Compound Interest: Formula, Examples and Assumptions

Compound interest means interest is added to a balance and later periods can earn interest on that earlier interest. The same arithmetic can grow savings or increase some debts. It is a mathematical mechanism, not a promised investment outcome: returns can vary, losses are possible, and fees, tax, inflation, contributions and withdrawals affect real results.

Simple interest and compound interest

Comparing simple and compound interest isolates the mechanism. The gap can widen over longer periods, although the outcome still depends on the rate and the assumptions shown.

Simple interest is calculated solely on the original principal. For example, 10,000 currency units at a fixed 7% simple annual rate earns 700 each year. After 30 years, that is 21,000 of interest and a 31,000 balance, under the stated no-fee, no-tax assumptions.

Compound interest is calculated on the initial principal plus accumulated interest. If 10,000 currency units earn a fixed 7% compounded annually, year one interest is 700 and year two interest is 749 because the second calculation starts from 10,700. After 30 years the formula gives approximately 76,123 before fees, tax and inflation. This is a worked illustration, not an expected market return. Change the assumptions in the Investment Return Calculator.

The compound-interest formula

For a fixed nominal rate with no contributions or withdrawals, the formula is:

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

Where:

• A is the final amount of money accumulated after n years, including interest.
• P is the principal investment amount (the initial deposit).
• r is the annual interest rate (in decimal format, e.g., 0.07 for 7%).
• n is the number of times that interest is compounded per year (e.g., 12 for monthly, 1 for annually).
• t is the number of years the money is invested.

Holding the quoted nominal rate constant, more frequent compounding produces a slightly higher effective annual rate. But products may quote rates differently: compare an effective annual rate such as APY/AER where available, then check fees and access conditions. The US Securities and Exchange Commission's Investor.gov compound-interest calculator is a public-authority tool for testing principal, contribution, time and estimated-rate assumptions.

The Rule of 72 as a rough check

Dividing 72 by a fixed annual percentage gives a rough estimate of the years needed for a balance to double. At 8%, the shortcut gives 9 years; the exact annual-compounding result is about 9.01 years. The shortcut does not predict an investment return. Test the stated rate in the Investment Return Calculator.

• At a fixed 4%, the shortcut gives 18 years.
• At a fixed 6%, it gives 12 years.
• At a fixed 8%, it gives 9 years.

The shortcut is approximate and is most useful for moderate positive rates. It does not account for fees, changing returns, contributions, withdrawals, tax or inflation; use the full formula or a calculator for planning.

Worked example: time and rate assumptions

At a fixed 5% rate compounded annually, 5,000 currency units becomes 5,000 × (1.05)¹⁰ ≈ 8,144 after 10 years and 5,000 × (1.05)²⁰ ≈ 13,266 after 20 years. The extra decade adds more than the first because growth is then applied to a larger balance. At 3% for 20 years, the same principal would be about 9,031; at 7%, about 19,348. These scenarios isolate the formula and are not forecasts.

For regular contributions, timing matters too: a deposit made at the beginning of each period gets one more compounding period than a deposit made at the end. When comparing calculators, confirm contribution timing, compounding frequency, rate convention and rounding.

Assumptions to check before using a projection

A future-value estimate is only as useful as the inputs and product terms behind it:

1. Give suitable goals time: Earlier contributions have more potential compounding periods, but first consider essential cash needs, expensive debt, time horizon and risk capacity.
2. Understand reinvestment: Reinvesting distributions can support compounding, but it can also create tax records, alter concentration or conflict with income needs. Check local account and tax rules.
3. Compare costs: Ongoing fees reduce the balance available to compound. The Investor.gov guide to investment fees explains common fee categories; product availability and disclosures vary by country.
4. Check local tax treatment: Countries offer different savings or retirement accounts, eligibility rules, contribution limits and withdrawal restrictions. Use the relevant tax authority rather than assuming US account names apply.
5. Use sustainable automation: Automatic transfers can support consistency, but check the balance and pause or change them when cash needs, fees or circumstances change.

Compounding can also increase debt

Interest and fees can also increase borrowing costs, but credit agreements differ in whether and how interest compounds, how minimum payments are set, and when fees apply. Read the agreement and model its actual APR, payment and fee assumptions with the Debt Payoff Calculator. Do not infer a payoff period from APR alone.

Nominal growth is not real purchasing-power growth

If a balance grows by 5% while prices rise by 3%, purchasing power does not grow by a simple 2% exactly. The real rate is approximately (1.05 ÷ 1.03) − 1 = 1.94%, before tax and fees. Inflation varies by country and year; use an official national statistics agency for local data. This distinction matters when comparing a future currency amount with today's spending power.

Sources and review notes

Updated 4 August 2026. Formula examples were recalculated using the assumptions shown. Investor.gov, a US Securities and Exchange Commission resource, is cited for its calculator and fee education. Those sources explain concepts but do not make the examples suitable for every product or country. Verify product disclosures, tax rules and deposit or investor protections with local authorities.

Closing thoughts

Compounding explains how repeated percentage changes accumulate; it does not guarantee wealth or financial independence. Use explicit rate, timing, fee, tax and inflation assumptions, test more than one scenario, and separate guaranteed deposit terms from uncertain investment returns.