The Quick Answer
Compound interest is interest earned on both your original deposit and on all interest earned so far. The formula is:
A = P × (1 + r/n)^(n×t)
Where P is the starting amount, r is the annual rate (as a decimal), n is how many times per year interest compounds, and t is the number of years.
A $10,000 deposit at 6% compounded monthly for 10 years grows to $18,193.97 — of which $8,193.97 is earned interest. The same deposit with simple interest would only reach $16,000.
Use the compound interest calculator to model any scenario instantly.
Why Compound Interest Matters
With simple interest, $10,000 at 6% earns exactly $600 per year, every year. The interest amount never changes because it is always calculated on the original $10,000. After 10 years: $16,000.
With compound interest, each period's interest is added to the balance. The next period then earns interest on that larger amount. Each cycle produces slightly more interest than the last. After 10 years with monthly compounding: $18,193.97.
That's $2,193.97 more — and the gap gets much wider over longer periods:
| Time period | Simple interest (6%) | Compound interest (6%, monthly) | Difference |
|---|---|---|---|
| 5 years | $13,000 | $13,489 | $489 |
| 10 years | $16,000 | $18,194 | $2,194 |
| 20 years | $22,000 | $33,102 | $11,102 |
| 30 years | $28,000 | $60,226 | $32,226 |
| 40 years | $34,000 | $109,357 | $75,357 |
The key insight: compound interest accelerates. The longer the time horizon, the more dramatic the effect. At 30 years, compound interest has earned more than double what simple interest earns.
The Compound Interest Formula Explained Step by Step
A = P × (1 + r/n)^(n×t)
Each variable:
- A = future value (the total amount you end up with)
- P = principal (the starting deposit)
- r = annual interest rate, expressed as a decimal (6% = 0.06)
- n = number of compounding periods per year (12 for monthly, 4 for quarterly, 365 for daily)
- t = time in years
Worked Example 1: Basic Compound Interest
$5,000 at 8% for 5 years, compounded quarterly.
- P = 5,000
- r = 0.08 (8% as a decimal)
- n = 4 (quarterly = 4 times per year)
- t = 5 (5 years)
Plug in:
A = 5,000 × (1 + 0.08/4)^(4×5)
A = 5,000 × (1 + 0.02)^20
A = 5,000 × (1.02)^20
A = 5,000 × 1.48595
A = $7,429.74
You deposited $5,000 and earned $2,429.74 in interest over 5 years.
Worked Example 2: $10,000 at 5% for 20 Years
This is one of the most commonly searched compound interest scenarios.
- P = $10,000, r = 0.05, n = 12 (monthly), t = 20
A = 10,000 × (1 + 0.05/12)^(12×20)
A = 10,000 × (1.004167)^240
A = 10,000 × 2.71264
A = $27,126.40
Your $10,000 grew to $27,126.40 — almost tripling in 20 years at just 5%.
Worked Example 3: Edge Case — 0% Interest
If the interest rate is 0%, the formula simplifies:
A = P × (1 + 0)^(n×t) = P × 1 = P
The balance never changes. This is the baseline — compound interest only works when the rate is greater than zero.
How Compounding Frequency Changes the Result
The more often interest compounds, the more you earn — but with diminishing returns as frequency increases.
Here's $10,000 at 6% for 10 years at different frequencies:
| Frequency | Periods/year (n) | Future value | Interest earned |
|---|---|---|---|
| Annually | 1 | $17,908.48 | $7,908.48 |
| Semi-annually | 2 | $18,061.11 | $8,061.11 |
| Quarterly | 4 | $18,140.18 | $8,140.18 |
| Monthly | 12 | $18,193.97 | $8,193.97 |
| Weekly | 52 | $18,214.59 | $8,214.59 |
| Daily | 365 | $18,220.44 | $8,220.44 |
| Continuous | ∞ | $18,221.19 | $8,221.19 |
Going from annual to monthly compounding adds $285.49. Going from monthly to daily adds only $26.47. The biggest improvement comes from the first increase in frequency.
Daily vs. Monthly Compounding
Many people search for whether daily compounding is meaningfully better than monthly. The answer: barely. On a $10,000 balance at 6% over 10 years, daily compounding earns just $26.47 more than monthly. On a $100,000 balance, the difference is $264.70 over 10 years. Unless you are dealing with very large balances or very long time periods, the difference is negligible.
