What compound growth actually leaves you with, once fees, tax and inflation have taken their share. The headline number every calculator shows is the one before all three — and at ordinary rates they remove more than half of it over thirty years.
Compound Interest Calculator
LiveThe formula
Compound interest is interest earning interest. Each period the balance grows by the rate, and next period that growth earns too:
A = P (1 + r/n)nt
P is the starting amount, r the annual rate as a decimal, n how many times a year it compounds, t the years.
A = P (1+i)N + PMT × [ ((1+i)N − 1) / i ]
i is the rate per period and N the number of periods. The second term is the future value of an annuity — each deposit compounds for however long is left after it arrives.
The calculator above runs this month by month rather than using the closed form, because fees, tax and rising deposits all change the amount in play each period and no single expression covers them together.
The fee is bigger than the tax
An annual fee sounds small next to a tax rate. It is not, because it compounds against you every year on the whole balance rather than once on the gains. $10,000 at 7% over 30 years:
| Fee | What it usually is | Ends at | Lost to the fee |
|---|---|---|---|
| 0% | Nothing charged | $81,165 | — |
| 0.03% | A broad index ETF | $80,438 | 0.9% |
| 0.5% | A cheap active fund | $69,857 | 13.9% |
| 1.0% | Typical active management | $60,121 | 25.9% |
| 2.0% | Advised platform plus fund | $44,522 | 45.1% |
Where the account sits changes the answer
Tax is not one number applied at the end. It depends on whether gains are taxed as they arrive or left alone until you withdraw:
| Account | When tax lands | $10,000 at 7% for 30 years, 24% rate |
|---|---|---|
| Taxable | Every year, on that year's gain | $49,755 |
| Tax-deferred 401(k), traditional IRA, SIPP | Once, on withdrawal | $64,085 |
| Tax-free Roth IRA, ISA | Never, on qualifying withdrawals | $81,165 |
The gap between taxable and deferred is $14,330 on the same investment — the same rate, the same deposits, the same tax percentage. Deferring means the money that would have gone to tax stays invested and compounds, and thirty years of that adds up to more than a fifth of the balance.
Inflation: why subtraction is wrong
A 7% return with 3% inflation is not a 4% real return. Rates are ratios, not quantities, so they divide rather than subtract — the Fisher relation:
real = (1 + nominal) / (1 + inflation) − 1
(1.07 / 1.03) − 1 = 3.88%, not 4.00%. The error looks trivial and compounds like everything else here: over thirty years it overstates the final figure by roughly 3.5%.
| Asset | Typical nominal | Real | Note |
|---|---|---|---|
| Broad equities, long run | ~10% | ~7% | With volatility that no projection shows |
| Government bonds | 2–4% | 1–2% | Sometimes negative in real terms |
| Savings account | 4–5% | 1–2% | In a high-rate environment |
| Cash under a mattress | 0% | −3% | Guaranteed loss at target inflation |
Deposits that stay flat, shrink
Saving $500 a month for thirty years does not mean saving $500 a month. In real terms the last deposit is worth about $206 at 3% inflation — the same number on the transfer, less than half the purchasing power.
Raising deposits each year keeps them level in real terms. Setting the escalation field to your inflation figure models exactly that, and the difference is large: $500 a month at 7% for 30 years reaches about $610,000 flat, or about $834,000 rising 3% a year. The extra deposits total far less than the extra balance, because the early increases compound the longest.
The Rule of 72, and when it breaks
Divide 72 by the rate to get the years to double. At 7%, roughly 10.3 years; the exact figure is 10.24, so the shortcut is within a few weeks.
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36.0 years | 35.0 | +2.9% |
| 7% | 10.3 | 10.24 | +0.6% |
| 10% | 7.2 | 7.27 | −1.0% |
| 20% | 3.6 | 3.80 | −5.3% |
| 40% | 1.8 | 2.06 | −12.6% |
It is accurate between roughly 6% and 10% and drifts outside that. Below 6% use 70; above 15% do the arithmetic properly. And remember it doubles the nominal figure — at 7% with 3% inflation, real purchasing power takes 18 years to double, not 10.
Sources: standard compound interest and annuity formulas · the Fisher relation for real rates · published expense ratios for index and active funds · long-run asset class returns. Figures in the tables are computed with the same engine as the calculator; the tax and fee examples use the assumptions stated in each row.
Sequence risk: the same average, a different outcome
A compound interest calculator assumes a steady rate. Real returns arrive unevenly, and while that changes nothing for a lump sum left alone, it changes a great deal once money is going in or coming out:
| Scenario | Returns | After 3 years |
|---|---|---|
| Lump sum, good first | +30%, 0%, −20% | $104,000 — identical |
| Lump sum, bad first | −20%, 0%, +30% | $104,000 — identical |
| Drawing $10,000 a year, good first | +30%, 0%, −20% | $78,000 |
| Drawing $10,000 a year, bad first | −20%, 0%, +30% | $68,000 |
Multiplication is commutative; withdrawals are not. Selling into a fall removes shares that would have recovered, and the money taken out in a bad year never participates in the good one. This is why the years immediately before and after retirement carry a risk that a smooth projection cannot show — and why no calculator on this or any other site can tell you whether a plan survives a bad decade.
