Compound Interest Calculator
This Compound Interest Calculator estimates how savings or an investment may grow when interest compounds over time. Choose a compounding frequency, enter an initial principal, set an annual interest rate and duration, and optionally include monthly contributions to see the future value, interest earned, and a year-by-year breakdown.
Run your numbers.
Change any value and the results update instantly. Nothing leaves your device.
Currency only changes how amounts are displayed. No amounts are converted between currencies.
Inputs
Default values are examples, not live rates. Replace them with figures from your own account or plan.
Results
Future value
Growth over time (horizontal axis: years; vertical axis: amount, K = thousand, M = million)
Set a duration of at least 1 year to see growth over time.
Yearly growth breakdown
| Year | Opening balance | Growth during the year | Contributions during the year | Closing balance | Total invested to date |
|---|
Year 0 is your initial principal. The contributions column shows deposits made during that year (12 monthly deposits at the end of each month). Growth is closing balance minus opening balance minus contributions. The last closing balance equals the future value above.
How this is calculated
Principal: A = P × (1 + r/n)^(n×t). Contributions are made at the end of each month and grow at the equivalent monthly rate i = (1 + r/n)^(n/12) − 1, giving C × ((1 + i)^m − 1) ÷ i, where m = 12 × t. At a 0% rate this is simply C × m. Total future value is the sum of the two parts.
Estimate only. It assumes a constant nominal annual rate and the selected compounding frequency. Actual account balances may differ because of taxes, fees, rate changes, withdrawals, and product-specific terms.
The math behind the calculator.
Every figure on this page comes from these formulas. Nothing is estimated by lookup tables or external services.
Compound interest formula
A = P × (1 + r/n)^(n×t)- A: future value
- P: initial principal
- r: nominal annual interest rate as a decimal (7% = 0.07)
- n: compounding periods per year (1, 2, 4, 12 or 365)
- t: duration in complete years
Each period earns r/n, so more frequent compounding adds interest to the balance sooner and later interest is calculated on a slightly larger amount.
Nominal vs. effective rate
EAR = (1 + r/n)^n − 1The rate you enter is the nominal rate. The effective annual rate (EAR) is what a single year actually earns once compounding is included. At 7% nominal, annual compounding gives exactly 7%, monthly compounding about 7.229%, and daily about 7.250%.
Optional monthly contributions
i = (1 + r/n)^(n/12) − 1FVc = C × ((1 + i)^m − 1) ÷ i
- C: monthly contribution, deposited at the end of each month
- i: monthly rate equivalent to the selected frequency's effective annual growth
- m: number of deposits, 12 × t
- If i = 0, FVc = C × m
Totals
Future value = A + FVcTotal invested = P + C × m
Interest earned = Future value − Total invested
Total growth % = Interest earned ÷ Total invested × 100
Future value is the final balance, not profit. Interest earned is what the balance gained above everything you put in. If nothing was invested, growth percentage is shown as a dash instead of dividing by zero.
Worked examples.
All three use a 10,000 starting amount, a 7% nominal annual rate and 10 years. Enter them above to check.
Annual compounding
≈ 19,671.5110,000 × 1.07^10. Interest earned is about 9,671.51, a total growth of about 96.72%.
Monthly compounding
≈ 20,096.6110,000 × (1 + 0.07/12)^120. The same nominal rate is applied 12 times a year, so interest is added sooner and the result is higher than annual compounding.
With 100 a month, annual compounding
≈ 36,776.69The principal grows to about 19,671.51 and 120 deposits (12,000 paid) grow to about 17,105.17, using i ≈ 0.5654% a month. With 22,000 invested, interest earned is about 14,776.69.
What Is a Compound Interest Calculator?
A compound interest calculator estimates the future value of money when interest is added to the balance at regular intervals and then earns interest itself. You enter the initial principal, a nominal annual interest rate, a number of years, and how often interest compounds. The calculator returns the projected balance, the interest earned, and a year-by-year view of the growth.
This version also accepts an optional monthly contribution, so it works as a compound interest calculator with monthly contributions as well as a one-time-deposit calculator. Change any input and the results update straight away. All calculations run in your browser, and nothing you enter is sent anywhere.
What Is Compound Interest?
Compound interest is interest calculated on the principal amount plus the interest that has already been added. Simple interest, by contrast, is calculated only on the original principal.
