Compound Interest Calculator

What this projection assumes

Everything on this page is a projection, not a forecast and certainly not a promise. It shows what the arithmetic gives if a particular set of assumptions holds for the whole period, and the most important of those assumptions is one you supply yourself: the rate. The calculator has no idea what your money will actually earn. It takes the number you type and carries it forward unchanged.

• The rate never changes. A real account or fund varies year to year, sometimes sharply and sometimes negatively. A constant rate is a simplification that makes the arithmetic possible, and it is why a projection over decades should be read as a shape rather than a figure.
• Contributions arrive at the end of every month, without fail. That is the ordinary annuity convention. Contributing at the start of each month instead earns one extra month of growth on every payment, so the real answer would be slightly higher. Missing payments makes it lower.
• Nothing is taken out. No inflation, no tax on the growth, no account fees, no fund expense ratio. Each of those reduces the real outcome, and inflation in particular means the final figure buys less than the same number does today.

None of that makes the calculation useless. It makes it a model, which is a good way to compare two rates or two contribution levels against each other, and a poor way to predict a balance on a particular date.

Working the growth out by hand

The page opens on 10,000 at 7 percent for 20 years, compounded monthly, with 100 added each month. Here is where the answer comes from.

1. Turn the annual rate into a monthly one. Compounded monthly, 7 percent a year is 0.07 ÷ 12 = 0.0058333 a month.
2. Count the months. 20 years is 240 of them.
3. Grow the starting sum. 10,000 × 1.0058333^240 = 40,387.39. That is the opening deposit alone, with no contributions at all.
4. Grow the contributions. Each 100 earns for however long it has left, which the annuity formula totals as 100 × (1.0058333^240 − 1) ÷ 0.0058333 = 52,092.67.
5. Add the two. 40,387.39 + 52,092.67 = 92,480.05.

Worth sitting with: you put in 34,000 of your own money, 10,000 at the start and 24,000 over twenty years. The other 58,480 is growth. And the contributions, which total more than twice the opening deposit, end up producing only slightly more than it does, because the opening deposit had the full twenty years to work and the last contribution had a month.

Edge cases, and what the answer means

• A rate of zero. The compounding formula divides by the rate, so at zero the calculator switches to plain addition: your starting sum plus every contribution, and nothing else. That is the correct answer, and it is a useful floor to compare a projection against.
• Compounding frequency matters less than people expect. Moving from annual to monthly compounding at 7 percent changes the outcome by a fraction of a percent a year. Moving from 7 percent to 8 percent changes it far more. Frequency is the detail; the rate is the substance.
• Contributions are monthly whatever the compounding frequency. Choosing daily compounding does not make the contributions daily. The tool converts the annual rate to an equivalent monthly rate and adds the contribution once a month.
• Long horizons magnify a wrong rate. A one point error over five years is small. Over forty it is enormous, because the error compounds along with everything else. Treat a long projection as a comparison between scenarios, not as a number to plan a date around.

Your figures stay in the page

Every amount you enter is processed by this page in your browser. The starting balance, the rate, the contributions and the projection are not sent to a server, not stored after you close the tab, and not visible to anyone else. There is no account and nothing to sign up for.

What the calculator does

You enter the starting principal, the annual interest rate, the time horizon, a compounding frequency, and an optional monthly contribution. The calculator returns the future balance, total contributions, and the interest portion of the final balance. A short year-by-year preview shows the first three years and the final year so you can see how the balance scales.

Why compounding frequency matters

At the same nominal annual rate, more frequent compounding produces a slightly higher final balance. For 7% compounded annually, $10,000 over 20 years grows to about $38,697. For 7% compounded monthly the same deposit grows to about $40,387. The gap widens with rate, time, and balance, but past monthly the additional gains are small.

How monthly contributions are modeled

Each contribution is added at the end of the month and compounds from then on. The calculator first converts the chosen compounding frequency into an effective monthly rate, then runs the standard future value of an annuity formula on that rate. This means contributions and compounding line up cleanly even when the compounding frequency is annual, quarterly, daily, or continuous.

Worked example

Starting principal $10,000, annual rate 7%, monthly compounding, 20 years, monthly contribution $100.

• Effective monthly rate: 7% ÷ 12 ≈ 0.5833%
• Total months: 20 × 12 = 240
• Principal future value: 10,000 × (1.00583)^240 ≈ $40,387
• Annuity future value: 100 × ((1.00583)^240 − 1) ÷ 0.00583 ≈ $52,093
• Future balance: ≈ $92,480
• Total contributions: 10,000 + 100 × 240 = $34,000
• Interest earned: ≈ $58,480

About 63% of the final balance is interest, which is the practical reason compounding matters so much over long time horizons.

Compound interest vs simple interest

Simple interest is calculated only on the original principal, so it grows linearly. Compound interest is calculated on principal plus accumulated interest, so it grows exponentially. Over short periods the two are close; over decades, compound interest pulls far ahead.

Common mistakes

• Treating APR and APY as the same number. APY is the effective rate after compounding; APR is the nominal rate.
• Comparing two scenarios with different compounding frequencies as if they were the same. Convert to APY (or use the calculator) before judging.
• Forgetting inflation. A nominal balance is not the same as purchasing power. Subtract an expected inflation rate from the annual rate to estimate the real return.
• Trusting a single rate to hold for decades. Markets fluctuate; use the projection as a planning estimate, not a forecast.
• Ignoring fees. Investment fees compound the same way returns do. A 1% annual fee over 30 years takes a real bite out of the final balance.

Related tools

• Simple interest calculator for the non-compounding variant: interest on the original principal only.
• Inflation calculator for the purchasing-power side of compounding (prices rising vs investment growing).
• APY calculator for converting a nominal rate plus compounding into an effective annual yield.
• CD calculator for fixed-term certificates of deposit at a stated APY.
• Savings calculator for goal-oriented planning: future balance, monthly amount needed, or time to a target.
• Future value calculator for the textbook FV formulas: lump sum, with payments, or solve for time.
• 401k calculator for retirement scenarios that include salary growth and employer match.
• Roth IRA calculator for projecting an individual after-tax retirement account.
• IRA calculator for Traditional or Roth IRA growth with a year-by-year table.
• 529 calculator for tax-advantaged college savings projections.
• Coast FIRE calculator for the portfolio size that compounds to your full FIRE number.
• Present value calculator for the inverse: today's value of a future amount.
• Loan calculator for compound interest on the other side of the ledger.
• Mortgage calculator for principal and interest plus taxes, insurance, PMI, and HOA.
• Car payment calculator for auto loans with sales tax, trade in, and down payment.
• Percentage increase calculator for comparing growth rates side by side.
• Simple interest vs compound interest explains the two formulas, the difference in growth, and when to use each.