What Is Compound Interest?
Compound interest is often called the "eighth wonder of the world" -- a quote widely attributed to Albert Einstein. Whether or not he actually said it, the concept is genuinely powerful: compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods.
Unlike simple interest, which only earns returns on your original deposit, compound interest creates a snowball effect. Each period, your interest earns interest, and that interest earns even more interest. Over time, this exponential growth can turn modest savings into substantial wealth.
Understanding how to calculate compound interest is one of the most valuable financial skills you can develop. Whether you're saving for retirement, evaluating an investment, or trying to understand how much your debt truly costs, this guide covers everything you need to know.
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The Compound Interest Formula Explained
The standard compound interest formula is:
A = P(1 + r/n)nt
Where:
- A = the future value of the investment/loan, including interest
- P = the principal (initial amount)
- r = the annual interest rate (as a decimal, so 5% = 0.05)
- n = the number of times interest compounds per year
- t = the number of years the money is invested or borrowed
To find just the interest earned (without the principal), simply subtract P from A:
Compound Interest = A − P = P(1 + r/n)nt − P
Step-by-Step Example
Let's say you invest $5,000 at 6% annual interest, compounded monthly, for 10 years.
- P = $5,000
- r = 0.06
- n = 12 (monthly compounding)
- t = 10 years
Plugging into the formula:
A = 5,000 × (1 + 0.06/12)12×10
A = 5,000 × (1 + 0.005)120
A = 5,000 × (1.005)120
A = 5,000 × 1.8194
A = $9,096.98
You earned $4,096.98 in compound interest -- nearly doubling your money! With simple interest, you'd have earned only $3,000 ($5,000 × 0.06 × 10).
Compounding Frequency: Daily vs. Monthly vs. Yearly
The frequency at which interest compounds has a real (though sometimes small) impact on your total returns. Here's a comparison using $10,000 at 5% interest for 10 years:
| Compounding Frequency | n value | Final Amount | Interest Earned |
|---|---|---|---|
| Annually | 1 | $16,288.95 | $6,288.95 |
| Semi-annually | 2 | $16,386.16 | $6,386.16 |
| Quarterly | 4 | $16,436.19 | $6,436.19 |
| Monthly | 12 | $16,470.09 | $6,470.09 |
| Daily | 365 | $16,486.65 | $6,486.65 |
| Continuous | ∞ | $16,487.21 | $6,487.21 |
As you can see, moving from annual to daily compounding adds about $197.70 over 10 years on a $10,000 investment. The difference between daily and continuous compounding is negligible -- less than a dollar.
Daily Compounding
Daily compounding (n = 365) is used by most savings accounts and some CDs. Your bank calculates interest every day based on your current balance. This is why high-yield savings accounts often advertise their APY rather than APR -- the APY reflects the benefit of daily compounding.
Monthly Compounding
Monthly compounding (n = 12) is the most common frequency for investments, loans, and credit cards. Mortgages, car loans, and personal loans typically use monthly compounding. Many mutual funds and ETFs also distribute and compound returns monthly.
Annual Compounding
Annual compounding (n = 1) is the simplest form and is used by some bonds and CDs. While it produces the lowest returns compared to more frequent compounding, the difference is often small enough that the interest rate itself matters more than the compounding frequency.
The Rule of 72: A Quick Mental Math Trick
The Rule of 72 is an elegant shortcut that lets you estimate how long it takes to double your money without a calculator:
Years to Double = 72 ÷ Annual Interest Rate
Examples:
- At 4% interest: 72 ÷ 4 = 18 years to double
- At 6% interest: 72 ÷ 6 = 12 years to double
- At 8% interest: 72 ÷ 8 = 9 years to double
- At 10% interest: 72 ÷ 10 = 7.2 years to double
- At 12% interest: 72 ÷ 12 = 6 years to double
The Rule of 72 is most accurate for interest rates between 2% and 12%. For higher rates, the Rule of 69.3 (using 69.3 instead of 72) is slightly more precise, though less convenient for mental math.
You can also use the rule in reverse: if you want to double your money in 5 years, you need approximately 72 ÷ 5 = 14.4% annual return.
Compound Interest with Regular Contributions
Most real-world investing involves regular contributions -- adding money periodically to your investment. The formula for compound interest with regular monthly contributions is:
A = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) / (r/n)]
Where PMT is the regular monthly payment.
Example: Monthly Investing
You start with $1,000 and contribute $200/month at 7% annual interest, compounded monthly, for 30 years.
- Initial investment grows to: $1,000 × (1.005833)360 = $7,612.26
- Monthly contributions grow to: $200 × [((1.005833)360 − 1) / 0.005833] = $227,414.94
- Total: $235,027.20
- Total contributed: $1,000 + ($200 × 360) = $73,000
- Total interest earned: $162,027.20
You contributed $73,000 of your own money, but compound interest added over $162,000 -- more than twice your contributions! This demonstrates why consistent investing over long periods is so powerful.
