Quick answer
Compound interest is interest paid on your original money and on the interest it has already earned [1]. Each year's interest joins the balance, so the next year's interest is a little larger. Over long periods, that snowball effect matters more than the starting amount.
Key points
- Compound interest is interest on the principal plus interest on earlier interest.
- Growth looks slow in the early years and speeds up later, so time is the biggest lever.
- Three things drive the result: the rate, how often interest compounds, and how much you add.
- The Rule of 72 is a quick estimate of doubling time, not an exact answer.
- Investment returns are not fixed; a steady rate in an example is an assumption, not a forecast.
#What is compound interest, in plain words?
The principal is the money you start with. Interest is what you earn for letting someone else use that money, usually stated as a yearly percentage. Investor.gov, the investor education site of the U.S. Securities and Exchange Commission (SEC), defines compound interest as "Interest paid on principal and on accumulated interest" [1].
The Consumer Financial Protection Bureau (CFPB) gives a simple example. Put $1,000 in an account paying 5% a year and you have $1,050 after one year. In year two the whole $1,050 earns 5%, so you gain $52.50 instead of $50 and end at $1,102.50 [2]. That extra $2.50 is interest earned on interest. It looks tiny, but it repeats every year on a bigger base.
Simple interest, by contrast, is paid only on the original principal. With simple interest, $1,000 at 5% earns exactly $50 every year, forever. The gap between the two methods is small at first and very large after a few decades.
#How does $10,000 grow over 30 years?
The table below follows a hypothetical $10,000 that earns a steady 6% a year, with interest added once a year and nothing withdrawn. It compares compound growth with simple interest on the same money. All figures were calculated in Python; they ignore taxes, fees and inflation.
| Year | Compound (interest added yearly) | Simple (interest on $10,000 only) | Gap |
|---|---|---|---|
| 0 | $10,000.00 | $10,000.00 | $0 |
| 5 | $13,382.26 | $13,000.00 | $382.26 |
| 10 | $17,908.48 | $16,000.00 | $1,908.48 |
| 15 | $23,965.58 | $19,000.00 | $4,965.58 |
| 20 | $32,071.35 | $22,000.00 | $10,071.35 |
| 25 | $42,918.71 | $25,000.00 | $17,918.71 |
| 30 | $57,434.91 | $28,000.00 | $29,434.91 |
$10,000 at a hypothetical 6% a year
- Compound
- Simple
Notice the shape. In the first five years the two lines barely separate. By year 30 the compound balance is more than double the simple one. This is why guides from Investor.gov stress starting early: in its classroom example, $100 at 5% a year grows to over $162 after 10 years and to nearly $340 after 25 years [3].
Worked example
Worked example: how big is each year's interest?
Same hypothetical $10,000 at 6% a year, compounded annually. Interest for a year = balance at the start of that year × 6%.
- Year 1 interest ($10,000 × 6%)
- $600.00
- Year 2 interest ($10,600 × 6%)
- $636.00
- Year 10 interest ($16,894.79 × 6%)
- $1,013.69
- Year 30 interest ($54,183.88 × 6%)
- $3,251.03
- Balance after 30 years (10,000 × 1.06^30)
- $57,434.91
The single year-30 interest payment is more than five times the year-1 payment, even though the rate never changed.
Hypothetical, calculated in Python. Real investments do not earn a fixed rate every year, and taxes, fees and inflation reduce real-world results.
#What makes compound interest grow faster or slower?
The CFPB names three levers: compounding more often, earning a higher interest rate, and adding more to your principal [2]. Compounding frequency means how often interest is calculated and added to the balance, such as yearly, monthly or daily. The SEC's free compound interest calculator on Investor.gov lets you change the starting amount, monthly additions, rate and frequency to see each effect [4].
| Compounding | Balance after 10 years | Difference vs yearly |
|---|---|---|
| Yearly | $17,908.48 | — |
| Monthly | $18,193.97 | +$285.49 |
| Daily (365) | $18,220.29 | +$311.81 |
Frequency helps, but much less than time and the rate. Regular additions matter even more. In a second hypothetical, someone adds $200 a month at a steady 6% (compounded monthly). After 20 years they have put in $48,000 and the balance is $92,408.18. After 30 years, $72,000 in and $200,903.01 at the end. After 40 years, $96,000 in and $398,298.15 at the end. The extra ten years at the end add more than the first twenty. This steady-contribution habit is also the idea behind dollar-cost averaging.
