Compound Interest Calculator

How the compound interest calculator works

Compound interest is what happens when the interest a balance earns is added back to that balance and then earns interest of its own. Simple interest pays only on the original principal, so it accumulates in a straight line. Compounding turns that line into a curve, because the base it is calculated on grows every period. For a lump sum with no additions, the calculator uses the standard formula:

The bracketed term is the growth factor for one period. Raising it to the power n × t simply applies that same growth once for every period in the horizon. Nothing more sophisticated is happening — the curve comes entirely from repeated multiplication rather than repeated addition.

Adding regular contributions

Most real balances are not left alone. If you add money on a schedule, you are layering an annuity on top of the lump sum, and each deposit compounds only for the time remaining after it arrives. A deposit made in year one grows for the whole horizon; one made in the final year barely grows at all.

Contributions and compounding often run on different clocks — you might deposit monthly into an account that compounds daily. To reconcile them, the calculator converts the annual rate into an effective rate for one contribution period:

The two pieces are then added: the grown principal plus the grown series equals the future value. Total interest is whatever is left once you subtract everything you actually deposited — principal plus all contributions — from that ending balance.

Why compounding frequency matters less than it seems

At a fixed stated rate, compounding more often does produce a larger balance, because interest begins earning interest sooner. But the size of that gain is routinely overestimated. The jump from annual to monthly compounding is noticeable; the jump from monthly to daily is close to negligible, because daily compounding already sits near the continuous limit that the sequence converges toward. The effective annual yield shown in the results makes this concrete: it translates the stated rate and its compounding schedule into the single annual rate that would produce the same growth if it compounded once a year. Comparing two offers on effective yield rather than stated rate puts them on the same footing.

Timing, and why the start of a period is worth something

The end-of-period setting is an ordinary annuity: the deposit lands after that period's interest has been credited, so it earns nothing until the next period. The start-of-period setting is an annuity due: the deposit is present for the current period and earns interest immediately. The difference is exactly one extra period of growth on the whole contribution stream, which is why the formula multiplies by (1 + i). Over a long horizon this raises the contribution portion of the balance by roughly the periodic rate — a few hundred dollars on a typical monthly plan, not a transformation.

What the model leaves out

The projection is deliberately clean, and that is also its limitation. It assumes a constant rate for the entire horizon, which no market-linked account delivers; real returns arrive unevenly, and the order in which good and bad years fall changes the outcome even when the average is identical. It ignores taxes, which depend on the account and the holder. It ignores account fees and expense ratios, which come directly out of the rate. And it reports nominal dollars, not purchasing power.

Two adjustments get you closer to reality without leaving the page. To think in today's dollars, enter your assumed return minus your assumed inflation rate; the resulting balance is then expressed in roughly constant purchasing power. To account for a fee drag, subtract the annual expense ratio from the rate before you run the projection. Both are approximations, but they move the estimate in the right direction and cost nothing to test.

Read the output as a shape rather than a prediction. What the year-by-year table reliably shows is the structure of compounding: interest is a small share of the early years and a larger share of the late ones, because each year's interest is calculated on a base that includes every prior year's interest. Which inputs are realistic for your own situation is a judgment the arithmetic cannot make for you.