Quick answer

Compound interest means that each period's interest is added to the balance, so later interest can be calculated on both the original principal and earlier interest. The same mathematics can describe savings growth, investment scenarios, inflation, fees, and debt.

Compounding is a calculation, not a guarantee. A bank account may state a known rate for a period; an investment return is uncertain and changes over time.

Use the compound interest calculator to compare a starting balance, monthly contributions, an assumed nominal annual rate, and a time period.

The basic formula

For one initial deposit with no later contributions:

A = P × (1 + r/n)^(n×t)

  • A is the ending amount.
  • P is the starting principal.
  • r is the nominal annual rate as a decimal.
  • n is the number of compounding periods per year.
  • t is the number of years.

If 1,000 earns a hypothetical 5% nominal annual rate compounded monthly for 10 years, the formula uses 0.05 ÷ 12 for the monthly rate and 120 monthly periods. The result is about 1,647 before taxes or fees.

At simple interest, interest is calculated only on the original principal. At compound interest, previously credited interest becomes part of the balance used in later periods.

Nominal rate, APY, and compounding frequency

A nominal annual rate does not by itself describe the exact one-year growth when compounding occurs more than once a year. The annual percentage yield, or APY, incorporates compounding frequency for a deposit product.

For example, 5% nominal interest compounded monthly produces an effective annual yield slightly above 5%. A calculator must therefore say whether its input is nominal or effective. The tool on this site treats the entered rate as a nominal annual rate divided by 12.

Comparing accounts by APY can be clearer when the institutions compound at different intervals. For loans, APR follows legal and product-specific rules and should not be treated as interchangeable with an investment-return assumption.

How monthly contributions change the calculation

With regular contributions, each deposit has a different amount of time to grow. A contribution made this month receives more compounding periods than one made near the end of the plan.

Our calculator assumes contributions occur at the end of each month. At a zero return, the result is simply:

starting balance + monthly contribution × number of months

With a nonzero constant monthly rate, the calculator adds the compounded starting balance to the future value of the monthly contribution series. If deposits are made at the beginning of each month instead, each has one additional period and the result is somewhat higher.

A worked contribution example

Suppose someone starts with 1,000 and contributes 250 at the end of each month for 20 years. The person contributes 61,000 in total: the 1,000 starting amount plus 60,000 in monthly deposits.

At a hypothetical constant 6% nominal annual rate compounded monthly, the calculator estimates a final value of roughly 118,800. Around 57,800 of that result is mathematical growth in the scenario, not money deposited.

Real investments do not deliver a smooth 6% every year. The example is useful for understanding the relationship between time, contributions, and rate—not for predicting what a particular investment will return.

Why time has a nonlinear effect

In early periods, the balance is smaller, so the absolute amount of growth looks modest. Later, the same percentage is applied to a larger base that includes prior gains and contributions. This is why doubling the time does more than simply double the growth in a constant-rate scenario.

The Rule of 72 is a rough mental estimate: divide 72 by an annual percentage rate to approximate the number of years required to double. At 6%, the estimate is 12 years. It is an approximation and becomes less accurate at very high or negative rates.

Fees compound too

An annual fee reduces the net return that remains invested. The cost is not only the fee charged this year; it also includes the growth that the removed money can no longer earn in later years.

For an investment scenario, compare a gross-return assumption with a lower net-return assumption after expected ongoing fees. The SEC's Investor.gov calculator includes fields for fees because even a difference that looks small each year can become substantial over a long period.

Inflation and purchasing power

A future balance is usually shown in nominal money. If prices rise, that money will buy less than the same amount buys today.

A rough real-return approximation is nominal return minus inflation, though the exact relationship is:

real return = (1 + nominal return) ÷ (1 + inflation) − 1

Taxes can reduce spendable results further and depend on account type, asset, transactions, holding period, and jurisdiction.

Debt uses the same mathematics—with extra details

Unpaid debt can also compound, but a simple investment formula may not reproduce a real credit agreement. Credit cards and loans can use daily periodic rates, minimum payments, fees, changing balances, promotional rates, and specific payment-allocation rules.

Do not model a debt decision using only an illustrative investment return. Use the lender's disclosures and an amortization or payoff calculator designed for that product.

How to use a compound-interest estimate responsibly

  1. Start with a conservative rate rather than the best historical period you can find.
  2. Compare several rates, including a low or negative scenario where appropriate.
  3. Include expected fees and consider taxes and inflation separately.
  4. Distinguish your contributions from estimated growth.
  5. Check whether the tool assumes deposits at the beginning or end of each period.
  6. Remember that a smooth rate hides volatility and the order in which returns occur.

A calculator is best used to explore relationships. It cannot determine an appropriate investment, risk level, or future market return.

Sources and further reading

To find recurring costs that could become monthly contributions, use the subscription cost calculator. For borrowing decisions, read How Credit Scores Work.