Compound Interest Calculator

Compound interest is interest calculated on both the original principal and on any interest that principal has already earned, which is why a balance grows exponentially rather than by a fixed amount each period. A deposit that earns 5% in year one earns 5% on a slightly larger balance in year two, because last year's interest is now part of the base.

This is the same exponential mechanism behind population growth or compounding returns anywhere else. Money is simply the quantity being multiplied.

The compound interest formula is A = P(1 + r/n)^nt, where n is the number of times interest is added to the balance each year. P is the starting principal, r is the annual rate as a decimal, and t is the number of years the money grows.

Setting n to 1 compounds once a year, n to 12 compounds monthly, and n to 365 compounds daily. The formula itself never changes, only how finely the year is sliced.

Simple interest is calculated only on the original principal every period, while compound interest is calculated on the principal plus all interest already added, so compound growth accelerates and simple growth stays linear. Simple interest on $1,000 at 5% adds exactly $50 every year forever; compound interest adds $50 in year one but a growing amount every year after.

Over short periods the two are close. Over a decade or more, the gap becomes large enough to change financial outcomes meaningfully.

More frequent compounding earns more interest because each compounding event adds that period's interest to the balance sooner, giving it more remaining time to earn interest of its own. Monthly compounding credits interest twelve times a year instead of once, so eleven of those twelve credits start earning immediately instead of waiting until year-end.

The effect is real but bounded. See the next question for the limit it approaches.

As compounding frequency approaches infinity, the discrete formula A = P(1 + r/n)^nt converges to the continuous formula A = Pe^rt, which is the highest future value any compounding frequency can produce at a given nominal rate. Daily compounding already sits extremely close to this ceiling; compounding by the hour or the second adds almost nothing further.

The continuous growth calculator computes this limiting case directly, without needing an n at all.

The nominal annual rate is the stated percentage before compounding is applied, while the effective annual rate is the actual percentage a balance grows by over one full year once compounding is taken into account. A 5.5% nominal rate compounded monthly produces an effective annual rate slightly above 5.5%, because interest added mid-year starts earning its own interest before the year ends.

The gap between nominal and effective rates widens as compounding frequency increases, which is exactly what the comparison table above this section demonstrates.

Not automatically. A higher nominal rate compounded less often can still beat a lower nominal rate compounded more often, so the compounding frequency and the rate both need to be compared together, not the frequency alone. This calculator projects the pure mathematics of A = P(1 + r/n)^nt for any rate and frequency you enter so the two can be compared side by side.

It is a mathematical projection tool, not financial advice. Real accounts can add fees, taxes, variable rates, or minimum-balance rules this formula does not include, so treat its output as a starting estimate rather than a guarantee.