The real takeaway: any compounding is dramatically better than no compounding (simple interest). Whether you compound monthly or daily matters far less than whether you compound at all.
Continuous Compounding
Continuous compounding is the theoretical limit — interest compounds an infinite number of times per year. The formula simplifies to:
A = P × e^(r×t)
Where e is Euler's number (approximately 2.71828).
Example: Continuous Compounding
$10,000 at 6% for 10 years, compounded continuously:
A = 10,000 × e^(0.06 × 10)
A = 10,000 × e^0.6
A = 10,000 × 1.82212
A = $18,221.19
Compare this to daily compounding ($18,220.44) — the difference is just $0.75. Continuous compounding is primarily a mathematical concept used in finance theory. In practice, daily compounding gets you 99.99% of the way there.
Adding Regular Contributions
Regular contributions have a powerful effect because each deposit also earns compound interest for its remaining time in the account.
The formula for the future value of regular contributions (annuity) is:
FV = C × [((1 + r/n)^(n×t) − 1) / (r/n)]
Where C is the contribution per compounding period. The total future value is the sum of the compounded principal plus this annuity value.
Example: $5,000 Start + $200/Month at 7% for 20 Years
- Total deposits: $5,000 + ($200 × 12 × 20) = $53,000
- Future value: $124,298.69
- Interest earned: $71,298.69
More than half of the final balance is interest, not deposits. This demonstrates the core power of combining regular contributions with compound interest.
Example: $0 Start + $100/Month at 6% for 30 Years
Even starting with nothing:
- Total deposits: $100 × 12 × 30 = $36,000
- Future value: $100,451.50
- Interest earned: $64,451.50
$36,000 in deposits became over $100,000 — with nearly two-thirds of the final balance being earned interest. This illustrates why starting early with even small amounts matters.
How Much Do Contributions Accelerate Growth?
Here's the effect of adding $200/month to a $10,000 initial deposit at 6%, compounded monthly:
| Time | Without contributions | With $200/month | Extra from contributions |
|---|---|---|---|
| 5 years | $13,489 | $27,430 | $13,941 |
| 10 years | $18,194 | $46,204 | $28,010 |
| 20 years | $33,102 | $92,408 | $59,306 |
| 30 years | $60,226 | $167,063 | $106,837 |
At 30 years, the contributions and their earned interest add over $100,000 to the balance.
APY: Comparing Apples to Apples
Banks often quote a nominal annual rate, but compound at different frequencies. APY (Annual Percentage Yield) is the effective annual rate after compounding:
APY = (1 + r/n)^n − 1
APY Examples
| Nominal rate | Compounding | APY |
|---|---|---|
| 6% | Annually | 6.000% |
| 6% | Quarterly | 6.136% |
| 6% | Monthly | 6.168% |
| 6% | Daily | 6.183% |
APR vs. APY: What's the Difference?
This is one of the most commonly confused financial concepts:
- APR (Annual Percentage Rate) is the nominal rate — the stated rate before compounding effects. APR is commonly used for loans and credit cards.
- APY (Annual Percentage Yield) is the effective rate — what you actually earn (or owe) after compounding. APY is commonly used for savings accounts and CDs.
A 6% APR compounded monthly has an APY of 6.168%. When comparing two savings accounts, always compare their APY — not their stated rates. A 5.9% account compounding daily (APY 6.077%) actually beats a 6.0% account compounding annually (APY 6.0%).
For loans, the same principle applies in reverse: a lower APR with frequent compounding can result in a higher effective cost than a slightly higher APR with annual compounding. The loan calculator can help model specific scenarios.
Compound Interest vs. Simple Interest
| Simple interest | Compound interest | |
|---|---|---|
| Interest basis | Original principal only | Principal + accumulated interest |
| Growth pattern | Linear (same amount each year) | Exponential (accelerating) |
| Formula | A = P × (1 + r×t) | A = P × (1 + r/n)^(n×t) |
| Graph shape | Straight line | Upward curve |
| Common usage | Some bonds, short-term loans | Savings accounts, investments, mortgages |
When Does Simple Interest Apply?
Simple interest is less common than compound interest, but it appears in:
- Some government bonds (e.g., US Treasury I Bonds pay simple interest on the principal)
- Short-term personal loans where interest is calculated on the original balance
- Promissory notes between individuals
- Some auto loans (though most use amortization schedules)
Most savings accounts, CDs, money market accounts, and investment returns use compound interest. The simple interest calculator can help compare the two side by side.
