Compound Interest Calculator

How to Use the Compound Interest Calculator

Five inputs, and the balance updates as you type. The two that change the answer most are the rate and the number of years — and years matters more than people expect, because the effect is exponential rather than linear.

1. Enter your starting amount. Whatever is in the account today. Leave it at zero if you are starting from nothing and only contributing monthly.
2. Set the contribution. This is added at the end of each compounding period, so with monthly compounding it is a monthly deposit. Keeping the two frequencies aligned is what makes the formula below exact.
3. Enter the annual rate. Use the nominal annual rate your provider quotes, not the APY — the calculator derives the yield itself and shows it in the third tile.
4. Choose the compounding frequency. Monthly is the common default for savings accounts and most investment platforms. Daily compounding adds surprisingly little over monthly; the frequency matters far less than the rate.
5. Read the split. The donut chart separates your starting amount, your contributions and the interest. Watching that third slice overtake the other two is the whole argument for starting early.

The year-by-year table shows the balance at each anniversary, computed period by period rather than by a shortcut, so the last row and the headline figure always agree to the penny. Use Share link to send someone a scenario with your numbers already filled in.

Compound Interest Formula

Compound interest has two parts: the lump sum growing on its own, and the stream of contributions, each of which has less time to grow than the one before it.

The second term is the future value of an ordinary annuity. It assumes each contribution arrives at the end of its period. Paying at the start instead — an annuity due — is worth one extra period of growth on every payment, roughly 0.6% more over twenty years at 7%.

Example

Both cases below are computed by hand so you can check the tool against them.

$10,000 plus $300 a month, 7% for 20 years

1. Periodic rate: 0.07 ÷ 12 = 0.00583333. Periods: 12 × 20 = 240.
2. Growth factor: 1.00583333²⁴⁰ = 4.038739.
3. Lump sum: 10,000 × 4.038739 = $40,387.39.
4. Contributions: 300 × ((4.038739 − 1) ÷ 0.00583333) = 300 × 520.9267 = $156,278.00.
5. Total: 40,387.39 + 156,278.00 = $196,665.39. You put in 10,000 + (300 × 240) = $82,000, so $114,665.39 of that balance is interest.

Why the frequency barely matters

Take the same $10,000 at 7% for 20 years with no contributions. Compounded yearly it becomes $38,696.84. Monthly, $40,387.39. Daily, $40,546.56. Moving from yearly to monthly gains about 4.4%; moving from monthly to daily gains another 0.4%. The effective annual yield on the monthly figure is 7.23% against a 7.00% nominal rate — which is the entire difference compounding frequency can make.

Now change the rate instead. At 8% rather than 7%, the same monthly case reaches $49,268.03 — a gain of nearly 22%. Rate beats frequency by a wide margin, and time beats both.

The same money, started ten years later

Take the $300 a month and start it at year ten instead of year one, running for the remaining ten years at the same 7%. Those contributions total $36,000 and grow to $51,925. Started at year one and run for twenty, the same $300 a month totals $72,000 and grows to $156,278. Doubling the number of payments more than tripled the result, because each early payment had twenty years of compounding behind it rather than ten. That asymmetry is the single most useful thing this calculator demonstrates.

How Interest Compounds Over Time

The number that makes compounding click is the doubling time. Divide 72 by the annual percentage rate and you get a close approximation of how many years a balance takes to double: at 7% that is about 10.3 years, at 9% about 8 years, at 3% about 24 years.

Read the last column carefully. The difference between 5% and 9% is not double — it is roughly triple, over thirty years. That gap is why fees matter: a 1% annual management charge does not cost you 1%, it costs you about a fifth of the final balance over a working life.

The other thing worth noticing is when the interest arrives. In the twenty-year example above, the first five years produce about $7,650 of interest and the last five produce about $55,100. Nothing dramatic happens early, which is precisely why most people give up before compounding does the interesting part.

The Assumptions Worth Arguing With

Three assumptions sit underneath every result on this page, and all three are worth arguing with.

The rate is constant. Real markets are not. A portfolio averaging 7% will have years at −18% and years at +26%, and the order those arrive in matters if you are withdrawing rather than contributing. For a savings account the assumption is safer; for equities, treat the result as a central estimate rather than a forecast and run it again at a lower rate.

Nothing is taken out. No tax on interest, no platform fee, no withdrawal. If your account is taxable, enter an after-tax rate. If you pay a 0.4% platform charge, enter 6.6% rather than 7%.

The money is in today's terms. $196,665 in twenty years is not $196,665 of today's buying power. At 2.5% inflation it is closer to $120,000. The inflation calculator converts between the two, and running your projection at a real rate — nominal minus inflation — gives you a figure you can actually plan against.

Common mistakes: entering a monthly rate in the annual field (a 0.58% monthly rate is 7% a year, not 0.58%); entering the APY where the nominal rate belongs, which double-counts the compounding; and comparing a compound result against a simple interest one without noticing which is which. Over one year they are close. Over twenty they are not the same universe.