Compound Interest Calculator
Watch a single deposit grow as interest earns interest — and see exactly how much the compounding frequency changes the outcome.
Interest on interest
Compounding adds each period's interest to the balance so the next period earns on a larger sum.
A constant-rate model
Real rates change; this projects steady growth to show how compounding works, not to predict markets.
What is compound interest?
The engine behind long-term growth
Compound interest is interest calculated on both your original principal and the interest already added to it. Unlike simple interest, which only ever pays on the starting amount, compounding lets your earnings generate earnings of their own, so a balance grows faster and faster over time. According to Investopedia, this "interest on interest" effect is what makes compounding one of the most powerful forces in personal finance — and the reason starting early matters so much.
The balance is the principal multiplied by a growth factor that depends on the rate, the frequency, and the time.
A = P × (1 + r ÷ n)^(n × t)Here P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years. Each period adds r ÷ n of interest, and raising the factor to n × t applies it across every period. For continuous compounding — the limit as n grows without bound — the formula becomes A = P × e^(r × t), using the mathematical constant e. The interest earned is simply the final balance minus the principal.
You deposit 10,000 at a 5% annual rate for 10 years, compounded monthly.
Find the periodic rate
5% ÷ 12 ≈ 0.4167% per month, over 120 months.Build the growth factor
(1 + 0.004167)^120 ≈ 1.6470.Apply it to the principal
10,000 × 1.6470 ≈ 16,470.Read the interest and APY
About 6,470 is interest, and monthly compounding turns the 5% nominal rate into an effective annual rate of about 5.12%.
The same nominal rate earns more the more often it compounds, because interest starts earning sooner.
More periods, more growth
Daily compounding beats annual at the same nominal rate, though the gap is small at low rates.
Effective annual rate (APY)
The APY converts any frequency into a single yearly figure you can compare fairly across accounts.
Continuous is the ceiling
Compounding continuously is the mathematical limit — the most a given nominal rate can ever yield.
This is why banks advertise an APY rather than just a nominal rate: it folds the compounding frequency into one comparable number. According to U.S. truth-in-savings rules, deposit accounts must quote the annual percentage yield precisely so savers can compare offers on equal terms. A 5% rate compounded daily is genuinely a slightly better deal than 5% compounded annually, and the APY is what makes that visible.
The final balance is what your deposit grows to over the term. The interest earned strips out your original principal to show what compounding added, and the effective annual rate shows the true yearly return once the compounding frequency is taken into account — always at least the nominal rate, and higher the more often interest is added. Read these together to judge an account or investment: two offers with the same headline rate are not equal if they compound differently, and the APY is the figure that settles the comparison. Because the projection assumes a single constant rate, rerun it with a lower rate to see a more cautious case.
The maths is exact; the assumptions deserve scrutiny.
A projection at a constant rate
This calculator assumes a single, unchanging rate and no deposits, withdrawals, taxes, or fees, none of which hold perfectly in real life. It compounds one lump sum, so it does not model regular contributions — use the future value calculator for that. It also ignores inflation, which erodes what the final balance can actually buy. It is provided for informational purposes only and is not financial advice; use it to understand compounding and compare scenarios, and consult a qualified financial advisor before making investment or savings decisions.