What actually happens when interest compounds?
Follow a worked example of compound interest, compare it with simple interest, and learn which assumptions change the result.
Compound interest can sound more mysterious than it is. The essential idea is that previous growth stays in the balance, so future growth applies to a larger amount. You do not need a large starting balance to understand it. You need a starting amount, a rate, a time period and a rule for when interest is added.
Follow the first three years
Suppose you start with 10,000 and receive 8% interest, compounded annually. There are no additional contributions, fees, withdrawals or taxes. This is a mathematical example, not a promised return.
| Year | Starting balance | Interest | Ending balance |
|---|---|---|---|
| 1 | 10,000.00 | 800.00 | 10,800.00 |
| 2 | 10,800.00 | 864.00 | 11,664.00 |
| 3 | 11,664.00 | 933.12 | 12,597.12 |
The rate stays at 8%, but the amount earned rises. In the second year, 64 of the interest comes from the first year’s 800. By year three, growth applies to the accumulated balance again.
What would simple interest do instead?
At simple interest, the same 8% applies only to the original 10,000 each year. That means 800 per year and an ending balance of 12,400 after three years. The compound example ends 197.12 higher. After ten years, annual compounding gives approximately 21,589.25, while simple interest gives 18,000.
Read the formula without the jargon
With annual compounding, the balance after t years is P × (1 + r)t. P is your starting money and r is the annual rate expressed as a decimal: 8% becomes 0.08. The exponent means applying the growth factor repeatedly. For three years, that is 10,000 × 1.08 × 1.08 × 1.08.
When interest compounds n times per year at a nominal annual rate, the formula becomes P × (1 + r/n)nt. The word nominal matters: an 8% nominal rate compounded monthly produces a different annual growth factor from an 8% effective annual rate.
What this example leaves out
A smooth curve assumes a constant rate. Real market investments can fluctuate and lose value. Fees, taxes and withdrawals can reduce the amount left to compound. Inflation affects what a future balance can buy. A calculator is useful for exploring assumptions, but those assumptions are not evidence that a particular investment will deliver the result.
Regular contributions also change the story: later deposits have less time to grow than the original balance. To understand that part, read how regular contributions affect growth. To understand nominal and effective rates, read our guide to compounding frequency.
Turn the example into your own question
Use the compound interest calculator to enter your starting amount and time horizon. Try a lower assumed rate as well as your first estimate. The resulting range is more informative than treating a single ending balance as certain.
Put the idea into numbers.
Open the free compound interest calculator →