Take 1,000 at 10% a year, compounded annually. After year one you have 1,100. In year two the 10% applies to 1,100 rather than 1,000, so you earn 110 and finish with 1,210. Simple interest would earn 100 each year and finish with 1,200. The extra 10 is interest earned on interest. Over short periods the gap is small. Over long periods compound growth becomes the dominant effect, because each period's interest enlarges the base for the next.
How to Use This Compound Interest Calculator
Work through the inputs from top to bottom:
- Initial Investment: the starting principal amount. Enter 0 if you plan to rely only on monthly contributions.
- Annual Interest Rate: the nominal rate per year, as a percentage from 0 to 100. This is an assumption you choose, not a live market rate.
- Investment Duration: complete years, from 0 to 100.
- Compounding Frequency: annually, semi-annually, quarterly, monthly or daily, which means 1, 2, 4, 12 or 365 periods per year.
- Additional Monthly Contribution: an optional amount deposited at the end of every month. Leave it at 0 for a single deposit.
- Currency format: changes the symbol and number format only. No amounts are converted.
The future value is the headline result. Below it you will find the initial principal, the total amount invested, the interest earned, and the total growth. The future value is the final balance, not profit. Subtract what you put in to get the interest earned. Open the yearly breakdown to see each year's opening balance, growth, contributions, and closing balance.
Compound Interest Formula
For a single deposit with no additional contributions, the compound interest formula is:
A = P × (1 + r/n)^(n×t)A is the future value, P is the principal amount, r is the nominal annual interest rate written as a decimal, n is the number of compounding periods per year, and t is the number of years. The rate is divided by n because each period earns only a fraction of the annual rate. At 7% compounded monthly, each period earns 0.07 ÷ 12.
Nominal rate vs. effective annual rate
The rate you enter is a nominal annual rate. When interest compounds more than once a year, the amount actually earned over twelve months is slightly higher than the nominal figure. That is the effective annual rate, calculated as (1 + r/n)^n − 1. At 7% nominal, annual compounding gives exactly 7%, while monthly compounding gives an effective annual rate of about 7.229%. Comparing effective rates puts different compounding frequencies on equal footing, and the calculator shows it in the results.
Compound Interest Calculation Example
Suppose you invest 10,000 at a 7% nominal annual rate, compounded annually, for 10 years, with no contributions, withdrawals, taxes, or fees.
A = 10,000 × (1 + 0.07/1)^(1×10)A = 10,000 × 1.07^10
A ≈ 10,000 × 1.967151 ≈ 19,671.51
The interest earned is 19,671.51 − 10,000 = 9,671.51, which is a total growth of about 96.72% on the amount invested. The calculator opens with these exact values, so you can confirm the result and then change one input at a time to see its effect.
Annual vs. Monthly vs. Quarterly vs. Daily Compounding
Compounding frequency decides how often interest is added to the balance. The table below keeps everything else identical: 10,000, a 7% nominal annual rate, 10 years, and no contributions.
| Frequency | Periods per year | Future value | Interest earned | Effective annual rate |
|---|---|---|---|---|
| Annually | 1 | 19,671.51 | 9,671.51 | 7.000% |
| Semi-annually | 2 | 19,897.89 | 9,897.89 | 7.122% |
| Quarterly | 4 | 20,015.97 | 10,015.97 | 7.186% |
| Monthly | 12 | 20,096.61 | 10,096.61 | 7.229% |
| Daily | 365 | 20,136.18 | 10,136.18 | 7.250% |
For a positive nominal rate, more frequent compounding generally produces a higher ending balance when all other assumptions are identical. The effect shrinks as frequency rises. Moving from annual to monthly adds about 425 here, while moving from monthly to daily adds about 40. Frequency is also only one factor. The stated rate, fees, taxes, minimum balances, and account terms can matter more, so compounding frequency alone does not tell you which financial product is best.
How Regular Contributions Affect Compound Interest
Regular deposits add new principal that begins earning interest of its own. The final balance therefore reflects what you paid in plus the growth on each deposit, and earlier deposits have longer to compound than later ones.
This calculator assumes each contribution is made at the end of the month. To keep contributions consistent with the frequency you select, it converts the effective annual growth factor, (1 + r/n)^n, into an equivalent monthly rate, i = (1 + r/n)^(n/12) − 1. The contributions grow as C × ((1 + i)^m − 1) ÷ i, where m is 12 times the number of years, and that amount is added to the future value of the initial principal. The two parts are tracked separately, so nothing is counted twice.
