Compound Interest Calculator

The question this tool answers is what compounding FREQUENCY is worth. A nominal annual rate — the number an institution quotes you — is defined by 12 CFR § 1030.2(o) as a rate that "does not reflect compounding," so on its own it does not tell you what you get paid. Divide it by the number of periods in a year to get the periodic rate, apply that rate once per period, and the interest credited in one period joins the balance that earns the next. The result over a year is the annual percentage yield: APY = 100 × [(1 + r/n)^n − 1]. At 5% nominal, compounding annually pays exactly 5.00%, semiannually 5.0625%, quarterly 5.0945%, and monthly 5.1162%. The gap widens with the rate, not with the frequency alone — at 1% nominal the whole monthly-versus-annual difference is about half a basis point, which is why frequency matters far more on a credit card than on a checking account. This calculator offers monthly, quarterly, semiannual and annual compounding, and accepts a starting principal up to $1,000,000,000, a per-period contribution up to $10,000,000, a rate up to 50%, and a term of 1 to 100 years. That 50% ceiling is not a guess about markets: decimal.js-light carries 34 significant digits here, and the widest inputs the form allows land at about 2.35e30 — 33 significant digits — so every cent printed is genuinely exact rather than an artefact of precision running out. Two modelling decisions shape the answer. First, contributions are made on the same schedule as compounding. That is deliberate: a nominal rate alone cannot say whether a deposit made between two compounding dates earns anything, because the answer depends on the institution’s balance-computation method under 12 CFR § 1030.7, which is not something you can look up on a statement. Tying the two timelines together puts the assumption in the form instead of hiding it in the arithmetic. Second, you choose whether each deposit lands at the beginning or the end of the period. Beginning-of-period deposits (an annuity due) sit in the account for the whole period and so earn that period’s interest; end-of-period deposits (an ordinary annuity) miss it. Over a long term that single line of difference is worth roughly one extra period of interest on the entire contribution stream. The non-obvious part is how the balance is built. Rather than evaluating a closed-form future-value formula, the calculator walks the account period by period and rounds each period’s interest credit to the whole cent before adding it — because that is what a real institution does. Closed-form totals and cent-rounded schedules disagree, by cents on short terms and by a few dollars across thirty years, and the schedule is the one that matches a statement. The interest credit is also written as balance × rate ÷ (100 × n) in one expression rather than precomputing the periodic rate, so a repeating decimal like 7%/12 never gets truncated before the multiplication and decide a half-cent by accident. If you want to see how a lump sum behaves under simple interest, daily compounding or after tax instead, the interest calculator covers that; to layer investment fees and inflation on top of a contribution schedule, use the investment calculator.