How often it compounds
The compounding frequency matters less than most people expect, and there is a hard ceiling on how much it can help:
| Compounded | $10,000 at 7%, one year | Effective annual rate |
|---|---|---|
| Annually | $10,700.00 | 7.0000% |
| Quarterly | $10,718.59 | 7.1859% |
| Monthly | $10,722.90 | 7.2290% |
| Daily | $10,725.01 | 7.2501% |
| Continuously | $10,725.08 | 7.2508% — the ceiling |
Going from annual to monthly compounding adds 0.23 percentage points. Going from monthly to infinitely often adds 0.02 more. The limit is er − 1, and daily compounding is already within a hundredth of a point of it. An account advertising “daily compounding” as a feature is advertising something worth about two dollars a year on $10,000.
Common mistakes
Frequently asked questions
How is compound interest calculated?
A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate, n the compounding periods per year and t the years. With regular deposits the future value of an annuity is added on top. This calculator runs it month by month instead, because fees, tax and rising deposits change the balance each period.
How much difference does an annual fee really make?
More than most people expect. On $10,000 at 7% over 30 years, a 1% fee removes 25.9% of the final balance and a 2% fee removes 45%. The fee compounds against you: each year's charge also costs you everything that amount would have earned afterwards.
Does daily compounding beat monthly?
Barely. At 7% over 20 years on $10,000: annual $38,697, monthly $40,387, daily $40,547. Monthly captures nearly all of the benefit, and the difference between any frequency is far smaller than a change in the rate or the fee.
What is a real return, and why not just subtract inflation?
The real return is what you gain in purchasing power. Because rates are ratios, they divide rather than subtract: (1.07 / 1.03) − 1 = 3.88%, not 4%. Subtracting is close enough for a quick estimate and overstates a thirty-year result by around 3.5%.
Should I use a taxable or tax-deferred account?
On the arithmetic alone, deferring wins: money that would have gone to tax each year stays invested and compounds. On $10,000 at 7% for 30 years at a 24% rate, taxable ends at $49,755 and tax-deferred at $64,085. Contribution limits, withdrawal rules and your rate in retirement all matter too, so treat this as the mathematical part of the answer rather than the whole of it.
Should my monthly deposit rise over time?
A flat deposit shrinks in real terms — $500 today is worth about $206 in thirty years at 3% inflation. Raising it with inflation keeps it level in what it actually buys, and the effect on the end balance is large: roughly $610,000 flat against $834,000 rising 3% a year, on $500 a month at 7%.
How long until my money doubles?
Divide 72 by the rate. At 7% that is 10.3 years against an exact 10.24. It holds well between 6% and 10% and drifts outside that range. Note it doubles the nominal amount — at 7% with 3% inflation, doubling your purchasing power takes 18 years.
Is this a prediction of what I will have?
No. It assumes a steady rate, and real returns arrive unevenly — the order matters, particularly once withdrawals start. Use it to compare choices: what a fee costs, what ten more years does, what raising the deposit changes. Those comparisons hold even though the exact figure will not.
Is anything I enter stored?
No. Everything runs in your browser with no server request, and works offline once the page has loaded. Nothing is written to disk and nothing persists after you close the tab.
Sources
- Formula.
A = P(1 + r/n)ntfor periodic compounding andA = Pertin the continuous limit. Both are standard; the second is the limit of the first as n grows without bound. - US Securities and Exchange Commission. “Investor Bulletin: How Fees and Expenses Affect Your Investment Portfolio.” The regulator’s own worked example of a 1% fee over 20 years, which reaches the same conclusion as this page.
- UK Financial Conduct Authority. COBS 13 Annex 2 and the PRIIPs regulation, which set out how projected returns must be shown net of charges and why gross figures are considered misleading.
- Fisher I. The Theory of Interest. Macmillan, 1930. The origin of the relation used here for real returns: (1 + nominal) ÷ (1 + inflation) − 1, rather than simple subtraction.
- Bengen WP. “Determining Withdrawal Rates Using Historical Data.” Journal of Financial Planning, 1994. The work that established sequence-of-returns risk as a distinct problem from average returns.
- Rule of 72. Accurate to within a few percent for rates between roughly 6% and 10%; the exact doubling time is ln(2) ÷ ln(1 + r). At 2% the rule overstates and at 20% it understates, which is why this page gives both.
Every figure and every curve on this page is computed from these formulas at monthly resolution. The diagram above plots 361 monthly balances for each of the three fee levels, sampled every two years for the drawn line.
Related calculators
See the full list of Financial calculators, or try:
- Savings Calculator — reaching a target by a date
- Investment Calculator — growth with irregular deposits
- Rule of 72 Calculator — doubling time and its limits
- Inflation Calculator — what a sum was worth then
- Retirement Calculator — whether the pot lasts
- CD Calculator — fixed-term deposit returns