How to Calculate Compound Interest (Formula + Examples)
Learn how to calculate compound interest with the exact formula, a worked example, and the Rule of 72 shortcut.
Learning how to calculate compound interest is one of the most valuable money skills you can build, because it explains how a modest amount of savings can grow into a substantial sum over time. In this guide you will see the exact formula, a step-by-step example, and a simple trick to estimate growth in your head.
What compound interest actually means
Compound interest is the interest you earn on both your original money — the principal — and on the interest that has already been added. Simple interest is calculated only on the principal, but compound interest earns "interest on interest." That snowball effect is exactly what makes long-term saving and investing so powerful.
The compound interest formula
The standard formula is: A = P × (1 + r/n)^(n·t). Each letter stands for one input:
- A — the final amount you end up with.
- P — the principal, or starting amount.
- r — the annual interest rate written as a decimal (8% becomes 0.08).
- n — how many times interest is added per year (monthly is 12).
- t — the number of years the money stays invested.
A step-by-step example
Suppose you invest 1,000 dollars at an 8% annual rate, compounded monthly, for 10 years. Plug the numbers in: P is 1,000, r is 0.08, n is 12, and t is 10. Working the formula out gives A = 1,000 × (1 + 0.08/12)^(120), which comes to about 2,219 dollars. You contributed 1,000 and earned roughly 1,219 in interest — more than doubling your money without adding a single extra deposit.
Simple vs. compound over time
The gap between simple and compound interest is small at first, then grows dramatically. Here is 1,000 dollars at 8% per year, compared side by side:
| Years | Simple interest | Compound interest |
|---|---|---|
| 5 | 1,400 | 1,469 |
| 10 | 1,800 | 2,159 |
| 20 | 2,600 | 4,661 |
| 30 | 3,400 | 10,063 |
After 30 years the compound total is nearly three times the simple one. Time, not luck, does the heavy lifting.
Compound interest is the reward for patience: the longer you leave your money alone, the harder it works for you.
The Rule of 72: a mental shortcut
To estimate how long it takes your money to double, divide 72 by the annual rate. At 8%, that is 72 ÷ 8 = 9 years to double. At 6% it takes 12 years. It is not perfectly exact, but it is close enough to make quick decisions without a calculator.
Does compounding frequency matter?
Yes, but less than most people expect. Daily compounding beats monthly, which beats yearly, because interest is added more often. At everyday rates the difference is real but modest, so the two variables that matter most remain the rate and the number of years. When you are ready to run your own numbers, our compound interest calculator handles every input instantly, and if you are comparing borrowing costs instead, the loan calculator shows the flip side of the same math.
Put it to work
Compound interest rewards two things above all: starting early and staying consistent. Even small, regular contributions can outgrow a larger one-time deposit made years later. For a trustworthy second opinion, the U.S. Securities and Exchange Commission offers a free calculator on Investor.gov. Understand the formula once, let time do the rest, and your future self will thank you.