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See compound interest in action

This free compound interest calculator projects how an investment or savings balance grows over time, separating the money you put in from the interest it earns. Set a starting amount, add an optional regular contribution, choose your rate, term and compounding frequency, and the future value, total interest and effective annual yield update instantly — no submit button and no sign-up.

It goes beyond a basic future-value tool: model monthly or annual contributions, an annual contribution increase, regular withdrawals, and an inflation adjustment, then read the result as a growth chart and a year-by-year breakdown you can export as CSV.

The compound interest formula

Compound growth follows A = P(1 + r/n)^(nt), where P is your principal, r is the annual rate as a decimal, n is how many times interest compounds each year, and t is the number of years. The core mechanic: interest is added back into the balance, so future interest earns on a bigger sum — interest on interest.

For continuous compounding, the formula becomes A = Pe^(rt). This calculator runs both, and when you add regular deposits it simulates the balance period by period so contributions, step-ups and withdrawals are all accounted for accurately.

Daily, monthly, quarterly and continuous compounding

How often interest compounds changes the outcome. A daily compound interest calculator result will be a touch higher than monthly, which beats quarterly and annual, because interest starts earning sooner. The built-in frequency comparison shows the same inputs side by side across daily, monthly, quarterly, annual and continuous compounding, so you can see exactly how much the frequency is worth.

In practice the rate and the length of time dominate. Doubling your time horizon or adding a percentage point of return moves the needle far more than switching from annual to daily compounding — but every bit helps, which is why the comparison is built in.

Contributions, withdrawals and real-world plans

Most goals involve adding money over time, so this works as a compound interest calculator with monthly contributions, a CD or savings calculator, and a 401(k) or retirement projection. Turn on the annual contribution increase to mirror pay rises, or add a regular withdrawal to model a pension drawdown — making it a genuine compound interest calculator with withdrawals.

Every scenario produces a year-by-year breakdown showing each year's opening balance, contributions, interest and closing balance, which you can download as CSV, plus a stacked growth chart you can save as a PNG or share by link.

Adjust for inflation

A balance decades from now won't have today's buying power. Switch on the inflation adjustment and the headline figure and chart can be shown in today's money, so a projected $1 million reads as what it would actually be worth in real terms. This is the difference between nominal returns and the real return that matters for planning. At a 3% annual inflation rate, $1 million in 30 years has the purchasing power of about $412,000 today.

How this compares to calculator.net, Investor.gov, and Bankrate

Calculator.net and Investor.gov (the US Securities and Exchange Commission's calculator) are accurate but limited: neither supports simultaneous contributions and withdrawals, neither produces an exportable CSV, and neither shows a visual growth chart. Calculator.net serves ads around the results page that can include financial product promotions.

Bankrate's compound interest calculator has a chart but lacks the annual contribution step-up and doesn't support withdrawals — so you can't model a retirement drawdown. NerdWallet's version runs server-side, which means your financial inputs are sent to their servers and may be used to serve targeted financial product ads.

This calculator runs entirely in your browser. No financial figure you enter is ever transmitted anywhere. There are no ads, no login required, and no feature locked behind a paywall. The shareable link stores your inputs in the URL so you can bookmark and revisit any scenario.

The compound interest formula, fully worked

The standard formula is A = P(1 + r/n)^(nt), where P is the principal (your starting amount), r is the annual interest rate expressed as a decimal (5% becomes 0.05), n is the number of compounding periods per year, and t is the time in years. The exponent (nt) is simply the total number of times interest gets added across the whole term. As n grows larger, each individual interest payment shrinks but accumulates more often, and the net result is a slightly higher final balance.

A worked example shows why compounding frequency matters. Take £10,000 at 5% for 10 years. Compounded annually (n = 1): A = 10,000 × (1.05)^10 = £16,288.95. Compounded monthly (n = 12): A = 10,000 × (1 + 0.05/12)^120 = £16,470.09. Compounded daily (n = 365): A = 10,000 × (1 + 0.05/365)^3650 = £16,486.65. Moving from annual to daily adds roughly £198 — real money, but far less impactful than an extra year of growth or a higher rate.

At the theoretical extreme, as n approaches infinity, the formula converges to A = Pe^(rt) — continuous compounding. Here e ≈ 2.71828 is the mathematical constant that Jacob Bernoulli discovered in 1683 while studying this exact limit. For the same £10,000 at 5% for 10 years, continuous compounding yields £16,487.21, only 56 pence above daily compounding. The gap between daily and continuous is essentially negligible in practice, which is why continuous compounding is mainly a tool for financial mathematics and bond pricing rather than consumer products.

