Compound Interest Calculator
See how your money grows with compound interest. Add regular contributions and watch the power of compounding over time. All calculations happen locally — nothing leaves your browser.
What is compound interest? Compound interest is interest calculated on the original principal plus every unit of interest already credited, so each period earns on a larger balance than the one before. The standard formula is A = P(1 + r/n)nt, where n is the number of compounding periods per year. At 7% compounded monthly, $10,000 grows to about $20,097 in ten years without a single extra deposit.
How to Use the Compound Interest Calculator
- Enter your starting principal — The balance you already hold. Leave it at zero if you are starting from nothing and want to see what deposits alone build.
- Set the annual interest rate — Enter the nominal annual rate your account or fund quotes, not the effective yield — the calculator derives the effective yield from the compounding frequency you pick next.
- Choose how long the money stays invested — Time is the variable with the most leverage, because growth is exponential in t. Try 10, 20 and 30 years on the same rate to see how unevenly the extra decades pay.
- Pick a compounding frequency — Daily, monthly, quarterly or annually. Savings accounts and most bonds compound monthly or quarterly; index funds have no formal compounding step, so annual is the honest choice when modelling them.
- Add a recurring deposit if you make one — The dashed green line on the chart tracks money you put in, and the blue line tracks total value. The vertical gap between them is interest earned.
- Read the chart and copy the summary — Use Copy Summary to paste the inputs and results into a note or spreadsheet. The page URL also updates with your figures, so a bookmark reopens the same scenario.
How Compound Interest Is Calculated
Simple interest pays only on the sum you originally deposited: $10,000 at 7% pays $700 every year, forever. Compound interest pays on the whole balance, including interest already credited, so the second year earns on $10,700 rather than $10,000. Repeat that for long enough and the interest-on-interest term overtakes the original deposit entirely. The closed-form expression is:
A = P(1 + r/n)ntA is the ending balance, P the principal, r the nominal annual rate expressed as a decimal, n the number of compounding periods in a year and t the number of years. Working the default case: P is 10,000, r is 0.07, n is 12 and t is 10, so the periodic rate is 0.07/12 and it is applied 120 times. The result is roughly $20,097 — the balance has doubled, and $10,097 of that never came from you.
Compounding frequency matters less than most people expect
Moving from annual to daily compounding on the same 7% rate adds about $465 over ten years on a $10,000 balance. Moving from monthly to daily adds about $39 — roughly four dollars a year. The reason is that each increase in n shrinks the periodic rate by exactly the same factor it increases the number of periods, so the gains taper off quickly and converge on a ceiling. That ceiling is continuous compounding, A = Pert, which on these inputs gives $20,138: only a dollar more than daily.
| Compounding | Periods per year (n) | $10,000 after 10 years at 7% | Effective annual yield |
|---|---|---|---|
| Annually | 1 | $19,672 | 7.000% |
| Quarterly | 4 | $20,016 | 7.186% |
| Monthly | 12 | $20,097 | 7.229% |
| Daily | 365 | $20,136 | 7.250% |
Principal only, no additional deposits. Continuous compounding, the theoretical limit, yields 7.251%.
Nominal rate, APR and APY
The rate a provider advertises and the rate you actually earn are different numbers whenever n is greater than one. The effective annual yield — APY on a US deposit account, AER in the UK — folds the compounding schedule into a single figure you can compare across products:
APY = (1 + r/n)n − 1A nominal 7% compounded monthly is an APY of 7.229%. A rival account advertising 7.15% compounded annually is genuinely worse, even though the headline looks better. Always compare APY with APY. On the borrowing side the same arithmetic runs against you: an APR quoted monthly understates what a revolving balance actually costs over a year, which is why a credit card at 22% APR behaves closer to 24.4% if you never clear the balance.
The Rule of 72
To estimate a doubling time without a calculator, divide 72 by the percentage rate. At 7% that predicts 10.3 years; the exact answer, ln(2) divided by ln(1.07), is 10.24 years. The approximation is closest between about 6% and 10% and drifts at the extremes, but it is accurate enough to sanity-check any projection in your head. Run it backwards for inflation too: at 3% inflation, prices double in roughly 24 years, which is why the same balance buys visibly less by the end of a long projection.
