Compound interest is interest earned on both your original money and the interest it has already earned. Because each year's growth is added to the balance, the balance grows faster every year, and time ends up mattering more than almost any other input.
Our free compound interest calculator projects the future value of a starting balance plus monthly contributions. This guide covers the formula, a worked example with real numbers, how compounding frequency and time change the result, and the mistakes that make projections look better than reality.
Simple interest vs compound interest
Simple interest is paid only on the original amount. Compound interest is paid on the original amount plus all interest added so far. The gap starts small and widens every year. Here is $10,000 earning 7% a year with no further deposits:
| Years | Simple interest | Compound interest (monthly) |
|---|---|---|
| 10 | $17,000.00 | $20,096.61 |
| 20 | $24,000.00 | $40,387.39 |
| 30 | $31,000.00 | $81,164.97 |
After 30 years the compounded balance is more than 2.6 times the simple-interest balance, even though the rate is identical.
The compound interest formula
For a single lump sum, the future value is:
A = P × (1 + r/n)^(n × t)For regular deposits made at the end of each period, the future value of those deposits is:
FV = PMT × [ (1 + r/n)^(n × t) − 1 ] / (r/n)P= starting amount (principal)PMT= amount deposited each periodr= annual interest rate as a decimal (7% = 0.07)n= compounding periods per year (12 for monthly)t= number of years
Add the two results together to get the total balance when you both start with a lump sum and keep contributing.
Worked example: $5,000 plus $500 a month at 7% for 20 years
- Monthly rate: 0.07 ÷ 12 = 0.0058333. Number of periods: 12 × 20 = 240.
- Growth factor: (1.0058333)240 ≈ 4.0387.
- Lump sum: 5,000 × 4.0387 = $20,193.69.
- Monthly deposits: 500 × (4.0387 − 1) ÷ 0.0058333 = $260,463.33.
- Total future value: 20,193.69 + 260,463.33 = $280,657.02.
You put in $125,000 ($5,000 plus 240 deposits of $500), so $155,657.02 of the final balance is interest. More than half of the money came from compounding rather than from you.
How compounding frequency affects growth
The more often interest is added, the sooner it starts earning interest of its own. The effect is real but smaller than people assume. Here is $10,000 at 6% for 10 years:
| Compounding | Balance after 10 years |
|---|---|
| Simple (no compounding) | $16,000.00 |
| Annually | $17,908.48 |
| Quarterly | $18,140.18 |
| Monthly | $18,193.97 |
| Daily | $18,220.29 |
Moving from annual to monthly compounding adds $285.49. Moving from monthly to daily adds only $26.32. The rate and the number of years matter far more than the frequency.
Why starting early matters most
Time is the exponent in the formula, so every extra year multiplies everything before it. Here is $300 a month at 7%, compounded monthly:
| Years saving | Total deposited | Future value |
|---|---|---|
| 10 | $36,000 | $51,925.44 |
| 20 | $72,000 | $156,278.00 |
| 30 | $108,000 | $365,991.30 |
Going from 20 to 30 years adds $36,000 of deposits but more than $209,000 of value. A quick way to estimate this is the Rule of 72: divide 72 by the annual rate to get the approximate years needed to double your money. At 7%, that is about 10.3 years; the exact figure is 10.24 years with annual compounding and 9.93 with monthly compounding.
How to use the compound interest calculator
- Open the compound interest calculator.
- Enter your Initial Investment, the amount you start with. Use
0if you are starting from nothing. - Enter your Monthly Contribution, the amount you plan to add every month.
- Enter the Annual Interest Rate (%), for example
7. - Enter the Investment Period (Years) as a whole number of years.
- Read the Projection: Future Value, Total Contributed and Interest Earned. The calculator compounds monthly and updates as you type, so you can change the rate or the years and watch the result move.
Common mistakes in compound interest projections
- Treating a projection as a promise. The calculator applies one constant rate every year. Savings rates change and investment returns swing from year to year, so run a cautious rate alongside an optimistic one.
- Ignoring fees. An annual fee comes straight off your return. $300 a month for 30 years grows to $365,991.30 at 7%, but a 1% yearly fee drops the net rate to 6% and the result to $301,354.51.
- Forgetting inflation. A future balance is stated in future dollars. Read how inflation reduces buying power, and check past figures with the inflation calculator.
- Confusing APR and APY. APY includes the effect of compounding:
APY = (1 + r/n)^n − 1. A 6% rate compounded monthly is a 6.17% APY. - Forgetting that debt compounds too. The same math raises the cost of borrowing. See how to calculate loan payments and test numbers in the loan calculator.
To measure how an investment actually performed, rather than project it, the ROI calculator converts a start and end value into an annualized return. All results are estimates for planning, not financial advice.
Frequently asked questions
What is compound interest?
Compound interest is interest calculated on the original amount plus all interest already earned. Because the interest itself earns interest, the balance grows faster each year than it would with simple interest.
How do you calculate compound interest?
Use A = P × (1 + r/n)^(n × t), where P is the starting amount, r the annual rate as a decimal, n the compounding periods per year and t the years. $10,000 at 6% compounded monthly for 10 years grows to $18,193.97.
How long does it take to double money with compound interest?
Divide 72 by the annual interest rate for a quick estimate. At 6% money doubles in about 12 years, and at 9% in about 8 years.
Does compounding frequency make a big difference?
It helps, but less than the rate or the time. $10,000 at 6% for 10 years grows to $17,908.48 with annual compounding and $18,220.29 with daily compounding, a difference of about $312.
What is the difference between APR and APY?
APR is the stated annual rate without compounding. APY (annual percentage yield) includes compounding, so it shows what you actually earn in a year. At 6% compounded monthly, the APY is 6.17%.