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Compound Interest Calculator

How a balance grows with interest and regular deposits, at any compounding frequency.

Enter a starting amount or a regular deposit, plus a rate, to watch it compound.

The nominal rate.

Most savings accounts compound daily and credit monthly.

Regular deposits

Each deposit then earns one extra period of interest. Over decades this is not a rounding difference.

Exact calculation. Given your inputs, this is the answer — no estimation involved.

How this calculator works

Compound interest means interest earning interest. The balance grows, the interest is calculated on the larger balance, and the effect accelerates. Over long periods it dominates everything else.

Interest may compound daily while you deposit monthly, and 365 does not divide by 12. Rather than fudge that, this steps through a fine grid and applies a growth factor that reproduces the stated compounding exactly over a full year — so the lump-sum case matches the closed-form formula to the cent, and the deposit case matches how a real account behaves.

The APY shown alongside your nominal rate is the figure to compare between accounts. A 5% rate compounded daily and a 5.1% rate compounded annually are almost identical; the APY makes that visible.

Whether you deposit at the start or the end of each period matters more than it looks. Depositing at the start earns one extra period of interest on every single deposit, which over thirty years is real money.

The formula

Exactly what happens to your numbers, step by step.

  1. A lump sum

    A = P(1 + r/n)^(nt)

    P is the principal, r the annual rate, n the compounding periods per year, t the years.

  2. Effective annual rate (APY)

    APY = (1 + r/n)ⁿ − 1

  3. Continuous compounding

    A = P·e^(rt)

    The theoretical limit as n approaches infinity. No real deposit account uses it.

A worked example

$10,000 at 5%, compounded monthly, for 10 years, with $200 deposited each month.

What you enter

Starting amount
$10,000
Rate
5% compounded monthly
Monthly deposit
$200
Years
10

The working

Total deposits
$24,000
Total put in
$34,000
Balance after 10 years
≈ $47,500
Interest earned
≈ $13,500
APY
5.116%

About $47,500 — of which $13,500 is interest

The interest is 40% of what you contributed. Run the same numbers for 20 years and interest exceeds contributions entirely — that crossover is what compounding is.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

  • The rate is constant for the whole period. Real savings rates change.
  • Deposits are the same every period.
  • No tax on the interest. In a taxable account, interest is generally taxed as income each year, which reduces the effective return.
  • No fees or minimum balance requirements.

Questions people ask

What is the difference between APR and APY?

APR is the nominal annual rate before compounding. APY includes the effect of compounding within the year. A 5% APR compounded monthly is a 5.116% APY, and APY is what actually lands in your account.

How often should interest compound?

More often is better, but the difference is small. On 5%, moving from annual to daily compounding raises the effective rate from 5% to about 5.127%. The rate itself matters far more than the frequency.

Does it matter when in the month I deposit?

A little. Depositing at the start of each period earns one extra period of interest on every deposit. Over ten years of monthly deposits that is roughly half a percent of the final balance.

What is the rule of 72?

A shortcut: divide 72 by the interest rate to estimate the years to double. At 6%, about 12 years. It is an approximation that works well for rates between roughly 4% and 12%.

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Sources and review

This calculator uses standard arithmetic with no external rules or published rates, so there is nothing to cite beyond the formulas shown above.

Methodology version 1.0.0 · Last reviewed