Calculation desk / interest & growth
Compound Interest Calculator
Estimate how a one-time principal grows when interest is compounded at a selected frequency.
Compound Interest Calculator: Project the future value of a single starting amount when earned interest is added back at a chosen number of evenly spaced periods per year. Compare annual, monthly or daily compounding using the same nominal annual rate. The result separates the final balance from growth above the original principal and assumes no further deposits. Runs 100% locally in your browser with zero server file uploads.
- Category
- Calculators
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Future value
$1,647.01
- Interest earned
- $647.01
Future value = principal × (1 + annual rate ÷ compounding periods)^(compounding periods × years)- This is an educational/planning estimate only, not personalized financial advice.
- Actual products, taxes, fees, contribution dates, and returns differ; confirm terms with the relevant provider.
- Inputs follow common calculator conventions such as initial amount, recurring contribution, time, estimated annual rate, and compounding frequency described by Investor.gov: https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
- Compounding periods are evenly spaced and the rate stays constant for the full period.
Formula and worked example
Future value = principal × (1 + annual rate ÷ compounding periods)^(compounding periods × years)
A worked example with sample values:
| Inputs | |
|---|---|
| Principal | $1,000.00 |
| Annual rate | 5% |
| Time | 10 years |
| Compounding periods | 12 |
| Results | |
|---|---|
| Future value | $1,647.01 |
| Interest earned | $647.01 |
Principal with monthly compounding
Let P be starting principal, r annual rate as a decimal, m periods per year and t years. Future value A = P × (1 + r ÷ m)^(m × t). Interest earned = A − P. Convert an entered percentage to r by dividing by 100 before applying the formula.
For P = $1,000, an illustrative 5% annual rate, m = 12 and t = 10, r = 0.05 and there are 120 periods. A = 1,000 × (1 + 0.05 ÷ 12)^120 = $1,647.009498. The widget displays $1,647.01 future value and $647.01 interest. With annual compounding at the same nominal rate, A = 1,000 × 1.05^10 = $1,628.89.
Effective yield and doubling time
Effective annual yield = (1 + r ÷ m)^m − 1. At 5% nominal with monthly compounding it is about 5.1162%. CFPB's APY definition (https://www.consumerfinance.gov/rules-policy/regulations/1030/2/) includes compounding frequency; OpenStax (https://openstax.org/books/contemporary-mathematics/pages/6-4-compound-interest) supplies the general growth formula.
Investor.gov defines the rule of 72 (https://www.investor.gov/introduction-investing/investing-basics/glossary/rule-72) as a quick doubling estimate: approximate years to double = 72 ÷ the positive annual percentage rate. Try the rule of 72 calculator alongside this projection. Neither calculation adjusts for inflation: a nominal future balance is money at the future date, rather than a guarantee of today's purchasing power.
How to use it
- Enter the amounts, rate and duration shown in the worked example or your own scenario.
- Calculate to update the result and review the assumptions.
- Compare the formula and example before using the result for planning.
Privacy & limitations
Inputs and calculations stay in your browser. No values are uploaded.
Related tools
Frequently asked questions
Why does more frequent compounding change the balance?
At the same positive nominal rate, earlier interest credits can earn interest in later periods. Increasing the frequency therefore increases this model's future value. At zero interest, frequency has no effect. Annual, monthly and daily mean 1, 12 and 365 periods respectively, not calendar-specific posting dates.
Should I enter APR or APY as the annual rate?
Enter a nominal annual interest rate for the chosen frequency. APY already includes compounding: entering an APY and compounding it again overstates the corresponding yield. A loan APR can include fees, so it is not automatically a deposit interest rate or a suitable growth input.
Can the compound calculator include monthly savings or withdrawals?
No. It grows one initial principal over the entire duration. Use savings growth for equal monthly deposits. Withdrawals, variable rates, taxes and account charges alter the balance and need their own cash-flow assumptions.
Embed this tool
Free to use on any website. Paste the code where the tool should appear; the link under it lets readers open the full page.
<iframe src="https://toea.com/embed/compound-interest-calculator" title="Compound Interest Calculator" width="100%" height="1110" style="border:0;max-width:680px" loading="lazy"></iframe>
<p style="margin:4px 0 16px;font-size:13px"><a href="https://toea.com/compound-interest-calculator">Compound Interest Calculator</a> · TOEA</p>
<script>addEventListener("message",function(e){if(e.origin!=="https://toea.com"||!e.data||e.data.type!=="toea-embed-height")return;document.querySelectorAll("iframe").forEach(function(f){if(f.contentWindow===e.source)f.style.height=e.data.height+"px"})})</script>Free tool · runs in your browser · no account required