TL;DR: Compound interest is interest calculated on a growing balance: the original amount, called the principal, plus every amount of interest already credited. Illustrative example only: $1,000 at an illustrative 5 percent annual rate, compounded once a year for 10 years, grows to about $1,628.89, since $1,000 multiplied by 1.05 to the power of 10 equals $1,628.89 when rounded to cents. Of that total, $1,000 is the original principal and about $628.89 is interest, since $1,628.89 minus $1,000 equals $628.89. Simple interest on the same terms would pay $50 a year on the original $1,000 only, for a total of $1,500. The $128.89 difference between $1,628.89 and $1,500 is the compounding effect in this example.
Key Takeaways
- Compound interest pays interest on interest. Simple interest pays interest only on the original principal.
- Three inputs drive the result: the starting amount, the rate, and above all the number of compounding periods, because growth accelerates as the balance grows.
- Compounding frequency matters at the margin: interest credited more often starts earning its own interest sooner.
- The same mechanism works against borrowers. Compounding on a debt grows the amount owed in exactly the same shape.
- This article explains the concept. To run your own figures, use a calculator tool such as our compound growth calculator guide.
Work the example year by year
All figures in this section are illustrative. Start with a principal of $1,000 and an illustrative annual rate of 5 percent, credited once a year. After year one, the balance is $1,000 multiplied by 1.05, which equals $1,050. The interest earned was $50. After year two, the 5 percent applies to the whole $1,050, not just the original $1,000. The balance becomes $1,050 multiplied by 1.05, which equals $1,102.50. The interest in year two was $52.50, since $1,102.50 minus $1,050 equals $52.50. That extra $2.50 over the first year's $50 is 5 percent of the first year's interest, and it is the whole concept in miniature: interest itself now earning interest.
Continue the same multiplication for ten years in total and the balance reaches $1,000 multiplied by 1.05 to the power of 10, which equals $1,628.89 when rounded to cents. The formula is general: final balance equals principal multiplied by one plus the rate, raised to the power of the number of periods. Change any one input and the result changes, but time has the distinctive effect, because each additional year multiplies a larger balance than the year before. Growth in the later years of a long example is therefore much larger in cash terms than growth in the early years, even though the percentage rate never changed. That acceleration is why explanations of long term investing return to compounding so often, and why the annualised version of the same idea appears in our guide to what is CAGR.
How is compound interest different from simple interest?
Simple interest is calculated only on the original principal for every period. On the illustrative terms above, simple interest pays $1,000 multiplied by 0.05, which equals $50, every year, regardless of how much interest has already accumulated. Over 10 years that is $50 multiplied by 10, which equals $500 of interest, and a final total of $1,500. Compound interest produced $1,628.89 on the same principal, rate, and term. The difference, $1,628.89 minus $1,500, equals $128.89, and it comes entirely from interest earning interest.
Over short periods the gap is small enough to ignore in rough planning. Over long periods it dominates the result, which is why the distinction matters for savings goals measured in decades and for debts left unpaid for years. When you compare any savings or borrowing product, the first question is which of the two mechanisms it uses, and the second is how often compounding happens. Monthly compounding credits interest twelve times a year, so each credit starts earning sooner than under annual compounding at the same stated annual rate. Comparing products on rate alone, without the compounding basis, compares incomplete numbers, a caution that also applies when using the planning approach in our savings goal calculator guide.
Where compounding helps you, and where it works against you
On the saving and investing side, compounding rewards starting and rewards patience, because the largest cash growth arrives in the later periods of any long example. Regular additions amplify it further, since each addition joins the balance and compounds from that point onward, which is the arithmetic underneath the regular investing pattern in dollar cost averaging explained.
On the borrowing side, the identical mechanism grows balances owed when interest is charged on unpaid interest. A debt balance that is not being paid down can therefore grow faster over time even with no new borrowing, in the same accelerating shape as the savings example above. Understanding compound interest is not mainly a savings lesson. It is the ability to recognise, on either side of a balance sheet, whether time is working for you or against you, and how strongly.
Two honest limits on the example. First, real investment returns are not a smooth 5 percent a year. They vary, sometimes sharply, and compounding a variable return produces a different path from the tidy table above, even when the average looks similar. Second, the example ignores taxes, fees, and inflation, all of which reduce the real growth of any actual balance. The concept is exact. Any single forecast built on it is an illustration, not a promise.
This article is educational information about how compound interest is calculated, not financial advice. Rates in the worked example are illustrative and are not the rate of any real product.
Sources and method
- Target keyword: "what is compound interest" from .saeo/keywords.yaml (queue entry added 2026-10-29). No search volume or difficulty figure is claimed; both are recorded as unknown in the queue entry.
- All figures are labelled illustrative examples. Arithmetic verified for this draft on 2026-10-29: $1,000 multiplied by 1.05 equals $1,050; $1,050 multiplied by 1.05 equals $1,102.50; $1,102.50 minus $1,050 equals $52.50; $1,000 multiplied by 1.05 to the power of 10 equals $1,628.89 rounded to cents; $1,628.89 minus $1,000 equals $628.89; $1,000 multiplied by 0.05 equals $50; $50 multiplied by 10 equals $500; $1,000 plus $500 equals $1,500; $1,628.89 minus $1,500 equals $128.89.
- Internal links checked against existing drafts in this folder on 2026-10-29: compound-growth-calculator, what-is-cagr, savings-goal-calculator, dollar-cost-averaging-explained.
- Distinction check: this explainer covers the concept and one worked example. compound-growth-calculator covers the tool for running personal figures. The overlap is limited to the pointer above.
