Compound Interest Calculator

Compound interest is interest calculated on both your original principal and the interest that has already accumulated. Simple interest, by contrast, is calculated only on the principal, so it grows in a straight line. A $10,000 investment earning 7% simple interest gains exactly $700 every year. The same $10,000 compounding monthly at 7% gains a similar amount in year one, but by year ten each year's gain is larger than the last, because interest is now earning interest on itself. This calculator uses monthly compounding — the more common convention for savings and brokerage accounts — so gains are added to the balance twelve times a year rather than once.

A quick way to estimate how long money takes to double, without touching a calculator, is the rule of 72: divide 72 by the annual rate of return, and the result is roughly the number of years to double. At a 6% annual return, that's 72 ÷ 6 = 12 years, close to the true value of about 11.9 years from the exact compounding formula. At 8%, the rule predicts 9 years, again nearly identical to the actual 9.0 years. The shortcut gets noticeably less accurate at higher rates — at 20%, it predicts 3.6 years while the true doubling time is closer to 3.8 years, and the gap widens further from there. It also silently assumes one constant rate with no withdrawals or added contributions along the way, so treat it as a mental estimate, not a substitute for running the actual numbers.

Time matters more than the rate you earn, because compounding is exponential rather than linear, and a decade's head start can be worth more than most people expect. Take $10,000 invested once, with nothing added afterward, at a steady 7% annual return: left alone for 40 years it grows to roughly $149,700, but the same $10,000 invested for only 30 years — because the investor started a decade later — reaches about $76,120. Waiting ten extra years to begin costs roughly $73,600 in this example, nearly half of what the earlier investor ends up with, even though both contributed the exact same amount of money. Small differences in starting date compound into large differences in outcome, which is why the biggest lever most people have isn't finding a higher return, it's starting sooner.

Regular monthly contributions change the shape of the curve. Adding even a modest amount every month — the same principle behind automatic 401(k) or IRA contributions — means new money keeps entering the account at today's dollar amount while older contributions keep compounding. Over a working career, most of the final balance in a retirement account often comes from contributions plus compounding on those contributions, not just the initial deposit. Long-run U.S. stock market returns, such as the S&P 500's historical average, are sometimes used as a rough reference point for the rate field, but past performance never guarantees future results.

Where the money sits changes the arithmetic more than most people expect, because in the United States the question is whether growth is taxed every year or only at the end. Inside a taxable brokerage account, dividends and interest are taxed in the year they arrive, so the share handed to the IRS never gets to compound. Qualified dividends fall into the 0%, 15%, or 20% brackets, but a dividend only qualifies if you held the shares more than 60 days during the 121-day period beginning 60 days before the ex-dividend date; miss that window and it is taxed as ordinary income. Higher earners add the 3.8% Net Investment Income Tax, charged on the lesser of net investment income or the amount by which modified adjusted gross income exceeds $200,000 for single filers and $250,000 for joint filers. Those two thresholds are written into the statute and are not indexed for inflation, so more households drift across them every year. The drag is easy to see: $10,000 at 7% for 30 years reaches about $76,120 with nothing removed, but skim 15% off the gain annually and the effective rate falls to roughly 5.95%, landing near $56,600 instead.

The same question is why a 401(k), a traditional IRA, or a Roth IRA behaves so differently from a plain brokerage account holding the identical fund. In the first two, growth is deferred and the tax arrives on withdrawal; in a Roth, qualified withdrawals come out untaxed. Nothing about the underlying investment changed, only how many times a slice is taken along the way, and that alone can decide which of two otherwise identical savers finishes ahead. To approximate a taxable account here, lower the rate you enter by your expected annual tax bite. To model a tax-advantaged one, enter the gross rate and keep in mind that a traditional account still owes tax at the far end.

How often interest compounds also matters, though usually less than people assume. Take $10,000 growing at a nominal 6% annual rate for 20 years: compounded once a year it reaches about $32,071; compounded monthly, the same nominal rate produces about $33,106 — roughly $1,000 more, a difference of about 3%. Switching from monthly to daily compounding adds only about another $95, well under a tenth of a percent. Moving from annual to monthly compounding has a real but modest effect, while moving from monthly to daily makes almost no practical difference. The rate itself matters far more than how finely it is sliced.

That small gap is exactly why American banks advertise deposits as an APY instead of a plain rate. The annual percentage yield already folds in how often the institution compounds, so two accounts quoting the same APY pay the same over a year even if one credits daily and the other monthly. This calculator works the other way around: you give it a nominal rate and a compounding frequency, and together they reproduce that APY. The practical rule is to compare a certificate of deposit against a high-yield savings account on APY alone, and to remember that loans are quoted as APR, which points in the opposite direction because it adds fees rather than compounding.

A steady annual rate is a simplification real markets don't follow, and volatility itself quietly erodes returns in a way a simple average return can hide. Imagine a portfolio that gains 50% in one year and then loses 50% the next: the arithmetic average of those two returns is 0%, which sounds like breaking even, but the actual result is a 25% loss overall — $10,000 grows to $15,000 and then falls back to $7,500. The rate that truly describes what happened is the geometric mean, about −13.4% per year, not the 0% arithmetic average. This gap between the two kinds of average is sometimes called volatility drag: the more a return swings up and down around its average, the more it eats into the compounding you actually experience, even when the simple average return still looks perfectly respectable.

The most useful thing to do with the balance at the bottom of this page is to change one input and watch what moves. Add a year of saving. Add a percentage point of return. Add fifty dollars a month. The ranking of those three levers is frequently the opposite of what intuition suggests, and seeing it once tends to settle arguments that spreadsheets full of assumptions never do. Two things travel with every result. Fees compound just as returns do, so a one-percentage-point annual fee turns a 7% gross return into 6% net and shrinks $10,000 over 30 years from about $76,120 to about $57,435, nearly $18,700 lost to costs alone. And every figure here is nominal rather than real: a balance growing 7% a year while prices rise 3% is gaining purchasing power at closer to 4%, so subtract your inflation assumption from the rate before entering it if you want the answer in today's dollars. The calculator also assumes one steady rate forever, which no market has ever provided. Read the output as an educational simulation of compounding under assumptions you chose, not a forecast or a recommendation.