The Rule of 72
A quick mental shortcut: divide 72 by your interest rate to estimate how many years it takes to double your money.
Years to double ≈ 72 ÷ interest rate
| Interest rate | Rule of 72 estimate | Actual (monthly compounding) |
|---|---|---|
| 2% | 36 years | 34.7 years |
| 4% | 18 years | 17.4 years |
| 6% | 12 years | 11.6 years |
| 8% | 9 years | 8.7 years |
| 10% | 7.2 years | 7.0 years |
| 12% | 6 years | 5.8 years |
The Rule of 72 is most accurate for rates between 2% and 15%. Outside that range, it becomes less precise.
Why 72?
The number 72 is used because it is a good approximation of 100 × ln(2), which equals about 69.3. The number 72 is preferred because it is divisible by more integers (2, 3, 4, 6, 8, 9, 12), making the mental math easier. Some financial professionals use the "Rule of 69.3" for greater accuracy with continuous compounding.
Rule of 72 for Tripling
To estimate the time to triple your money, use the Rule of 115 instead:
Years to triple ≈ 115 ÷ interest rate
At 6%: 115 ÷ 6 ≈ 19.2 years (actual: 18.6 years with monthly compounding).
How $10,000 Grows Over Time
One of the most commonly searched questions is: "How much will $10,000 be worth in X years?" Here's a reference table at various rates with monthly compounding and no additional contributions:
| Years | 3% | 5% | 7% | 10% |
|---|---|---|---|---|
| 5 | $11,616 | $12,834 | $14,176 | $16,453 |
| 10 | $13,494 | $16,470 | $20,097 | $27,070 |
| 15 | $15,675 | $21,137 | $28,492 | $44,539 |
| 20 | $18,208 | $27,126 | $40,387 | $73,281 |
| 25 | $21,152 | $34,813 | $57,254 | $120,569 |
| 30 | $24,573 | $44,677 | $81,165 | $198,374 |
At 7% for 30 years, your $10,000 grows to over $81,000. At 10% for 30 years, it grows to nearly $200,000. This is the effect of compounding over long time periods — the growth becomes exponential rather than linear.
The Effect of Starting Early
One of the most powerful demonstrations of compound interest is comparing two scenarios: starting early with small amounts versus starting later with larger amounts.
Example: Starting at 25 vs. 35
Person A starts saving $200/month at age 25 and stops at 35 (10 years of contributions). They then leave the money invested until age 65. Total contributed: $24,000.
Person B starts saving $200/month at age 35 and continues until age 65 (30 years of contributions). Total contributed: $72,000.
At 7% annual return, compounded monthly:
| Person A (started at 25) | Person B (started at 35) | |
|---|---|---|
| Years of contributions | 10 | 30 |
| Total contributed | $24,000 | $72,000 |
| Balance at 65 | $349,102 | $243,994 |
Person A contributed $48,000 less but ended up with $105,000 more. The extra 10 years of compounding on those early contributions more than compensated for the fact that Person B contributed three times as much money.
This is not financial advice — it's a mathematical illustration of how compounding rewards time over amount.
Common Mistakes
1. Confusing Rate and APY
A "6% rate compounded monthly" is not the same as "6% APY." The rate is the nominal figure; APY is the effective annual return. Always check which one is being quoted. See the APR vs. APY section above.
2. Ignoring Inflation
Compound interest grows your nominal balance, but inflation erodes purchasing power. A 6% return with 3% inflation gives roughly 3% real growth. This calculator and this article show nominal values. For inflation-adjusted projections, use an inflation calculator.
3. Assuming Constant Rates
The formula uses a fixed rate. In practice, interest rates on savings accounts, bonds, and investments fluctuate year to year. The result is an estimate based on the rate you enter, not a guarantee of future performance.
4. Forgetting That Time Matters More Than Rate
Doubling your time horizon has a far bigger effect than slightly increasing your rate. Starting 10 years earlier often matters more than finding an extra 1-2% return. The starting early example above demonstrates this clearly.
5. Ignoring Taxes and Fees
Interest and investment gains are often subject to taxes. A 6% gross return with a 25% tax rate on interest becomes approximately 4.5% after tax. Management fees on investment accounts also reduce the effective rate. These factors are not included in the basic compound interest formula.
