Compound Interest Calculator: How the Formula Works and How to Use It
Standard compound-interest math (lump sum, contributions, APY, inflation-adjusted real wealth), plus optional modeling: contribution vs. compounding frequency, raises on savings, employer match, milestones, year-by-year export, delay comparison, and shareable links. Free; all calculations run in your browser.
How compound interest is calculated
The standard formula
- A (Future value):The balance at the end of the period—the "Nominal" result before inflation adjustment.
- P (Principal):Your initial deposit or investment. The starting amount that earns interest over time.
- r (Annual interest rate):The stated annual rate as a decimal (e.g. 7% → r = 0.07). Enter the percentage; we convert it.
- n (Compounding frequency):How many times per year interest is applied. Annual = 1, monthly = 12, daily = 365. We also support biweekly (26), semimonthly (24), weekly (52), and continuous.
- t (Time in years):The length of the investment. The formula compounds over n×t total periods (e.g. 30 years × 12 months = 360 for monthly).
- Scope & limits:Inflation uses the rate you enter for real (purchasing-power) figures. Tax treatment is not modeled. All math runs in your browser; no data is sent to servers. Results are estimates—for major decisions, consult a qualified professional.
For a single lump sum we use:
where:
For continuous compounding we use
(e ≈ 2.718). With flat monthly contributions, no annual contribution increase, and no employer match, lump-sum growth plus contributions follows the same discrete-compounding logic summarized above. If you turn on annual contribution increases, employer match, or a non-monthly contribution schedule, the tool uses a month-based simulation so deposit timing and caps stay consistent with your inputs.
Compounding frequency and APY
How frequency affects returns
- Annual (n=1):Interest applied once per year. Lowest effective yield but simplest to reason about.
- Monthly (n=12):Common for savings and many investments. Interest applied 12 times per year.
- Daily (n=365):Typical for high-yield savings. Slightly higher effective yield than monthly.
- Continuous:Theoretical maximum (infinite periods per year). Shown as an upper bound; real accounts use discrete compounding.
Compounding frequency is how often interest is added to your balance. More frequent compounding means interest earns interest sooner, so effective yield rises slightly.
APY vs. stated rate
- Stated rate:The advertised rate (e.g. 7% per year).
- APY:Effective annual yield. For example, 7% compounded monthly gives APY ≈ 7.23%; compounded daily, ≈ 7.25%.
- Why it matters:When comparing savings or investment options, always compare APYs—they reflect what you actually earn.
APY (Annual Percentage Yield) is your true annual return after compounding. We show APY so you can compare different accounts and frequencies fairly.
Real value and inflation
Nominal vs. real future value
- Nominal value:The actual balance at the end of the period (e.g. $1,000,000 in 30 years).
- Real value:Purchasing power in today’s dollars. At 3% inflation, $1M in 30 years ≈ $411K in today’s dollars.
- Inflation gap (in the breakdown):Nominal minus real at the horizon—a single number for how much of the headline balance is “paper” vs. today’s purchasing power.
- Formula:where i is the annual inflation rate and t is time in years.
Nominal value is the dollar amount you’ll have. Inflation reduces purchasing power, so we also show real value (in today’s dollars): nominal ÷ (1 + inflation rate)^t.
To build real wealth, your return should meaningfully exceed expected inflation. A 7% return with 3% inflation implies about 4% real growth.
Optional features in this tool
What you can turn on
- Contribution frequency:Independent from compound frequency—e.g. biweekly deposits into a monthly-compounding account.
- Annual contribution increase:Grows the per-period contribution each year (e.g. to mimic raises).
- Ages / horizon:Optional current and target age can set years until a goal and feed milestone timing in the analysis section.
- Employer match:Match rate, cap as % of salary, and salary—employer dollars are tracked separately in the breakdown.
- Analysis & detail:Milestone strip, collapsible year-by-year table with CSV export, and a light-themed frequency comparison table (same growth/match assumptions as the main result).
- Delayed start comparison:See wealth lost if investing starts later with a shorter horizon, plus chart overlay when enabled.
- Share:Copy link encodes inputs in the URL via replaceState.
Everything below is optional; leaving defaults gives a straightforward lump-sum plus contribution projection.
Who it’s for
Savers and investors
Project growth on savings-style assumptions, compare stated rates and compounding frequencies, and see nominal vs. real outcomes on one screen.
People modeling paychecks and plans
Align deposit frequency with how you actually save; add optional match and raises when you want retirement-style realism without leaving this page.
Related tools
Inflation and purchasing power
To explore inflation in more detail, use our Inflation Calculator to see how purchasing power changes over time for a given amount.
Retirement and tax-advantaged growth
For employer-matched retirement savings and tax-advantaged growth, use our 401(k) Calculator to model contributions, match, and long-term balance.
