k), Traditional IRA)Contributions reduce taxable income; gains compound untaxed until withdrawal. Withdrawals taxed as ordinary income.
Tax-free (Roth IRA, Roth 401(k))Contributions made post-tax; qualified withdrawals are completely tax-free, including all gains.
Expense ratiosA 0.5% annual fee compounds into 15%+ erosion over 30 years. Index ETFs (0.03–0.10%) crush actively managed funds (0.5–1.5%).
Inflation-adjusted FVMultiply this calculator's result by (1.025)−n to see purchasing power in today's dollars.
5 principles of long-term investing
1. Start earlyStarting in your 20s vs 30s — same monthly contribution, ~2× difference at retirement. Time is the most powerful variable.
2. AutomateDon't rely on willpower. Set up automatic transfers the day you get paid.
3. Low-cost index fundsA 0.5pp expense difference compounds to 6 figures over 30 years. Passive index ETFs typically beat active funds.
4. Maximize tax-advantaged accounts401(k) match → Roth IRA → 401(k) max → taxable brokerage. Always capture the employer match first (free money).
5. Don't time the marketMarket-timing attempts almost always underperform buy-and-hold. Stick with dollar-cost averaging (DCA).
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Frequently Asked Questions
What's the difference between simple and compound interest?
Simple interest applies only to the original principal, while compound interest applies to both the principal and accumulated interest. For $100,000 at 7% over 30 years: simple yields $310,000, while compound yields $761,226 — a $451,226 difference. The longer the period, the more dramatic the gap (this is what Warren Buffett calls the 'snowball').
If I save $500 a month for 30 years, will I really have $610,000?
At a 7% annual return, $500/month over 30 years ($180,000 invested) grows to approximately $609,985 (3.4× the principal). Over 5 years it's only 1.2×, and over 10 years 1.4× — but 30 years yields 3.4× because compound growth eats time. Note: this doesn't account for inflation or taxes, so real purchasing power is roughly 70% of the nominal value.
Does a 1 percentage point difference in return really matter?
Significantly. For $1,000/month over 30 years: 5% returns $832,259, 7% returns $1,219,971, and 10% returns $2,260,488. A 1 percentage point difference creates $150K–$400K gaps over 30 years. In long-term investing, even a 0.5% expense ratio compounds into massive losses.
What is the Rule of 72?
72 ÷ annual return rate = approximate years for principal to double. At 7% → ~10.3 years, 9% → 8 years, 12% → 6 years. The exact formula ln(2)/ln(1+r) differs by less than a year. Useful as a quick mental-math heuristic.
How do taxes affect compound interest?
Taxes vary by country and account type. In tax-deferred accounts (401(k), Traditional IRA), gains compound untaxed until withdrawal. In taxable brokerage accounts, dividends and realized gains are taxed annually, lowering the effective rate. This calculator computes pre-tax compound growth — your real return depends on jurisdiction and account structure.
Are tax-advantaged retirement accounts worth it?
Yes, substantially. In a 401(k), Roth IRA, or similar account, gains compound without annual tax drag. Over 30 years, the difference between taxable and tax-advantaged compounding can exceed 25% of the final balance — often hundreds of thousands of dollars. Maximize tax-advantaged contributions before taxable accounts.
Formulas & References
Last reviewed: 2026-05-08
- Lump-sum future value — FV = P × (1 + r)n [equivalent to Excel's FV function]
- Monthly contribution future value — FV = M × ((1 + r)n − 1) / r [annuity future value]
- r = monthly rate (annual ÷ 12), n = total months
- Tax-advantaged accounts (US) — SEC investor.gov
- Long-term capital gains (US) — IRS Publication 550, IRS Topic 409
⚠️ This calculator uses pure mathematical formulas. Real-world returns differ due to volatility, inflation, and taxes specific to your jurisdiction.