Compound Interest Calculator: Formula and Growth Examples

By Max Fonji

Last reviewed: September 27, 2026

A compound interest calculator estimates how a balance could change when earnings stay in the account and begin earning additional returns. Enter a starting amount, a rate, and a time period. If the calculator supports contributions, you can also include money added along the way.

The result answers a conditional question: What would happen if these assumptions held? It does not tell you what an investment will actually earn.

For example, $10,000 growing at a constant 8% a year for 30 years would become approximately $100,626.57, with no additional deposits, taxes, fees, or withdrawals. Change the rate or the timeline, and the outcome changes.

This guide explains the formulas, shows checked examples, and helps you avoid common input mistakes. Explore our financial calculators

Key takeaways

• Compound interest means earning interest on both your original deposit and accumulated interest.
• A calculator’s rate definition matters. A nominal annual interest rate and an annual percentage yield (APY) are different inputs.
• Contribution timing changes the answer. Deposits at the beginning of a month have more time to grow than deposits at the end.
• More frequent compounding improves the result when the same positive nominal annual rate is held constant. It does not automatically make one account better than another.
• Investment projections are scenarios. Returns, fees, taxes, inflation, and withdrawals can change actual results.

How to use a compound interest calculator

Start with the amount you have now and a contribution you can realistically maintain. Then enter the time horizon and the rate assumption.

The SEC’s Investor.gov compound interest calculator provides fields for an initial investment, monthly contributions, years, an estimated annual rate, a rate variance range, and compounding frequency. [1]

Before comparing results from two tools, check that they use the same inputs and conventions.

For the monthly-contribution examples below, the model uses a nominal annual rate divided by 12, monthly compounding, and deposits at the end of each month. Rates remain constant. Taxes, fees, inflation, and withdrawals are excluded unless stated otherwise.

What is compound interest?

Compound interest is interest calculated on a balance that includes previously earned interest.

Suppose you deposit $1,000 at a fixed 5% rate, compounded annually:

• After year one, the balance is $1,050.
• In year two, 5% applies to $1,050, producing $52.50 of interest.
• The balance after year two is $1,102.50.

The second year’s interest is larger because the first year’s interest stayed in the account.

With simple interest on the original $1,000 at the same annual rate, interest would be $50 each year. After two years, the balance would be $1,100.

For another worked comparison, see compound interest versus simple interest.

The compound interest formula

For a starting balance with no additional contributions:

A = P × (1 + r/n)^(n × t)

For 8%, enter 0.08 in the formula. For monthly compounding, n = 12; for annual compounding, n = 1.

Example: $10,000 at 8% for 30 years

Assume annual compounding and no additional deposits:

A = $10,000 × (1.08)^30 = $100,626.57

The ending balance consists of:

• Original principal: $10,000.00
• Modeled growth: $90,626.57

For comparison, simple interest on the original principal would produce:

$10,000 + ($10,000 × 0.08 × 30) = $34,000

The compound-interest balance is $66,626.57 higher under these assumptions. The assumed 8% rate is an illustration, not a forecast or an available account offer.

Adding monthly contributions

When equal deposits are added at the end of each month, the future-value formula is:

FV = P × (1 + i)^N + C × [((1 + i)^N − 1) / i]

Where:

• P is the initial balance.
• C is the monthly contribution.
• i is the monthly rate.
• N is the number of months.

For a nominal annual rate compounded monthly, i = r/12. For a timeline measured in years, N = 12 × years.

At a zero interest rate, use the simpler formula FV = P + C × N. This avoids dividing by zero.

Example: $10,000 plus $500 a month

Assume a 7% nominal annual rate, monthly compounding, and $500 deposited at the end of every month for 30 years.

The projection uses 360 monthly periods and a monthly rate of 0.07/12. Intermediate calculations retain full precision; displayed amounts are rounded to cents.

How the balance develops

The same assumptions produce these milestones:

These are smooth mathematical projections. An investment account can rise or fall between deposits and may finish below the amounts shown.

Why deposit timing matters

If each $500 contribution is made at the beginning of the month instead, the ending balance becomes $694,708.72 under the same assumptions.