$200 a month at a hypothetical 6%: money added vs ending balance
#Is the Rule of 72 accurate?
The Rule of 72 is a mental shortcut. Investor.gov explains: "If you know the interest rate, the Rule of 72 can tell you approximately how long it will take for your investment to double in value." You divide 72 by the yearly rate; at 9%, money doubles in about 8 years [3]. The key word is approximately.
The exact doubling time for yearly compounding is ln(2) ÷ ln(1 + rate). We calculated both for common rates. The shortcut is very close between roughly 6% and 10%, drifts a little at higher rates, and overstates the wait noticeably at very low rates.
| Yearly rate | Rule of 72 (72 ÷ rate) | Exact years | Shortcut error |
|---|---|---|---|
| 1% | 72.0 | 69.66 | +2.34 years |
| 2% | 36.0 | 35.00 | +1.00 year |
| 4% | 18.0 | 17.67 | +0.33 years |
| 6% | 12.0 | 11.90 | +0.10 years |
| 8% | 9.0 | 9.01 | −0.01 years |
| 10% | 7.2 | 7.27 | −0.07 years |
| 12% | 6.0 | 6.12 | −0.12 years |
| 20% | 3.6 | 3.80 | −0.20 years |
#Does compounding work against you too?
Yes. The same math applies to anything that charges interest on a growing balance. If unpaid interest on a debt is added to what you owe, you then pay interest on that interest. That is why the order of money decisions matters, which we cover in pay off debt or invest. Ongoing costs also compound: a yearly fund fee is taken from a balance that would otherwise have kept growing, as explained in expense ratios and fund fees.
Inflation is the other quiet drag. A balance can grow in dollars while buying less, because prices rise too. See what inflation is for how to think about growth after rising prices.
Common beginner mistakes
Waiting for a bigger amount before starting
In the examples above, time does more work than the starting sum. A small amount left alone for longer can end larger than a bigger amount started later.
Treating an example rate as a promise
A fixed 6% is a teaching assumption. Stock and fund returns go up and down, and some years are negative. Use examples to understand the mechanism, not to plan on a specific number.
Using the Rule of 72 for precise planning
It is close in the middle range but off by more than two years at a 1% rate. For real decisions, run the exact numbers in a calculator.
Forgetting fees, taxes and inflation
Each of these trims the rate that actually compounds for you. A one-point difference in the rate changes the 30-year result a lot.
What's the bottom line?
Compound interest is simple in idea and powerful over time: interest joins the balance and starts earning too. The early years look unimpressive, and the later years do most of the work, which is why time and regular additions matter more than finding a slightly better rate. Use the Rule of 72 for a rough sense of scale and a calculator for real decisions. Then look at the other side of the same math — why an emergency fund comes first and how high-interest debt compounds against you.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal. Compound interest is also paid on interest you already earned, so the balance grows on a larger base each period.
Does compound interest apply to stocks?
Stocks do not pay interest, but the idea is similar: if gains and dividends stay invested, future gains are earned on a larger amount. Unlike a savings rate, stock returns are not fixed and can be negative.
How often should interest compound?
More frequent compounding helps slightly. In our example, daily compounding added about $312 over 10 years on $10,000 compared with yearly. The rate, the time and your additions matter much more.
Where can I test my own numbers?
Investor.gov, run by the SEC, offers a free compound interest calculator where you can change the starting amount, monthly additions, rate and compounding frequency.
Sources
Grade A = primary source (regulator, government agency, official rulebook or the index provider's own documents). Numbers in brackets in the text point here.
- U.S. SEC — Investor.gov. Compound Interest (glossary) (2026). Accessed 2026-10-03.A
- Consumer Financial Protection Bureau. How does compound interest work? (2026). Accessed 2026-10-03.A
- U.S. SEC — Investor.gov. What is compound interest? (2026). Accessed 2026-10-03.A
- U.S. SEC — Investor.gov. Compound Interest Calculator (2026). Accessed 2026-10-03.A
This page is general education, not personal financial, tax or legal advice. Figures in worked examples are hypothetical and calculated before taxes and fees unless stated. Rules and limits change; check the linked primary sources for the current version. How we check every page.
