Compound Interest Calculator
Project how a principal sum grows under compounding, with optional recurring contributions, across any compounding frequency — and see exactly how much of the result is interest.
Compound Interest Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Results are a model, not a quotation — an institution's own figures govern.
- Every input is an assumption; change one and the answer changes with it.
- Rounding is applied only at the display layer, so totals may differ by a cent from a statement that rounds each line.
In short: Compound interest is calculated as A = P(1 + r/n)^(nt), where P is principal, r the annual rate, n the compounding periods per year and t the years. Unlike simple interest, each period's interest earns interest in subsequent periods, producing exponential rather than linear growth.
Formula
A = final amount · P = principal · r = annual rate (decimal) · n = compounds per year · t = years
Worked Example
- Convert the rate. 7% becomes 0.07 as a decimal.
- Find the periodic rate. 0.07 ÷ 12 = 0.00583333 per month.
- Count the periods. 12 × 10 = 120 monthly compounds.
- Apply the formula. A = 10,000 × (1.00583333)120 = $20,096.61.
- Isolate the interest. $20,096.61 − $10,000.00 = $10,096.61 earned.
Analyst's note. At 7% compounded monthly the sum slightly more than doubles in ten years. Simple interest on the same terms returns only $17,000.00 — the $3,096.61 difference is interest earning interest, and it widens dramatically with time.
Strengths & Limits Of This Model
Where this engine is strong
- Runs entirely in your browser — no figure you type is transmitted or stored.
- Shows the full working, so every number can be traced and challenged.
- Free, unmetered and free of affiliate incentives.
Where it stops
- Generalised assumptions cannot capture every individual circumstance.
- Jurisdiction-specific rules and mid-year changes may not be reflected.
- A model output is not a substitute for a professional review of your position.
Practical Use Cases
Retirement and long-horizon saving
Compounding rewards time far more than timing. Model contributions starting today against the same contributions starting in five years — the gap is usually larger than most savers expect. Pair this with the Retirement Calculator for a full drawdown picture.
Comparing account offers
Two accounts quoting the same nominal rate can pay materially different amounts if their compounding frequencies differ. Compare on effective annual rate, shown in the output cards, or use the APY Calculator directly.
Understanding debt working against you
The same mathematics governs credit card balances, only in reverse. Run your card balance at its purchase APR to see the true cost of carrying it, then plan repayment with the Credit Card Payoff Calculator.
Methodology & Editorial Standards
This engine applies the standard compound interest identity A = P(1 + r/n)^(nt), extended with the ordinary annuity future-value term when a recurring contribution is supplied. Contributions are treated as end-of-period (ordinary annuity) rather than beginning-of-period. The engine implements the standard published formula for this calculation. Inputs are validated for domain and sign before evaluation, and any undefined case returns an em-dash rather than a spurious value.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Compound Interest Calculator — 20 Expert FAQs
20 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is compound interest in simple terms?
Compound interest is interest that earns interest. In the first period you earn interest on your principal only. In the second, you earn it on the principal plus the interest already credited. Repeated over many periods this produces exponential rather than linear growth, which is why long horizons matter so much.
What is the compound interest formula?
A = P(1 + r/n)^(nt). A is the final amount, P the principal, r the annual rate as a decimal, n the number of compounding periods per year, and t the number of years. To isolate the interest alone, subtract P from A.
How does compounding frequency affect the result?
More frequent compounding produces a higher result, but with diminishing returns. On $10,000 at 7% for ten years, annual compounding yields $19,671.51, monthly yields $20,096.61, and daily yields $20,136.18. The step from annual to monthly matters far more than the step from monthly to daily.
What is the difference between APR and APY?
APR is the nominal annual rate before compounding is considered. APY is the effective annual rate after compounding. A 12% APR compounded monthly is a 12.6825% APY. Deposit products are best compared on APY.
What is the Rule of 72?
Divide 72 by the annual percentage rate to approximate the years required to double your money. At 7% that suggests roughly 10.3 years; the exact figure is 10.24 years. The rule is a fast mental check, not a substitute for the formula.
How much difference does starting early make?
Enormous. $10,000 compounding at 7% monthly becomes $20,096.61 after ten years, $40,387.39 after twenty, and $81,164.97 after thirty. The final decade contributes more growth than the first two combined, because compounding acts on a much larger base.
Should contributions be at the start or end of the period?
This engine treats contributions as end-of-period, the ordinary annuity convention used by most institutions. Beginning-of-period contributions (an annuity due) earn one extra period of interest and produce a slightly higher result.
Does this account for tax or inflation?
No. The output is a nominal, pre-tax figure. To express the result in today's purchasing power, run it through the Inflation Calculator; to model tax drag, reduce the rate input by your effective tax rate on investment income.
Can compound interest work against me?
Yes, and it is the primary reason revolving debt is so costly. Credit card balances compound at purchase APRs commonly above 20%, so an unpaid balance grows on exactly the same exponential curve that benefits a saver.
What is continuous compounding?
The theoretical limit as compounding frequency approaches infinity, given by A = Pe^(rt). At 7% over ten years on $10,000 it returns $20,137.53 — only marginally above daily compounding, which is why it is mostly of academic rather than practical interest.
Why is my bank's figure slightly different?
Institutions differ in day-count convention (360 versus 365 days), in whether they credit interest on the posting date or value date, and in rounding policy at each credit. These produce small divergences that compound modestly over long periods.
Is a higher rate or more frequent compounding better?
Rate almost always dominates. Moving from 7% to 8% annual compounding adds far more than moving from annual to daily compounding at 7%. Prioritise the rate, then treat frequency as a secondary consideration.
Is this compound interest calculator free to use?
Yes. It is free, requires no account, and has no usage limits. ApexConverter is funded by contextual advertising, never by selling user data.
Is my data sent to a server?
No. The engine runs as Vanilla JavaScript inside your browser under our Zero-Server Client-Side Execution model. Your figures are computed locally and are never transmitted, logged, or stored.
How accurate is this calculator?
It applies the standard closed-form formula in IEEE-754 double precision, rounding only at the display layer. The engine is reconciled against an independent reference implementation before release.
Does it work on mobile?
Yes. The interface is mobile-first with numeric keypad hints and is tested down to a 320-pixel viewport with no horizontal scrolling.
Can I use it offline?
Largely, yes. Because computation is client-side, the page continues to calculate without a network connection once it has loaded.
Which currency does it use?
Amounts display in US$ accounting format, but the underlying mathematics is currency-agnostic. The result is identical in any currency, so simply read the figures in your own.
Why does a result show an em-dash?
An em-dash indicates the calculation is not defined for the inputs given — typically a division by zero or a value outside the valid domain. We show a dash rather than a misleading number.
How do I report an error?
Email apexconverter.praxiscalc@gmail.com with the tool URL, your exact inputs, the output received and the output you expected. Verified mathematical errors are patched within 72 hours.