APR vs APY — the number that actually matters

Banks and lenders quote two fundamentally different rates. APR (Annual Percentage Rate) is the nominal, stated rate before compounding is applied — it is what a lender advertises. APY (Annual Percentage Yield), called AER (Annual Equivalent Rate) in the UK, is the effective rate once compounding is factored in, and it is what you actually earn or pay over a year. The conversion is: APY = (1 + APR/n)^n − 1. A savings account paying 6% APR compounded monthly has an APY of (1 + 0.06/12)^12 − 1 = 6.168%. The US Truth in Savings Act and UK FCA rules both require institutions to disclose the effective rate so consumers can compare like for like.

In practice, most US high-yield savings accounts and money market accounts compound daily using a 360-day year convention, then credit interest monthly. This means the quoted APY is calculated on 360 days even though a calendar year has 365, producing a marginally lower effective yield than the headline suggests — a detail worth knowing when comparing very high-rate accounts. UK Cash ISAs typically compound annually, so the AER and the gross rate are the same figure. US Certificates of Deposit (CDs) compound daily or monthly depending on the issuer, while US Series I bonds compound semi-annually — their composite rate is reset every six months based on CPI, so the compounding and rate interact differently from a fixed-rate product. For any product, always compare on APY/AER, never on the nominal APR.

Credit card APR is quoted as a yearly rate but applied daily (daily periodic rate = APR ÷ 365). If you carry a balance, the effective annual cost on a 20% APR card is (1 + 0.20/365)^365 − 1 ≈ 22.13% — more than two percentage points above the advertised figure. This compounding on debt is why a £3,000 credit card balance paid down only at minimum payment levels (typically 1–2% of balance per month) can balloon to over £6,000 in five years on a 22% APR card, even without any new spending.

The Rule of 72 — and when to use Rule of 114 instead

The Rule of 72 is the fastest mental shortcut in personal finance: divide 72 by the annual interest rate (as a percentage) and you get the approximate number of years for a balance to double. At 6%, money doubles in roughly 72 ÷ 6 = 12 years. At 9%, about 8 years. The rule works because the exact doubling time is ln(2) / ln(1 + r) ≈ 0.693 / r, and 72 is close enough to 69.3 while being divisible by more of the common rates (2, 3, 4, 6, 8, 9, 12). The related Rule of 70 is preferred by economists when modelling GDP doubling time, since 70 divides neatly by 2, 5, 7, and 10 — the rates that appear most often in macroeconomic projections.

For tripling rather than doubling, use the Rule of 114: years to triple = 114 ÷ rate %. This follows the same logic — ln(3) ≈ 1.099, and 114 ÷ 100 ≈ 1.099/r when r is expressed as a fraction. So at 6%, money triples in about 114 ÷ 6 = 19 years. The exact answer is ln(3) / ln(1.06) ≈ 18.85 years, so the approximation is accurate to within a few weeks. For quadrupling, simply apply the Rule of 72 twice — two doubling periods.

Both rules are accurate between roughly 2% and 20% and become less reliable at the extremes. At 1% the Rule of 72 suggests 72 years to double, but the true figure is about 69.7 years — an error of 3.3 years. At 30% the rule predicts 2.4 years but the real answer is closer to 2.64 years. For practical financial planning in the 4–10% range that covers most savings rates and long-run equity returns, the rules are precise enough to use without a calculator, making them invaluable for back-of-the-envelope checks on projections.

Inflation-adjusted returns: real growth vs nominal growth

A compound interest projection in nominal terms can be misleading if inflation erodes purchasing power over the same period. The Fisher equation gives the relationship: (1 + real rate) = (1 + nominal rate) / (1 + inflation rate), which simplifies to the approximation real rate ≈ nominal rate − inflation rate. At 5% nominal growth and 3% annual inflation, the real rate of return is roughly 1.94% — not the 2% the approximation suggests, but close enough for planning. That distinction matters: compound growth at 1.94% over 10 years is meaningfully different from 5%.

A concrete example: £10,000 invested at 5% nominal for 10 years grows to £16,289 in nominal terms. Apply 3% annual inflation and the real value of that £16,289 in today's money is 16,289 / (1.03)^10 = £12,114. The investment still beats inflation — you gain about £2,114 of real purchasing power — but the nominal headline of £6,289 of growth overstates the benefit by roughly 3× in real terms. This is why this calculator's inflation adjustment converts the result into today's money, so projections reflect genuine wealth creation rather than the illusion of nominal growth.

The practical implication is that nominal returns below the inflation rate represent a real loss, even when the balance grows. A savings account paying 2% during a period of 4% inflation leaves you with more pounds but fewer things you can buy with them. Targeting a real return — after inflation, and ideally after tax too — is the correct frame for long-term savings and retirement planning. The UK's CPIH measure (Consumer Prices Index including housing costs) averaged 2.5–3% over the decade to 2024, so a 5% gross return translates to roughly 1.5–2.5% real, not 5%, before tax is even considered.