Compound interest is interest that earns interest. Each time interest is added to your balance, the next round of interest is calculated on the larger amount. Over a few months the effect is tiny. Over decades it becomes the main reason a savings or investment balance grows. This guide explains the formula, walks through real numbers, and shows how to test your own figures with our compound interest calculator.
With compound interest, the balance after t years is A = P × (1 + r/n)n×t. $10,000 at 7% a year, compounded annually, grows to about $38,697 after 20 years. Simple interest on the same amount would give only $24,000.
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Simple vs compound interest
Simple interest is paid only on the original amount (the principal). If you put in $10,000 at 7% simple interest, you earn $700 every year, no more and no less. After 20 years you have $10,000 + 20 × $700 = $24,000.
Compound interest is paid on the principal and on the interest already added. In year one you earn $700. In year two you earn 7% of $10,700, which is $749. In year three you earn 7% of $11,449, which is about $801. The yearly gain keeps growing because the balance it is calculated on keeps growing.
The compound interest formula
A = final amount
P = starting amount (principal)
r = annual interest rate as a decimal (7% = 0.07)
n = times interest is added per year (1 = yearly, 12 = monthly)
t = number of years
For yearly compounding, n = 1 and the formula simplifies to A = P × (1 + r)t. To find the interest earned, subtract the principal from the result: interest = A − P.
A worked example, year by year
Take $10,000 earning 7% a year, compounded annually, with no further deposits. Here is how the balance compares with simple interest:
| Years | Compound balance | Simple-interest balance | Extra from compounding |
|---|---|---|---|
| 10 | $19,672 | $17,000 | $2,672 |
| 20 | $38,697 | $24,000 | $14,697 |
| 30 | $76,123 | $31,000 | $45,123 |
| 40 | $149,745 | $38,000 | $111,745 |
The gap is small at first and then widens quickly. Between year 30 and year 40 the compounded balance nearly doubles, while the simple-interest balance rises by only $7,000.
Does compounding frequency matter?
It matters, but less than most people expect. Here is $10,000 at 6% for 10 years, compounded at different frequencies:
| Compounding | Times per year | Balance after 10 years |
|---|---|---|
| Annually | 1 | $17,908 |
| Quarterly | 4 | $18,140 |
| Monthly | 12 | $18,194 |
| Daily | 365 | $18,220 |
Going from yearly to monthly adds $286. Going from monthly to daily adds only $26 more. The rate and the time period matter far more than the compounding schedule. When comparing accounts, look at the APY (annual percentage yield), which already includes the effect of compounding, so different accounts can be compared fairly.
Adding money every month
Most people do not invest a lump sum once. They add money regularly. If you deposit $200 at the end of every month and earn 7% a year compounded monthly, the balance after 30 years is about $243,994. You paid in $72,000 ($200 × 360 months), so roughly $171,994 of the final balance is interest.
That is the compounding effect: more than two-thirds of the end result came from growth rather than from your own deposits.
Why starting early matters
Time is the most powerful input in the formula. Compare two savers who both earn 7% a year, compounded monthly, and put in $200 a month:
| Sam | Priya | |
|---|---|---|
| Starts saving at | Age 25 | Age 35 |
| Stops contributing at | Age 35 (10 years) | Age 65 (30 years) |
| Total paid in | $24,000 | $72,000 |
| Balance at age 65 | about $280,968 | about $243,994 |
Sam pays in only a third as much money but ends up with more, because Sam's money had an extra 10 years to compound. This is an illustration with a constant 7% return. Real investment returns vary from year to year and are never guaranteed, but the principle holds: the earlier the money goes in, the longer it works.
The Rule of 72
The Rule of 72 is a quick mental shortcut to estimate how long it takes money to double. Divide 72 by the annual interest rate (as a whole number):
At 4%: 72 ÷ 4 = 18 years
At 6%: 72 ÷ 6 = 12 years
At 7%: 72 ÷ 7 = about 10.3 years
At 9%: 72 ÷ 9 = 8 years
It is an approximation. The exact doubling time at 7% is 10.24 years, so the shortcut is close. It works best for rates between about 4% and 12%.
Compounding works against you on debt
The same mathematics applies to money you owe. Suppose a credit card balance of $5,000 has a 24% annual rate, which is 2% per month. If you made no payments for a year, the balance would grow to $5,000 × 1.0212 = about $6,341, which is more than the $6,200 that simple interest would give. This is why paying down high-interest debt is often treated as a guaranteed return: every dollar of balance you remove stops compounding against you.
What these numbers do not tell you
- The examples use a constant rate. Real investments rise and fall, and savings account rates change.
- Inflation reduces what a future balance can buy, so $149,745 in 40 years will buy less than it does today.
- Taxes and fund fees reduce the return you actually keep.
- Results here are estimates for learning, not financial advice or a forecast.
How to use the compound interest calculator
Enter your starting amount
Put in the money you already have, or 0 if you are starting from nothing.
Add a monthly contribution
Enter what you plan to add each month. Try a small and a larger amount to compare.
Set the rate and years
Use a cautious rate you are comfortable with, not the best year you have seen.
Read the breakdown
The calculator shows the future value, how much you put in, the interest earned and a year-by-year table.
Test your own numbers
Change the amount, rate and years and see how the balance responds.
Open the Compound Interest CalculatorFrequently Asked Questions
Conclusion
Compound interest rewards time and consistency. The formula is simple, but its effect on a long timeline is large: a bigger starting balance, regular deposits and extra years all raise the result, while high-interest debt makes the same effect work against you. Try your own figures in the compound interest calculator, then see how loans work in our loan calculator.
This guide is for general education only and is not financial advice. Projections assume a constant rate of return, which real investments do not provide.