6. Confusing Compounding Frequency with Payment Frequency
A savings account that compounds monthly doesn't necessarily pay interest monthly. Compounding frequency determines how often interest is calculated and added to the balance. Payment frequency determines how often you can withdraw it. They are often the same but not always.
Frequently Asked Questions
What is compound interest in simple terms?
Compound interest is "interest on interest." You earn interest on your original deposit, and then in the next period, you earn interest on the original deposit plus the interest you already earned. This creates a snowball effect where your money grows faster over time.
How do I calculate compound interest?
Use the formula: A = P × (1 + r/n)^(n×t). Divide the annual rate by the number of compounding periods, add 1, raise it to the power of total periods, then multiply by your principal. Or use our compound interest calculator for instant results with a year-by-year breakdown.
How much will $10,000 be worth in 10 years?
It depends on the interest rate. At 5% compounded monthly: $16,470. At 7%: $20,097. At 10%: $27,070. See the full reference table above for more rates and time periods.
How much will $10,000 be worth in 20 years?
At 5% compounded monthly: $27,126. At 7%: $40,387. At 10%: $73,281. The longer the time period, the more dramatic the effect of even small differences in rate.
What is the difference between APR and APY?
APR is the nominal annual rate before accounting for compounding. APY is the effective annual rate after compounding. APY is always equal to or higher than APR. A 6% APR compounded monthly gives a 6.168% APY. When comparing savings accounts, use APY. The APR vs. APY section explains this in detail.
Does compound interest work against you on loans?
Yes. On loans, compound interest means you owe interest on your unpaid interest. This is why credit card debt can grow so quickly — unpaid balances compound, often daily. The same mathematical principle that helps savings grow works against borrowers.
How much should I save per month?
This depends on your goal, time horizon, and expected rate of return. The compound interest formula can model different scenarios. For example, to reach $100,000 in 20 years at 7%, you would need about $200/month with a $10,000 starting balance. Use the savings goal calculator to find the exact contribution needed for your target.
Is daily compounding better than monthly?
Technically yes, but the difference is tiny. On $10,000 at 6% for 10 years, daily compounding earns $26.47 more than monthly. See daily vs. monthly compounding above for the full comparison.
What is continuous compounding?
Continuous compounding is the theoretical limit where interest compounds an infinite number of times per year. The formula is A = P × e^(rt). In practice, daily compounding is nearly identical to continuous compounding. See the continuous compounding section for worked examples.
What is the Rule of 72?
The Rule of 72 is a mental math shortcut: divide 72 by the interest rate to estimate how many years it takes to double your money. At 6%, your money doubles in about 12 years (72 ÷ 6). See the Rule of 72 section for a full accuracy table.
Can compound interest make you rich?
Compound interest is a mathematical function, not a wealth strategy. It demonstrates that consistent saving over long periods produces exponential growth. The practical result depends on the interest rate available, how much you save, and how long you leave it invested. What compound interest shows clearly is that time is the most powerful variable — starting early with small amounts can outperform starting late with large amounts.
How does compound interest work on a savings account?
A savings account with compound interest calculates interest on your balance at regular intervals (usually daily or monthly), then adds that interest to your balance. Your next interest calculation uses the new, higher balance. Most savings accounts in the US compound daily and credit interest monthly.
What is the difference between compound interest and compounding returns?
Compound interest refers specifically to interest calculated on principal plus accumulated interest. Compounding returns is a broader term that includes any type of reinvested return — including stock dividends, capital gains, and interest. The math is the same, but "compound interest" typically applies to fixed-rate instruments like savings accounts and bonds.
What This Calculator Does Not Do
- It does not account for taxes on earned interest or capital gains
- It does not adjust for inflation (use the inflation calculator for that)
- It assumes a fixed interest rate for the entire period
- It assumes contributions are made at regular intervals
- It does not model variable or tiered interest rates
- It does not provide financial advice
This tool and this article are educational. They demonstrate how the compound interest formula works mathematically. For decisions about investments or savings, consult a qualified financial professional.
Try It Yourself
Use the compound interest calculator to model your own scenario. Enter your starting amount, rate, time period, and optional contributions to see the future value, total interest earned, and a year-by-year breakdown with an interactive growth chart.