How often should interest compound?

More frequent compounding grows balances slightly faster at the same nominal APR. Daily compounding is closer to the theoretical maximum for a given rate than annual compounding.

Does compound interest include taxes or fees?

Simple calculators usually show pre-tax growth and ignore fees. Real accounts may have expense ratios, advisory fees, or taxable distributions that reduce net returns.

How do monthly contributions affect compound interest?

Each contribution starts earning interest from the time it is deposited. Over long horizons, regular deposits often add more to the ending balance than the starting principal alone.

Compound Interest Calculator: Formula, APY & Examples

Q: What is the compound interest formula?

A = P(1 + r/n)^(n t) where P is principal, r is annual rate (decimal), n is compounds per year, and t is years. With regular contributions, each deposit grows for the remaining periods.

Q: What is the difference between APR and APY?

APR is the nominal annual rate. APY (effective annual yield) includes compounding: APY = (1 + r/n)^n − 1.

Q: Is the compound interest calculator free?

Yes. ToolMars compound interest calculator is free, private, and needs no account.

Compound interest is interest earning interest — the reason long-term savings grow faster than simple interest. A free compound interest calculator projects future value from principal, rate, time, compounding frequency, and optional monthly contributions.

This guide explains the standard formula, APR vs APY, why frequency matters, and a worked example you can verify in the tool. For trading P&L (not compounding savings), see the trading P&L calculator.

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Free compound interest calculator — APY estimate, interest earned, no signup.

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Compound Interest Formula

A = P(1 + r/n)^(n t)
APY = (1 + r/n)^n − 1

P = starting principal · r = annual nominal rate (as a decimal) · n = compounds per year · t = years · A = ending amount.

Example without contributions

$10,000 at 7% for 10 years, compounded monthly (n = 12): A = 10000 × (1 + 0.07/12)^(120) ≈ $20,096. Interest earned ≈ $10,096 — roughly doubling over a decade at that rate.

APR vs APY

APR (or nominal rate) is the headline yearly rate before compounding frequency. APY folds compounding into an effective yearly yield so you can compare products fairly. At 7% nominal compounded monthly, APY is a bit above 7%.

Compare savings accounts by APY, not only advertised APR.
Loans may quote APR differently — read fee disclosures separately.

Project future value with compounding & contributions

Free compound interest calculator — APY estimate, interest earned, no signup.

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Why Compounding Frequency Matters

Annual, quarterly, monthly, and daily compounding all use the same nominal rate but different n. More frequent compounding slightly increases ending value. The jump from annual to monthly is noticeable; from monthly to daily is smaller. The calculator lets you switch frequencies to see the gap.

Adding Monthly Contributions

Real savers rarely leave a lump sum untouched. Each monthly deposit compounds for the remaining years. Over long horizons, contributions often dominate the ending balance. Try $10,000 start + $200/month at 7% for 10 years in the compound interest calculator — the contribution line alone is $24,000 deposited, and interest stacks on top of both.

Estimates only. Markets fluctuate; fees and taxes reduce net returns. This tool assumes a constant rate and ignores inflation — use it for planning scenarios, not guarantees.

Related Tools

Compound Interest Calculator — future value, contributions, APY
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Project future value with compounding & contributions

Free compound interest calculator — APY estimate, interest earned, no signup.

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Frequently Asked Questions

What is the compound interest formula?

A = P(1 + r/n)^(nt). Contributions compound for remaining time after each deposit.

What is the difference between APR and APY?

APR is nominal; APY includes compounding over a year.

Is the compound interest calculator free?

Yes on ToolMars.