Compound Interest Calculator
Compound interest is interest earning interest. The distinguishing feature is not the rate but the shape: the balance grows slowly for a long time and then steeply, because each period's growth is calculated on a base that already includes every previous period's.
That shape is why the single most valuable input is time, and why the calculator below reports how much of the final balance was contributed and how much appeared on its own. On a long horizon the second figure usually exceeds the first by a wide margin.
Project the balance
Use a realistic long-run return rather than a recent one. A projection built on an exceptional few years produces a plan that only works if they repeat.
The formula, and what each part does
A lump sum compounds as A = P(1 + r/n)^(nt): the principal multiplied by one plus the periodic rate, raised to the number of periods. Regular contributions add a second term, which the calculator handles by stepping through each period rather than by formula.
Of the four inputs, time enters as an exponent and everything else enters linearly. That is the whole reason time dominates — doubling the principal doubles the result, while doubling the years does something considerably larger.
The practical version: money invested at twenty-five and left alone frequently ends up ahead of a much larger amount invested at forty, despite far smaller total contributions. Nothing about that is a trick of the arithmetic; it is what an exponent does.
Compounding frequency matters less than people expect
Daily compounding beats annual at the same nominal rate, but the gap is small — the difference between the two on a typical rate is a fraction of a percentage point of effective yield.
What makes frequency worth understanding is comparison. APR is a nominal rate and APY includes the effect of compounding, so two accounts quoting the same APR at different frequencies are not equivalent. Compare APY against APY.
Where frequency genuinely matters is on debt at a high rate, since the same mechanism works against you. A card compounding daily at a high APR costs meaningfully more than the stated rate implies.
| Compounding | On a 6% nominal rate, effective yield |
|---|---|
| Annually | 6.00% |
| Quarterly | 6.14% |
| Monthly | 6.17% |
| Daily | 6.18% |
Contributions do the heavy lifting early
In the first several years the balance is dominated by what you put in, because there is not yet much to compound. The growth line is nearly flat and it is easy to conclude that nothing is working.
The crossover — where cumulative growth passes cumulative contributions — typically arrives somewhere in the second decade at ordinary rates, and everything after it belongs increasingly to the compounding rather than to you.
This is the argument for automating contributions rather than deciding on them monthly. The early years produce no visible reward and are the years that matter most, which is exactly the combination human judgement handles badly.
What the projection does not include
- Inflation. A balance projected in nominal dollars buys less than the figure suggests — subtract expected inflation from the return to see it in today's money.
- Tax. Growth in a taxable account is reduced by tax on dividends and gains; tax-advantaged accounts change the picture substantially.
- Fees. An expense ratio comes straight off the return, and a one percent annual fee across thirty years removes a very large share of the final balance.
- Sequence. Real returns arrive unevenly, and a smooth average conceals that a bad decade near the start is far worse than the same decade near the end.
- Contribution changes. Most people can raise contributions over a career, which the flat monthly figure ignores.
Choosing a rate honestly
The return you enter is the single largest determinant of the answer and the one most often chosen optimistically. A projection at ten percent and one at six describe different lives on the same contributions.
For a savings account the rate is knowable — it is the APY, and it moves. For invested money it is an assumption, and the defensible approach is a long-run average across a full cycle including the bad years, not the trailing performance of a good one.
Run the projection twice, at a realistic rate and at a pessimistic one. If the plan only works at the optimistic figure, it is not a plan, and finding that out now is considerably cheaper than finding it out at retirement.
Using it for debt as well as savings
The same arithmetic governs money owed, which is why a balance left on a high-rate card grows in exactly the shape a savings balance does, in the wrong direction.
This is the comparison worth making before choosing between extra debt payments and extra saving. A guaranteed return equal to the debt rate is what clearing it produces, and consumer debt rates generally exceed any return you would assume for investments.
The exception is an employer retirement match, which is an immediate return no interest rate competes with. Take the match, clear high-rate debt, then invest — in that order, and the arithmetic supports it rather than merely the convention.
Frequently asked questions
Each period's interest is calculated on a balance that already includes all previous interest, so growth accelerates over time. Time enters the formula as an exponent while the other inputs are linear, which is why the horizon matters more than the amount.
APR is a nominal annual rate; APY includes the effect of compounding within the year. Two accounts quoting the same APR at different compounding frequencies are not equivalent — compare APY against APY.
Less than most people expect — on a typical rate the gap between daily and annual is a fraction of a percentage point of effective yield. It matters more on high-rate debt, where the same mechanism works against you.
For a savings account, the current APY. For invested money it is an assumption, so use a long-run average across a full cycle including the bad years — and run the projection at a pessimistic rate too. A plan that only works at the optimistic figure is not a plan.