For example, 10,000 at the start plus 100 a month, at 7% compounded annually for 10 years, gives a monthly equivalent rate of about 0.5654%. The principal grows to about 19,671.51 and the contributions, 12,000 paid in total, grow to about 17,105.17. The total is about 36,776.69 against 22,000 invested, so interest earned is about 14,776.69. Real accounts may credit interest only on set dates or use different day-count rules, so actual balances can differ from this simplified model.
Benefits of Compound Interest
Compound interest rewards time. Because growth builds on earlier growth, a longer horizon can have a larger effect than a modest change in the starting amount, and starting earlier gives each deposit more periods to compound. Leaving earnings reinvested rather than withdrawn lets the base keep growing. Recurring savings add to the principal steadily, which is why a monthly habit can matter even when each deposit is small.
These are properties of the mathematics, not promises about outcomes. Whether any real account or investment grows at the rate you assume depends on the product and on market conditions.
Limitations of Compound Interest Calculations
A calculator can only project the assumptions you give it. Real results may be affected by:
- Changing rates: this calculator assumes one constant nominal annual rate for the whole duration.
- Transaction timing: deposits are assumed at the end of each month, and withdrawals are not modelled.
- Taxes and fees: neither is deducted, and both can reduce what you keep.
- Inflation: a larger balance does not necessarily mean greater buying power.
- Product-specific terms: minimum balances, interest credit dates, and day-count conventions vary between accounts.
Treat the output as a mathematical projection for planning and learning. It does not predict actual investment performance.
Frequently asked questions.
What is a compound interest calculator?
A compound interest calculator estimates how an initial amount grows when interest is added to the balance at regular intervals and then earns interest itself. Enter the principal amount, annual interest rate, duration, and compounding frequency to see the future value and interest earned. This Compound Interest Calculator also supports optional monthly contributions.
What is the compound interest formula?
For a single deposit, the compound interest formula is A = P × (1 + r/n)^(n×t), where A is the future value, P is the principal, r is the nominal annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years.
How is compound interest calculated?
Divide the annual rate by the number of compounding periods per year, add 1, raise the result to the power of periods per year multiplied by years, then multiply by the principal. Subtract the principal from the result to get the interest earned. The calculator does these steps for you and keeps full precision until the final display rounding.
How much will 10,000 grow at 7% interest over 10 years?
About 19,671.51, which means roughly 9,671.51 of interest. This assumes annual compounding, no additional contributions, no withdrawals, and no taxes or fees. With monthly compounding at the same nominal rate, the result is about 20,096.61.
What is the difference between simple interest and compound interest?
Simple interest is calculated only on the original principal, so it adds the same amount each year. Compound interest is calculated on the principal plus previously added interest, so the amount added grows over time. For 10,000 at 7% over 10 years, simple interest gives 17,000 in total, compared with about 19,671.51 under annual compounding.
Is monthly compounding better than annual compounding?
For the same positive nominal rate and otherwise identical terms, monthly compounding produces a slightly higher balance than annual compounding. That does not make one product better than another, because the stated rate, fees, taxes, and account terms also matter. Compare the effective annual rate and the full terms of each product.
How does compounding frequency affect future value?
More frequent compounding adds interest to the balance sooner, so later interest is calculated on a slightly larger amount. With 10,000 at 7% for 10 years, the future value is about 19,671.51 annually, 19,897.89 semi-annually, 20,015.97 quarterly, 20,096.61 monthly, and 20,136.18 daily. The extra gain gets smaller with each step up in frequency.
Can I add monthly contributions to this calculator?
Yes. Enter an Additional Monthly Contribution. The calculator assumes it is deposited at the end of every month and grows at the monthly rate equivalent to the selected frequency's effective annual growth. Contributions are tracked separately from the initial principal, so nothing is counted twice. Leave the field at 0 for a standard compound interest calculation.
Does compound interest account for inflation, taxes, and fees?
No. This calculator assumes a constant nominal annual rate and does not model inflation, taxes, fees, withdrawals, or rate changes. Any of these can lower real or after-tax results, so treat the output as a mathematical projection rather than a prediction.
Is compound interest guaranteed to produce investment gains?
No. Compound interest is a mathematical effect of the rate you assume, not a promise of results. Some savings products offer fixed rates, but investment returns vary and can be negative. This calculator projects growth from the assumptions you enter and does not predict actual performance.
Financial disclaimer
This calculator provides estimates based on the inputs and assumptions entered. It assumes a constant nominal annual interest rate, the selected compounding frequency, and the stated contribution schedule. Actual account balances may differ because of taxes, fees, rate changes, withdrawals, inflation, and product-specific terms. Results are for educational purposes only and do not constitute financial advice.