Project the growth of an investment or savings account with regular contributions.
Compounding means the interest you earned last year starts earning interest this year. That sounds like a small refinement to simple interest. Over twenty years it is the difference between doubling your money and nearly tripling it, and over forty years it is the difference between a comfortable retirement and a large one.
The mechanism is not mysterious. Each period, the balance is multiplied by the same factor. Applied many times, multiplication behaves very differently from addition, which is why the early years look disappointing and the late years look implausible. A deposit that earns 7% grows by $700 in year one on a $10,000 balance. In year twenty, the same 7% is applied to a balance twenty times larger.
Where P is the starting principal, n is the number of compounding periods per year, t is the number of years, and PMT is the deposit made once per compounding period. The second term is the future value of an annuity, which prices a series of identical deposits. The formula assumes deposits arrive at the end of each period, which is the conservative convention.
One detail matters for reading the results. This calculator converts a monthly deposit into the chosen compounding frequency, so at annual compounding the year's deposits are treated as if they arrived at year end and earned nothing that year. That is slightly pessimistic, and it is why the annual and daily results differ by more than the interest rate alone would suggest.
$10,000 to start, $500 a month for 20 years, 7% compounded monthly. The monthly rate is 0.5833%, and the growth factor over 240 months is 4.0387. The starting $10,000 becomes $40,387, and the deposits accumulate to $260,464, for a total of $300,851. You put in $130,000, so $170,851 is interest, or 56.8% of the final balance.
The useful way to read that ratio is that more than half the money in the account was never deposited. It arrived because earlier interest was left alone to earn more interest. Nothing about that is automatic: withdraw the interest each year and the account ends at exactly $130,000.
| Years | Future value | You contribute | Interest | Interest share |
|---|---|---|---|---|
| 5 | $49,973 | $40,000 | $9,973 | 20.0% |
| 10 | $106,639 | $70,000 | $36,639 | 34.4% |
| 15 | $186,971 | $100,000 | $86,971 | 46.5% |
| 20 | $300,851 | $130,000 | $170,851 | 56.8% |
| 25 | $462,290 | $160,000 | $302,290 | 65.4% |
| 30 | $691,150 | $190,000 | $501,150 | 72.5% |
| 40 | $1,475,521 | $250,000 | $1,225,521 | 83.1% |
Read the last column as a progress bar for patience. At five years, compounding is a rounding error. At forty years it is the majority of the outcome. The jump from 30 to 40 years adds $784,371 of value, of which only $60,000 comes from additional deposits. That single decade produces more than the first twenty years combined.
The same point in one comparison: the first ten years produce $36,639 of interest, and the second ten produce $134,212. The second decade is worth 3.7 times the first, with the same deposit, same rate, and no additional skill.
| Annual rate | Future value | Interest earned |
|---|---|---|
| 3% | $182,359 | $52,359 |
| 4% | $205,613 | $75,613 |
| 5% | $232,643 | $102,643 |
| 6% | $264,122 | $134,122 |
| 7% | $300,851 | $170,851 |
| 8% | $343,778 | $213,778 |
| 10% | $452,965 | $322,965 |
Four percentage points, from 3% to 7%, are worth $118,492 over twenty years. Another three points, from 7% to 10%, are worth $152,114. Each point is worth more than the one before it, which is the mathematical case for caring about fees: a 1% expense ratio is not a 1% cost, it is the difference between the 6% and 7% rows.
Compare rates with deposits directly, holding everything else at the default. Adding $100 a month produces $352,943, a gain of $52,093. Finding an extra percentage point produces $343,778, a gain of $42,928. A modest increase in the deposit beats a full percentage point of extra return over twenty years, and the deposit carries no market risk. That ordering flips if you stretch the horizon to forty years, where a single point of return compounds into a larger gain than an extra $100 a month.
| Frequency | Future value | Difference from monthly |
|---|---|---|
| Daily | $302,374 | +$1,523 |
| Monthly | $300,851 | $0 |
| Quarterly | $297,755 | −$3,096 |
| Annually | $284,670 | −$16,181 |
Daily compounding is worth about half a percent of the final balance over monthly, which is why banks advertise it and why it rarely changes a decision. The effective annual rate at 7% is 7.250% compounded daily and 7.229% compounded monthly, a gap of two basis points. The real difference between products is in the nominal rate and the fees, not in how often interest is credited.
Divide 72 by the annual return to get the years needed to double your money. At 7%, that is 10.3 years, and the exact figure is 10.2. At 3% it is 24 years, and at 10% it is 7.3. The rule is a good mental check on any projection someone hands you, because a claim that money doubles in five years implies a 14.4% return, which is a claim worth questioning.
What the rule cannot do is account for deposits. It doubles a lump sum. A plan with monthly contributions grows faster than the doubling time suggests, and that is the case most people are actually in.
Taxes. Interest and dividends in a taxable account are taxed as they arrive, which removes money that would otherwise have compounded. A 7% return taxed at 22% each year compounds at about 5.5% instead, and over twenty years that is the difference between $300,851 and $246,526, roughly. Tax-advantaged accounts exist precisely to avoid this drag, and the Roth versus traditional IRA calculator prices the trade between paying tax now and paying it later.
Inflation. A future value is a nominal number. At 3% inflation, $300,851 in 2046 buys what about $166,600 buys today. The inflation calculator converts between the two, and doing that conversion before comparing a projection against a goal is the step most people skip.
Fees. A fund charging 1% against one charging 0.05% takes a full percentage point off the return every year, and the effect compounds exactly like interest. On the default case, a 1% drag lowers the result to roughly $264,000, a loss of about $37,000.
Compounding is the engine under most of this site. The savings goal calculator puts a deadline on the same math and solves for time instead of value. The CD interest calculator runs it at a fixed rate with a fixed term, which is what a certificate of deposit actually is. And the FIRE calculator turns the accumulated balance into a withdrawal rate and asks when the money can replace a paycheck.
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously credited interest. On $10,000 at 7% for twenty years, simple interest pays $14,000 in total, and monthly compounding pays $30,387 if you leave it alone. The gap is the interest that interest earned, and it grows with the square of time rather than linearly.
For a broad US stock portfolio held for decades, 7% nominal is a common planning figure and sits close to the long-run average after fees. It is far too optimistic for a five-year horizon, where a single bad year can erase the average. For a savings account or a CD, use the rate the institution actually advertises, which is what the 4% default on this site reflects.
Monthly or daily is plenty. The difference between monthly and daily compounding on the default case is $1,523 over twenty years, and the difference between annual and monthly is $16,181. If a bank offers a higher nominal rate with less frequent compounding, take the higher rate and do not worry about the schedule.
Because most people save monthly. The calculator converts the monthly figure into an equivalent per-period deposit so the annuity formula stays consistent with the compounding schedule. At annual compounding that means treating the year's contributions as arriving at year end, which understates the result slightly. Monthly compounding avoids the issue and is the better setting for a monthly saver.
Exactly the same way, in the opposite direction. A credit card charging 24% APR compounds daily, which produces an effective annual rate near 27%. That is why a balance carried for a year costs far more than the advertised rate suggests, and why paying it down is the highest guaranteed return available to most households. The debt payoff calculator runs the same math on the liability side.
The balance keeps compounding on whatever is already there. In the default case, stopping after ten years leaves $106,639 growing at 7% with no additions, which reaches $430,687 by year forty. Stopping contributions is not the same as stopping growth, and the gap between the two is the reason people are told not to raid long-term accounts for short-term needs.
Same compounding math, different starting question.