What This Projection Leaves Out
The formula assumes one fixed rate applied evenly, and real money rarely behaves that way. Four gaps are worth holding in mind before you treat a number here as a plan.
Volatility. A fund averaging 7% does not deliver 7% each year; it delivers a scatter of gains and losses whose compounded result is lower than the arithmetic mean of those years. That is a mathematical property of compounding, not bad luck. Tax. Interest in a taxable account is usually taxed as it accrues, which lowers the rate that actually compounds. Tax-sheltered accounts are the main reason the untaxed version of this formula is worth aiming for. Inflation. The output is in nominal money. To see purchasing power, subtract your inflation expectation from the rate before you enter it, or run the result through the Inflation Calculator. Fees. An annual charge is subtracted from the rate, so a 0.75% fund fee turns a 7% return into 6.25% and costs far more over thirty years than the percentage suggests.
These results are informational and educational, not investment advice, and no rate you enter is a prediction. Speak to a licensed financial adviser before making decisions about savings, debt or investments.
Frequently Asked Questions
Simple interest is charged only on the original principal, so it grows in a straight line. Compound interest is charged on the principal plus all interest already added, so it grows exponentially. On $10,000 at 7% for 10 years, simple interest pays $7,000; monthly compounding pays about $10,097. The gap widens with every additional year.
More often is better, but by less than most people assume. On $10,000 at 7% over 10 years, annual compounding gives about $19,672 and daily gives about $20,136 — a difference of roughly $465 across a decade. Monthly to daily is worth about $39. Choose the frequency your account actually uses and put your attention on the rate and the time horizon instead.
For a diversified stock portfolio held for decades, 7% is a common planning assumption: broad US equity indices have averaged roughly 10% a year in nominal terms over very long periods, which lands near 7% once inflation is removed. It is an average across good and bad decades, not something you can count on in any given year, and past performance does not guarantee future results. For a savings account or bond, use the rate the provider actually quotes.
No. The arithmetic runs in JavaScript in your browser and no value is transmitted to a server. Your inputs are written into the page URL so you can bookmark or share a scenario, which also means you should avoid sharing that link if the amounts are sensitive.
Whichever you enter is what you get out. Entering the nominal rate gives a future dollar figure; entering the rate minus your inflation assumption gives an answer in today's purchasing power. Mixing the two is the most common error in long projections — a $1M balance in 2055 at 3% inflation buys about what $412,000 buys today.
Three usual causes. Your bank may compound daily but credit interest monthly, which changes the intra-month figures. It may quote APY while you entered it as the nominal rate, overstating growth. Or tax may be withheld at source, so the rate that actually compounds is lower than the advertised one. Check which figure the provider is quoting before comparing.
Use this tool when a balance grows and nothing is repaid: savings, an index fund, a certificate of deposit. Use the Loan Calculator when a fixed payment is amortising a debt, because the balance falls each month and the interest is charged on a shrinking figure. For a specific target amount and deadline, the Savings Goal Planner solves for the deposit instead.
Yes, and faster than most borrowers expect, because credit card and overdraft rates are far higher than investment returns. A balance at 22% APR compounded monthly effectively costs about 24.4% a year if nothing is repaid, which doubles it in roughly three years by the Rule of 72. Clearing high-rate debt is mathematically equivalent to earning that rate risk-free.
Use Cases
Retirement Savings Projection
Project how your retirement savings will grow over decades with compound interest and regular monthly contributions to plan your financial future.
Investment Growth Comparison
Compare different investment scenarios side by side to see how varying interest rates, time periods, and contribution amounts affect your returns.
Compound vs Simple Interest
Understand the dramatic difference between compound and simple interest to make informed decisions about savings accounts and investments.
Student Loan Accrual
Calculate how educational loan interest accrues over time to understand the true cost of student debt and plan repayment strategies effectively.
Savings Account Comparison
Compare savings account yields and CD rates to find the best place to park your money and maximize your interest earnings over time.