Compound Interest Calculator

How compound interest works

Compound interest is interest you earn on both your original money and the interest it has already earned. Each period the balance is a little larger, so the next round of interest is calculated on that bigger number — interest starts earning interest. Over long stretches this snowball effect is what turns steady saving into surprisingly large sums, and it is exactly what the compound interest calculator above is built to show.

To use it, enter a starting balance, an annual interest rate, how long the money stays invested, and how often it compounds — then add a regular contribution if you make one. The tool works as an interest on interest calculator, showing how much of your final balance came from contributions versus growth. Because the same engine can compute compound interest at any frequency, you can treat it as a general compounding calculator or, when you only need a quick number, as a way to estimate compound interest before committing to a plan.

Doing this by hand is tedious. Figuring compound interest one period at a time, then carrying the new balance forward, is slow and error-prone — and that is before you add deposits. This calculator removes the busywork: it will figure compound interest across hundreds of periods instantly and acts as a cumulative interest calculator that totals every dollar of growth along the way. It is sometimes called a complex interest calculator, but the idea is simple once you watch the balance build. If you want to compute compound interest with regular deposits, just open the contributions section.

Compound interest formula

The standard compound interest formula for a lump sum is:

where A is the final balance, P is the principal (your initial amount), r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the number of years. When you also make regular deposits, the future value of that contribution stream is added on top:

Here PMT is the contribution added each period. This combined accumulated interest formula is what the calculator evaluates, and the interest earned is simply the final balance minus everything you put in.

When interest compounds continuously — the limit of ever-more-frequent compounding — the discrete formula gives way to the continuous compound interest formula:

where e ≈ 2.71828. Selecting "Continuously" in the calculator uses this version for the initial amount and values any contributions at the equivalent effective annual rate.

Simple interest vs compound interest

The difference between the two comes down to whether interest earns interest. With simple interest, you only ever earn a return on the original principal. The simple interest formula is:

so the balance grows in a straight line. With compounding, past interest is added to the balance and earns its own return, so growth curves upward and accelerates. Writing the compound and simple interest formula side by side makes the gap obvious: simple interest is A = P (1 + r t), while compound interest is A = P (1 + r/n)^nt.

The comparison block in the results applies that compound interest and simple interest formula to your exact inputs, so you can see the dollar gap created purely by interest on interest. For short periods the two are close; over decades, compounding pulls far ahead. Watching that gap widen is the clearest lesson this tool teaches.

Daily, monthly, and yearly compounding compared

How often interest compounds changes the result, though usually less than people expect. More frequent compounding means interest is added — and starts earning — a little sooner, so daily beats monthly, which beats yearly, at the same stated rate. Set the frequency to daily and the tool becomes a daily compound interest calculator; in fact this compound interest calculator compounded daily uses the same engine as every other frequency, only with n set to 365. Used that way it doubles as a compounded daily calculator for savings products that credit interest every day.

Switching to monthly shows monthly compound interest, the most common setting for everyday savings accounts, while annual compounding is typical for some bonds and longer-term instruments. The jump from yearly to monthly is noticeable; the jump from daily to continuous is tiny, because there is a mathematical ceiling on how much extra frequency can add. Try a few settings to see how little the frequency matters compared with the rate and the time you stay invested.

Related calculators

This page focuses on the mechanics of growth — how a balance compounds at a chosen rate and frequency. If you want to project a savings or retirement plan with an expected market return, total ROI, and an inflation adjustment, use our investment calculator. The two are close cousins: the compound interest calculator highlights the math of interest on interest, while the investment calculator frames the same growth as a forward-looking plan for your contributions.