The contribution portion of the formula receives one extra month of growth. The original $10,000 still grows for the same 30 years.

When a calculator disagrees with another calculator, check the deposit timing before assuming either result is wrong.

APY versus nominal interest rate

APY already reflects compounding. The CFPB’s Regulation DD appendix explains how annual percentage yield incorporates the interest rate and compounding frequency. [2]

A nominal annual rate is the rate used before applying compounding within the year. For a constant nominal rate r compounded n times yearly:

APY = (1 + r/n)^n − 1

For a balance earning a constant 5% APY for one year, $1,000 becomes $1,050, assuming no deposits, withdrawals, or fees. Do not divide 5% APY by 12 and compound it again as though it were a nominal rate.

To model equal monthly periods from APY:

Monthly effective rate = (1 + APY)^(1/12) − 1

For 5% APY, that is approximately 0.407412% per month. Actual bank calculations may use daily balances and calendar-day conventions.

Read more about the distinctions in APY versus APR. APR for borrowing can involve additional conventions; it should not automatically be treated as a deposit yield.

Does daily compounding make a big difference?

The effect depends on the amount, rate, and timeline. Compare frequencies while keeping the same nominal rate and cash flows.

For $5,000 at a fixed 5% nominal annual rate over 10 years, with no additional deposits:

Daily compounding adds approximately $98.85 compared with annual compounding. That is about 3.14% more interest, calculated as the additional interest divided by the annual-compounding interest. It is not a 3.14-percentage-point increase in the annual rate.

This comparison holds the nominal rate constant. It does not show that a daily-compounding account beats another account with a higher APY. Compare yield, fees, balance requirements, withdrawal access, and how long the quoted terms apply. [2]

Test more than one rate

A single rate can hide how sensitive the outcome is to your assumptions.

For $10,000 initially and $500 deposited monthly over 30 years:

All rows use monthly compounding and end-of-month deposits. These are sensitivity examples, not expected returns for a particular portfolio. They are not a complete range of possible outcomes: losses are possible, and 0% is not a guaranteed minimum.

If the goal only works at the highest assumption, examine the contribution amount, timeline, and goal size rather than simply assuming a higher return. Use a budgeting and saving plan to assess what you can contribute consistently.

Starting earlier: a consistent comparison

An earlier start gives each contribution more time to grow, but the result also depends on the rate, deposit timing, and amounts.

Consider a 40-year illustration with a constant 8% annual rate and annual compounding:

• Saver A contributes $5,000 at the end of each of years 1–10, then adds nothing for years 11–40.
• Saver B contributes $5,000 at the end of each of years 11–40.

Both savers use the same end-of-year deposit convention. Saver A’s earlier deposits finish ahead in this example. That does not mean starting earlier always beats contributing more; different rates, amounts, and timelines can change the comparison.

What a compound growth projection leaves out

Market fluctuations

Stocks and funds do not generally pay a fixed compound interest rate. Their total returns can include price changes and distributions. A constant-rate model is a simplified way to explore reinvested growth, not a description of how markets move.

For example, a 20% gain followed by a 20% loss turns $100 into $96. The arithmetic average of those returns is 0%, but the investor has lost money. Timing can matter even more when deposits or withdrawals occur between returns.

Investor.gov explains that investments carry different risks, including potential loss and inflation risk. [3] For the basics, see our beginner investing guide.

Inflation

A future dollar amount does not have the same purchasing power as the same number of dollars today.

To express a future balance in today’s dollars using an assumed constant inflation rate:

Present purchasing power = Future balance / (1 + inflation rate)^years

For effective annual growth and inflation rates, the exact real return is:

Real return = (1 + growth rate) / (1 + inflation rate) − 1

For 7% effective annual growth and 3% inflation, the real return is approximately 3.88%. Subtracting the two rates gives a rough approximation of 4%.

Fees and taxes

Fees reduce the money available to grow. Check whether a return assumption is before or after investment expenses so you do not count the same fee twice. Investor.gov describes both ongoing fees and transaction costs. [4]

Taxes depend on the account, income type, transactions, and applicable rules. Do not subtract your marginal tax rate directly from an assumed investment return or treat all investment growth as taxed annually. A basic calculator that excludes taxes is showing a before-tax illustration.

