Compound Interest Calculator

What Compounding Actually Is

Interest that earns interest. Simple interest pays on the original amount forever. Compound interest adds each payment to the balance, so the next payment is calculated on a larger number.

The difference is small then enormous. Over one year it is negligible. Over thirty it is most of the result, which is why the effect feels like nothing is happening for a decade.

The share panel above is the real story. When interest is a small slice of the final balance you are essentially just saving. When it exceeds what you paid in, compounding has taken over.

It works against you too. Credit card balances compound in exactly the same way, which is why an unpaid balance grows faster than the spending that created it.

How to Use This Calculator

Start with what you have and what you can add. The monthly contribution usually matters more than the starting amount over long periods, which the year by year table makes obvious.

Use the rate your account actually quotes. That is the nominal rate. The effective annual rate shown alongside is what it turns into once compounding is applied, and it is the number to compare between accounts.

Leave inflation on. A large number in thirty years is not comparable to money today. The adjusted figure says what the balance would actually buy.

Read the table, not just the total. The point where the green bar overtakes the blue one is the moment compounding starts doing more work than you are.

The Formula and Where It Breaks

The standard formula covers a lump sum. A starting amount multiplied by one plus the rate per period, raised to the number of periods. That part is uncontroversial.

Contributions need a second formula. The future value of an annuity, which assumes contributions arrive exactly as often as interest compounds.

That assumption fails constantly. Paying in monthly against quarterly compounding breaks it, and most calculators apply it anyway, which is wrong by a small amount that grows with the term.

Simulating each month avoids the problem. Interest accrues on the balance actually present and is credited at real compounding boundaries, which needs no assumption about the two frequencies matching.

Why Compounding Frequency Matters

More often is better, and by less than people expect. At five percent over ten years, daily compounding beats annual by about one and a half percent of the total. Real, but not the difference between accounts.

The gains shrink as frequency rises. Annual to monthly is a meaningful step. Monthly to daily is almost nothing, because it approaches a limit rather than growing without bound.

That limit is continuous compounding. Compounding infinitely often gives the original multiplied by e to the power of rate times time, and daily is already very close to it.

The rate matters far more than the frequency. A quarter of a percent more interest outweighs any change in how often it is applied, so compare rates first.

Effective Annual Rate

It makes two accounts comparable. Five percent compounded monthly and five percent compounded annually are different products advertised with the same number. The effective rate resolves that.

Five percent monthly is 5.12 percent effective. Small in one year and noticeable over twenty, which is exactly the kind of difference the headline rate hides.

Regulated products usually quote it. In many jurisdictions savings accounts must publish an equivalent annual figure precisely so that this comparison is possible.

For borrowing it works the same way. The effective rate on a credit card is considerably higher than the monthly rate suggests, for the same reason.

Time Beats Amount

Early contributions do disproportionate work. Money paid in during year one compounds for the whole term. Money paid in during year twenty compounds for a decade less.

Ten years of head start is hard to catch. Someone saving modestly from twenty five often finishes ahead of someone saving considerably more from thirty five, purely because of the extra decade.

Try it above. Halve the contribution and add ten years, and watch what happens to the final figure. It is the most convincing thing this calculator does.

Consistency matters more than size. A regular small amount left alone outperforms an irregular larger one interrupted by withdrawals, because every withdrawal removes future compounding as well as the money.

Inflation and Real Returns

Nominal growth is not purchasing power. A balance that grew fivefold over thirty years while prices tripled has not grown fivefold in any sense that matters.

The real return is roughly the difference. Six percent interest against two and a half percent inflation is about three and a half percent of actual gain, and it is that figure which compounds in real terms.

Below inflation is a loss. An account paying two percent while prices rise three percent loses you money every year, however positive the balance looks.

Tax comes off the nominal figure. Interest is usually taxed on the amount earned rather than the real gain, so the after tax real return is lower again than the adjustment above suggests.

The Rule of 72

Divide 72 by the rate for the doubling time. At eight percent, money doubles in about nine years. It is a mental shortcut you can use without a calculator.

It is accurate between about four and twelve percent. Within that band it is within a few percent of the exact answer, which is shown above for comparison.

It drifts at the extremes. At one percent or thirty percent it is noticeably off, because the approximation it comes from only holds for moderate rates.

It works for inflation too. At three percent inflation, prices double in about twenty four years, which is a useful way to think about long horizons.

Common Mistakes to Avoid

Ignoring inflation entirely. It turns an impressive projection into an ordinary one, and it is the single most common omission in savings planning.

Assuming a constant return. Savings accounts change their rates and investments do not return a smooth percentage. This is a projection under one assumption, not a forecast.

Forgetting fees and tax. A one percent annual fee removes far more than one percent of the final balance, because it also removes everything that percentage would have earned.

Comparing nominal rates across products. Without the effective rate you are comparing two numbers that do not mean the same thing.

Frequently Asked Questions