Compound Interest Calculator
Calculate compound interest with annual, monthly, daily, or continuous compounding. Estimate future investment growth, compare compounding frequencies, and see how your savings can grow over time.
Growth Over Time
Formulas Used
Compound Interest:
Continuous Compounding:
Recurring Contributions:
Continuous Compounding with Contributions:
Where:
- P = principal
- r = annual interest rate as a decimal
- n = compounding periods per year
- t = time in years
- e = Euler's number, approximately 2.71828
- M = monthly contribution
- C = contribution per compounding period, calculated from the monthly contribution as M × 12/n
- p = completed compounding periods
- m = completed months
- A = final amount
Understanding Compound Interest
Compound interest is interest earned on both your original investment and the interest that has already been added to it. Over time, this compounding effect can significantly increase the value of your savings or investments.
Use the calculator above to estimate future growth based on your initial deposit, interest rate, contribution amount, and compounding frequency.
Want to see it used on real numbers? The Compound Interest Guide walks through an emergency fund, a house down payment, and a 25-year retirement scenario step by step, using the exact fields on this page.
What Is Continuous Compounding?
Continuous compounding represents the theoretical limit of compound interest where interest is added an infinite number of times per year. Instead of compounding annually, monthly, or daily, the investment grows continuously every moment.
The continuous compounding formula is:
Why Is There an "e"?
The number e appears because continuous compounding assumes interest is being added every instant of time.
As compounding frequency increases from annual to monthly, daily, hourly, every second, and finally continuous compounding, the standard compound interest formula approaches a limit:
Annual → Monthly → Daily → Hourly → Every Second → Continuous
Continuous compounding is essentially the mathematical limit of increasingly frequent compounding.
Because interest is constantly being added to the balance, continuous compounding produces slightly higher returns than daily compounding at the same annual rate.
What you can calculate
- Future investment value
- Total contributions over time
- Total interest earned
- Growth from recurring monthly deposits
- Effects of different compounding frequencies
- Investment growth scenarios with variable interest rates
Inputs explained
- Principal Amount – your starting balance or initial investment.
- Monthly Contribution – recurring deposits added during the investment period, this can be zero if you want to calculate without contribution.
- Annual Interest Rate– expected yearly return expressed as a percentage. Historical note: the S&P 500 has returned roughly 6.7% per year after inflation since 1957, though actual returns vary widely from year to year.
- Compounding Frequency – how often interest is added to the balance, such as monthly, quarterly, or daily.
- Time Period – total investment duration in years.
- Interest Rate Variance Range – optional high and low growth scenarios used for the chart projection.
Compound interest formula
Standard compound interest is calculated using:
A = P(1 + r/n)^nt
Where:
- A = final amount
- P = principal investment
- r = annual interest rate
- n = compounding periods per year
- t = time in years
Why compounding frequency matters
More frequent compounding generally increases the final investment value because interest is added and reinvested more often. Daily compounding usually produces slightly higher returns than monthly or annual compounding at the same nominal interest rate.
Example calculation
Suppose you invest $10,000 at a 7% annual return compounded monthly, while contributing an additional $200 each month for 20 years. The calculator estimates the final balance, total contributions, and total interest earned while also visualizing growth over time.