How to use the compound interest calculator
- Enter the starting amount, the annual interest rate and the time in years.
- Pick how often interest is compounded: daily, monthly, quarterly, semiannually or annually.
- Optional: open More options to add a recurring contribution, how often you add it and whether it is made at the start or end of each period.
- Read the future balance, total interest and effective annual yield (APY). The yearly table shows how the balance grows, and the CSV has the same rows.
Formula
Balance = P x (1 + r/m)^(m x t)
P = starting amount, r = annual rate as a decimal, m = compounding periods per year, t = years
APY = (1 + r/m)^m - 1
Each contribution grows at the same effective annual rate from the day it is deposited
When contributions match the compounding schedule (for example monthly deposits with monthly compounding), the result equals the standard annuity formula. Nothing is rounded until the number is displayed.
Worked examples
Starting amount only: $10,000 at 5% for 10 years. Compounded monthly it grows to $16,470.09. Compounded annually it grows to $16,288.95. Compounded daily it reaches $16,486.65. More frequent compounding helps, but only slightly. The monthly case has an APY of 5.1162%.
With monthly contributions: add $200 at the end of every month for 10 years on the same $10,000. You deposit $24,000 in total and the balance reaches $47,526.55, so interest earned is $13,526.55.
Contribution timing: if the $200 is deposited at the start of each month instead, each deposit earns one extra month of interest and the balance is $47,655.95, which is $129.40 more.
Why time matters more than frequency
The difference between monthly and daily compounding on $10,000 at 5% for 10 years is about $16.56. The difference between 10 and 20 years is thousands of dollars. Starting early and keeping the money invested has a far bigger effect than choosing a slightly more frequent compounding schedule. Contributions add to this effect because each new deposit starts compounding too.
Nominal rate versus APY
The rate you type in is the stated annual rate before compounding. The APY shows the effective rate after compounding, which is what you would earn in a single year with no deposits. Savings accounts usually advertise APY, while loans usually advertise APR. When comparing a savings account to an investment, put both on the same basis.
Savings accounts versus investments
A fixed-rate bank account can follow this math closely, but investments such as stocks do not earn a steady return. Real returns vary from year to year and can be negative, so a single average rate is only an illustration. The ROI calculator shows the annualized return for a past result, and the savings calculator is built around goals.
Assumptions and limits
- The interest rate is constant for the whole period and is not guaranteed in real accounts or investments.
- Compounding uses the stated annual rate divided by the number of periods, with 365 periods a year for daily.
- Contributions are equal, regular and earn the same effective annual rate from the day they are deposited. If contributions are used, the time must be a whole number of contribution periods.
- Taxes, account fees, inflation and withdrawals are not modeled.
- Values are shown rounded to the cent. The calculation itself is not rounded in between.
- This is a projection for illustration, not financial advice.
Frequently asked questions
What is the compound interest formula?
Balance equals the starting amount times (1 plus the rate divided by the number of compounding periods) raised to the power of periods per year times years. With regular deposits, each deposit is grown the same way for the time it stays invested.
What is the difference between compound and simple interest?
Simple interest is paid only on the original amount, while compound interest is also paid on interest already earned. Over long periods the gap grows quickly. See the simple interest calculator to compare.
Does more frequent compounding always help?
Yes, but with diminishing returns. Going from annual to monthly compounding adds the most, and going from monthly to daily adds very little. The APY shown in the results makes the effect easy to compare.
Should contributions be at the start or end of the period?
Use start if you deposit right after payday or at the beginning of each month, and end if you deposit once the period is over. Start-of-period deposits earn one extra period of interest each.