Compound interest explained, with examples
Compound interest is interest that earns interest. Each time it is added to your balance, the next round is worked out on the larger amount, so growth speeds up the longer you wait. It is the reason time matters so much for savings, and why debt can grow quickly.
Try it now: Compound Interest Calculator, Loan EMI Calculator.
Simple and compound interest
With simple interest you earn only on the amount you started with. Put 10,000 in at 5 percent for 10 years and you earn 500 a year, so you end with 15,000. With compound interest, each year’s interest is added to the balance, so the same 10,000 at 5 percent compounded yearly grows to 16,288.95. The extra 1,288.95 is interest earned on interest.
A year-by-year example
Take 10,000 at 5 percent compounded yearly. After year 1 you have 10,000 × 1.05 = 10,500. In year 2 the interest is 5 percent of 10,500, which is 525, so you have 11,025. In year 3 the interest is 551.25 and the balance is 11,576.25. The interest paid grows every year even though the rate never changes, and that growing step is what compounding means.
The formula
The balance after t years is A = P × (1 + r/n)^(n × t). P is the starting amount, r is the yearly rate as a decimal (5 percent is 0.05), n is how many times a year interest is added, and t is the number of years.
Does compounding more often matter?
A little. Here is 10,000 at 5 percent for 10 years with different frequencies:
| Compounded | Balance after 10 years |
|---|---|
| Yearly | 16,288.95 |
| Monthly | 16,470.09 |
| Daily | 16,486.65 |
Adding regular deposits
Deposits make the biggest difference. Saving 500 a month at 6 percent, compounded monthly, for 10 years puts in 60,000 and grows to 81,939.67, so 21,939.67 of it is interest. The earlier a deposit is made, the longer it compounds, which is why depositing at the start of each period earns slightly more than at the end.
The rule of 72
To estimate how long money takes to double, divide 72 by the yearly rate in percent. At 6 percent that is about 12 years, and the exact figure is 11.9. At 8 percent it is about 9 years.
Compound interest on debt
The same rule applies when you owe money. A balance of 1,000 on a card that charges 2 percent a month, left unpaid for a year, becomes 1,268.24, because each month’s interest is added to what you owe. This is why paying even a little more than the minimum matters, and why a loan calculator is worth using before you borrow.
How to use the calculator
Enter your starting amount, the yearly rate and the number of years, then choose how often interest is compounded. Add a regular deposit if you will keep saving. You get the final balance, how much of it is your own money and how much is interest, a chart that splits each year into the two, and a year-by-year table so you can check every figure.
What the formula leaves out
Real returns vary from year to year, and fees, taxes and inflation reduce what you keep. Treat the result as an illustration of how time and rate work together, not a forecast. The same maths, run the other way, shows why a loan costs more the longer you take to repay it.