The compound interest formula
A = P × (1 + r/n)^(n × t)
A is the final amount, P the starting amount, r the annual interest rate as a decimal, n the number of times interest is compounded per year and t the number of years. Simple interest, by contrast, is P × (1 + r × t): interest is always calculated on the original amount only.
A worked example
Invest 100,000 at 8% a year for 10 years. With simple interest you end up with 180,000.00. With interest compounded once a year, the amount becomes 100,000 × 1.08^10 = 215,892.50. Compounded monthly, it is 221,964.02, and compounded daily it is 222,534.58. More frequent compounding helps, but the gain from monthly to daily is small compared with the gain from simply staying invested longer.
Why time matters more than frequency
The table shows 100,000 at 8% compounded annually compared with simple interest:
| Time | Compound (annual) | Simple interest |
|---|---|---|
| 5 years | 146,932.81 | 140,000.00 |
| 10 years | 215,892.50 | 180,000.00 |
| 20 years | 466,095.71 | 260,000.00 |
| 30 years | 1,006,265.69 | 340,000.00 |
The two lines start together and then pull apart. In the final decade of 30 years, compounding adds far more than the whole first decade did.
Nominal rate versus effective rate
A quoted rate of 8% compounded monthly is not the same as 8% a year. The effective annual rate is (1 + r/n)^n − 1 = 8.30%. When comparing deposits or loans, compare the effective annual rate so that different compounding frequencies are treated fairly.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual rate in percent. At 8%, 72 ÷ 8 = 9 years. The exact answer is ln 2 ÷ ln(1.08) = 9.01 years, so the shortcut is close. It works best for rates between about 6% and 10%.
Regular deposits and real-world limits
The formula above covers a single starting amount. When you add money every month, the result is a series of compounding deposits, covered in the guide on SIP versus lumpsum. Remember that real returns change from year to year, taxes and fees reduce growth, and inflation reduces what the money can buy. A calculator shows the arithmetic, not a forecast.
Try it with your own numbers
Use the Compound Interest Calculator to test different amounts, rates and compounding frequencies, or the FD Calculator and PPF Calculator for deposit-style tools.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original amount. Compound interest is calculated on the original amount plus interest already earned.
Does compounding daily beat compounding monthly?
Slightly. The extra gain is small compared with the effect of time and the interest rate itself.
How accurate is the Rule of 72?
It is a quick estimate and is most accurate for annual rates of roughly 6% to 10%.
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