Compound Interest Calculator

Compounding is one small idea applied repeatedly. In each period, the balance earns a return. That return is added to the balance. In the next period, the enlarged balance earns the return — so the interest itself starts earning interest. Simple interest never does this. It pays only on the original principal, which means it grows in a straight line: the same dollar amount every period, forever. Compound interest grows on everything accumulated so far, which makes the curve bend upward. Over a single year the two are nearly indistinguishable. That is exactly why the difference is underestimated — the mechanism is invisible at the timescale most people evaluate it on, and decisive at the timescale that actually matters. The gap between the two does not grow steadily; it grows faster the longer it runs.

With no contributions, the growth is balance = principal × (1 + i)^n, where i is the rate per period and n is the number of periods. Adding a regular deposit makes it easier to describe step by step than in closed form. Each month the balance is updated as: balance = balance × (1 + i) + contribution with i derived from the annual rate you entered. This calculator adds the contribution at the end of each month, so a deposit begins compounding the following month rather than the one it was made in. That is the conservative convention; a tool that credits contributions at the start of the period will produce a slightly higher figure from identical inputs, which is worth knowing when two calculators disagree by a small margin. The result is a projection of arithmetic, not a forecast. It answers what happens if a fixed rate holds for the entire period — which is a useful question and not a description of how any real market behaves.

A quick mental shortcut for compounding: divide 72 by the annual percentage rate and you get the approximate number of years for a balance to double. At 8%, roughly nine years. At 6%, roughly twelve. At 3%, roughly twenty-four. It is an approximation — the exact answer comes from logarithms — and it is most accurate in the middle range of rates, drifting at very high ones. But it makes the structure visible. Doubling time depends on the rate alone, not on the amount, and each doubling adds as much as everything that came before it combined. That is what the two lines on the chart are showing. One is the total you have contributed, which rises in a straight line. The other is the balance. They start nearly together and separate slowly, then not slowly at all. The moment the accumulated interest exceeds everything you put in is not a special event — it is simply where an exponential curve overtakes a linear one, and on long horizons at moderate rates, it does. The same logic explains why an early contribution is worth more than a late one of equal size: it is exposed to every remaining doubling.

Nothing in the mechanism cares which direction the money flows. On a debt that compounds, the unpaid interest is added to the balance, and next period's interest is charged on the larger balance. This is why revolving credit at a high rate is so difficult to escape by paying the minimum: the payment can be smaller than the interest accruing, or barely larger, so the balance moves slowly or not at all while the compounding continues. The curve that builds savings over decades erodes a repayment plan over months. It is also why the frequency of compounding matters on both sides. Interest added daily produces a slightly larger effective yearly figure than interest added annually at the same nominal rate. The disclosed APY on a deposit account captures that; on the borrowing side, the disclosed APR is a nominal cost-of-credit measure and may include certain fees, so the two are not interchangeable.

The rate field decides the output more than any other input, and it is the easiest place to produce a comforting number that means nothing. A constant rate is a modeling convenience. Real investment returns vary year to year, and a sequence of returns averaging some figure does not produce the same ending balance as that figure applied every year — variability itself affects the outcome, and the order in which good and bad years arrive matters, particularly once you are withdrawing. Past performance does not indicate future results, and any long-run average quoted for any asset class is a historical description, not a rate anyone is entitled to. Three deductions are also missing from the projection. Inflation erodes purchasing power, so if you want the answer in today's dollars, enter a rate net of expected inflation rather than a nominal one. Taxes may apply to interest, dividends and gains depending on the account and your circumstances. Fees — fund expense ratios, advisory fees, account charges — subtract from the return every year and compound against you exactly as returns compound for you. The honest use of this page is to see the *shape* of compounding and how sensitive it is to time and rate, and to compare scenarios against each other. It is not a projection of what any particular account will be worth, and it is not a recommendation about where to put money.