Simple interest comparison
For loans or accounts that use simple interest (interest only on principal, no compounding), use our Simple Interest Calculator to compare the difference—compound interest grows faster over long horizons.
Compound Interest Calculator FAQ
What is compound interest and how does it work?
Compound interest is interest calculated on both your initial principal and the interest already earned. Unlike simple interest, which only grows your original deposit, compound interest causes your balance to accelerate over time — the longer you leave money invested, the faster it grows. This "interest on interest" effect is why starting early matters so much.
What is the compound interest formula?
The standard formula is A = P(1 + r/n)^(nt), where A is the final balance, P is the principal, r is the annual rate (as a decimal), n is compounding periods per year, and t is time in years. Enter your values above to see the result.
How much will $10,000 grow with compound interest?
At 7% compounded monthly, $10,000 grows to approximately $20,097 in 10 years, $40,388 in 20 years, and $81,165 in 30 years — without adding a single extra dollar. This illustrates why time in the market is the most powerful variable in the formula.
What is the difference between compound interest and simple interest?
Simple interest is calculated only on your original principal — $10,000 at 7% for 30 years yields $21,000 in interest. Compound interest on the same deposit yields over $71,000. The gap widens dramatically with time, which is why compound interest is the foundation of long-term wealth building.
How does compounding frequency affect my balance?
More frequent compounding means slightly higher returns. On $100,000 at 7% over 30 years, daily compounding yields about $4,200 more than annual. The difference between monthly and daily is minimal — roughly $200 over 30 years. Rate matters far more than frequency: a 1% rate increase outweighs any compounding frequency upgrade.
What is APY and how is it different from APR?
APR (Annual Percentage Rate) is the stated rate before compounding. APY (Annual Percentage Yield) reflects the actual return after compounding is applied. A 7% APR compounded monthly has an APY of 7.23%; compounded daily, 7.25%. When comparing savings accounts or investments, always compare APYs — they reflect what you actually earn.
What is the Rule of 72?
The Rule of 72 is a quick mental math shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 7%, your money doubles in roughly 10.3 years. At 6%, about 12 years. At 10%, about 7.2 years. It assumes compound interest and works best for rates between 5–15%.
How do regular contributions affect compound growth?
Adding regular contributions dramatically accelerates growth. $10,000 invested once at 7% for 30 years grows to ~$81,000. Add $200/month and the balance reaches over $285,000. You can model both lump sum and recurring contributions above to see the difference for your own numbers.
How does inflation affect my compound interest returns?
Inflation erodes purchasing power over time. If your investment grows at 7% but inflation averages 3%, your real return is approximately 4%. At 3% inflation, $1 million in 30 years has the purchasing power of roughly $411,000 today. This is why long-term financial planning focuses on real returns — your nominal growth needs to meaningfully outpace inflation to build actual wealth.
What is the difference between contribution frequency and compound frequency?
They are independent. Contribution frequency is how often you deposit (weekly, biweekly, monthly, etc.)—aligned with paychecks. Compound frequency is how often interest is credited to the account (daily, monthly, annual, etc.). The calculator models both separately so you are not forced to assume deposits match the account’s compounding schedule.
What does annual contribution increase (%) do?
It optionally grows your per-period contribution each calendar year—useful when you expect raises and want to save more over time. At 0%, behavior matches a flat contribution schedule. When this is greater than zero (or when employer match or non-monthly contributions are set), the tool uses a detailed time-stepped simulation so totals stay consistent with the schedule you enter.
How does employer match work in this calculator?
Optional fields: match percentage (e.g. 100% dollar-for-dollar), match up to a percent of salary (the cap), and annual salary. Employer dollars are applied each month based on your employee deposits that month, capped by the monthly dollar limit implied by your salary and cap percentage, then multiplied by the match rate. Employer totals appear separately in the breakdown; turn match fields off to match a no-match scenario.
Can I save or share my scenario?
Yes. Use Copy link next to the short explanation at the top of the calculator. It copies a full URL whose query string encodes every input that affects the math (principal, contribution amount, contribution and compound frequencies, years, optional ages, expected return, inflation, annual contribution increase, employer match fields, delay years, and whether delay comparison is on). The address bar stays in sync as you change fields (replaceState, so back/forward is not flooded). Opening the copied link restores the same scenario.
What does “Compare: what if I started later?” mean?
It runs a second scenario with the same total time horizon and the same return, inflation, and contribution settings—but periodic contributions and employer match only begin after the delay. Your initial principal still compounds during the wait; you are not contributing yet. Annual contribution increases count from the first year you actually contribute. You see cost of waiting, optional side-by-side numbers, and a delayed line on the chart when enabled.