Changes in contributions or rates

Income interruptions, withdrawals, variable savings rates, and changing contributions can alter the result. A fixed-input projection assumes those changes do not happen. Revisit the inputs when your circumstances change.

Common calculator mistakes

1. Entering APY into a nominal-rate field. Confirm how the tool interprets the rate.
2. Mixing monthly and annual deposits. Use matching periods and timing conventions.
3. Rounding too early. Keep precision inside the calculation and round displayed results.
4. Treating all growth as interest. For investments, “modeled growth” or “investment return” may be more accurate.
5. Choosing an account by compounding frequency alone. Compare the actual yield and account terms.
6. Using a savings-growth tool to estimate credit-card payoff. Debt calculations need payment amounts, timing, fees, and the lender’s interest rules. Use a dedicated debt payoff calculator.

Frequently asked questions

How much could $10,000 grow in 30 years?

At a constant 8% rate compounded annually, with no added deposits, it would grow to approximately $100,626.57 before taxes and fees. This is a hypothetical calculation, not a promised investment result.

How much could $500 a month grow in 30 years?

With a $10,000 starting balance, a 7% nominal annual rate compounded monthly, and end-of-month deposits, the result is approximately $691,150.47. Of that amount, $190,000 is contributed money. A different starting balance or rate convention changes the answer.

Why do compound interest calculators give different answers?

They may interpret annual rates differently, use different deposit timing, compound at different intervals, or round intermediate values. Compare the assumptions as well as the numbers entered.

Can I lose money even if a calculator shows growth?

Yes. A hypothetical investment growth calculation does not eliminate market risk. A positive rate entered into a calculator produces a positive-growth scenario; it does not establish how likely that scenario is.

Does this calculation include inflation, taxes, or fees?

The example tables in this guide exclude them. The inflation section shows how to adjust purchasing power separately. For any interactive tool, check its stated assumptions before interpreting its result.

Turn the result into a useful plan

Use the calculation to identify what your goal requires: a starting balance, affordable contributions, a timeline, and a set of assumptions you understand.

Compare several scenarios. Separate contributed money from modeled growth. Revisit the plan when rates, costs, income, or the goal changes.

Compounding can help retained earnings grow, but financial outcomes also depend on resources, risk, costs, and circumstances. Understanding the calculation gives you a clearer way to evaluate those trade-offs.

Calculation methodology and review

The worked examples were recalculated for this revision. Monthly-contribution examples use FV = P(1+i)^N + C[((1+i)^N−1)/i], with i = nominal annual rate/12 and deposits at month end. The zero-rate case uses P + CN. Beginning-of-month deposits multiply only the contribution term by (1+i).

The frequency comparison has no contributions and assumes 365 daily periods per year. The two-saver comparison uses end-of-year deposits for both savers. Calculations retain precision until the final displayed result is rounded to cents. All example rates are hypothetical and constant.

September 27, 2026 revision: Corrected numerical examples, clarified rate and deposit-timing conventions, replaced unsupported claims, and updated source links. This review applies to the article’s text and examples; an interactive calculator has its own implementation and should state its assumptions.

Sources

1. U.S. Securities and Exchange Commission, Investor.gov. Compound Interest Calculator.
2. Consumer Financial Protection Bureau. Appendix A to Regulation DD: Annual Percentage Yield Calculation.
3. U.S. Securities and Exchange Commission, Investor.gov. What Is Risk?.
4. U.S. Securities and Exchange Commission, Investor.gov. Understanding Fees.

Sources accessed September 27, 2026. Numerical tables are calculations for this article using the stated assumptions, not forecasts supplied by these organizations.

About the author

Max Fonji is the founder and writer behind The Rich Guy Math, a personal-finance education website focused on explaining money concepts through clear language, calculations, and practical examples. Learn more about Max and the site’s editorial policy.

Educational disclaimer

This article provides general financial education, not personalized investment, tax, or legal advice. Projections depend on assumptions and do not guarantee future results. Investments can lose value. See our full disclaimer.