Compound Interest vs. Simple Interest
The difference between compound and simple interest becomes dramatic over long periods:
| Year | Simple Interest (5%) | Compound Interest (5%) | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,500 | $0 |
| 5 | $12,500 | $12,762.82 | $262.82 |
| 10 | $15,000 | $16,288.95 | $1,288.95 |
| 20 | $20,000 | $26,532.98 | $6,532.98 |
| 30 | $25,000 | $43,219.42 | $18,219.42 |
| 40 | $30,000 | $70,399.89 | $40,399.89 |
After 40 years, compound interest at 5% on $10,000 yields $70,399.89 -- more than double the $30,000 from simple interest. The gap widens exponentially the longer you stay invested.
APR vs. APY: Understanding the Difference
Two terms you'll encounter frequently when dealing with compound interest:
- APR (Annual Percentage Rate): The stated annual interest rate, without accounting for compounding. This is what lenders are required to disclose.
- APY (Annual Percentage Yield): The effective annual rate after accounting for compounding. This is what you actually earn (or pay).
The formula to convert APR to APY:
APY = (1 + APR/n)n − 1
For example, a 5% APR compounded monthly:
APY = (1 + 0.05/12)12 − 1 = 5.116%
When comparing savings accounts, always compare APY, not APR. When comparing loans, the APR is more relevant as it's standardized by regulation.
Real-World Applications of Compound Interest
1. Retirement Savings (401k & IRA)
Retirement accounts are the perfect vehicle for compound interest because they grow tax-deferred (or tax-free in a Roth). A 25-year-old contributing $500/month to a 401(k) with an average 7% return will have approximately $1.2 million by age 65. Total contributions: $240,000. Compound interest contribution: nearly $1 million.
2. High-Yield Savings Accounts
In 2026, many high-yield savings accounts offer 4-5% APY with daily compounding. Parking your emergency fund in one of these accounts means your money works for you while remaining fully accessible. On a $20,000 emergency fund, that's roughly $800-$1,000 per year in passive interest.
3. Index Fund Investing
The S&P 500 has historically returned about 10% annually (roughly 7% after inflation). With compound interest and dividend reinvestment, $10,000 invested in an S&P 500 index fund in 2000 would be worth approximately $66,000 in 2026 -- a 560% return.
4. Debt: When Compounding Works Against You
Compound interest is your worst enemy when you're in debt. A $5,000 credit card balance at 22% APR with only minimum payments ($100/month) would take over 9 years to pay off, with total interest of about $5,800 -- more than the original balance!
This is why paying off high-interest debt should usually be a priority before investing. The guaranteed "return" of eliminating 22% interest often beats the uncertain return of investing.
Tips to Maximize Compound Interest
- Start early. Time is the most powerful ingredient. Even small amounts invested early outperform large amounts invested later.
- Be consistent. Set up automatic contributions. Regularity beats timing the market.
- Reinvest dividends. Always opt for dividend reinvestment (DRIP) to maximize compounding.
- Minimize fees. A 1% annual fee might seem small, but over 30 years it can consume 25-30% of your total returns.
- Use tax-advantaged accounts. 401(k)s, IRAs, and Roth accounts let compound interest work without the drag of annual taxes.
- Avoid withdrawals. Every withdrawal resets part of your compounding. Let it grow.
- Increase contributions over time. As your salary grows, increase your investment contributions proportionally.
- Pay off high-interest debt first. Eliminating compound interest working against you is mathematically equivalent to earning that rate of return.
Continuous Compounding: The Mathematical Limit
For the mathematically curious, continuous compounding represents the theoretical maximum of compounding -- where interest is calculated and added to the principal infinitely many times per period.
The formula uses Euler's number (e ≈ 2.71828):
A = P × ert
Example: $10,000 at 5% for 10 years with continuous compounding:
A = 10,000 × e0.05 × 10 = 10,000 × e0.5 = 10,000 × 1.6487 = $16,487.21
Compare this to daily compounding ($16,486.65) -- the difference is just $0.56 over 10 years. In practice, continuous compounding is used more in financial modeling and derivatives pricing than in consumer products.
Common Mistakes to Avoid
- Ignoring inflation. A 5% return with 3% inflation is really only a 2% real return. Always think in real (inflation-adjusted) terms for long-term planning.
- Confusing APR and APY. They can differ significantly, especially at higher rates. Always check which one is quoted.
- Forgetting about taxes. In taxable accounts, you owe taxes on interest each year. This reduces the effective compounding rate.
- Underestimating time. Many people start saving too late. The difference between starting at 25 vs. 35 can be hundreds of thousands of dollars.
- Interrupting compounding. Withdrawing funds or stopping contributions disrupts the exponential growth curve.
Explore More Financial Tools
Now that you understand compound interest, explore our other calculators to take control of your finances:
- Compound Interest Calculator -- Calculate your growth instantly
- Savings Goal Calculator -- How much do you need to save each month?
- Retirement Calculator -- Plan your retirement with compound growth
- ROI Calculator -- Measure your investment returns
- Mortgage Calculator Guide -- Understand your mortgage payments
- How to Calculate Percentage -- Master percentage math
Use our free compound interest calculator to project your investment growth. Calculate Compound Interest →
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Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which only earns on the original amount, compound interest grows exponentially over time.
What is the compound interest formula?
The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (decimal), n is the number of times interest compounds per year, and t is the number of years.
How does compounding frequency affect returns?
More frequent compounding yields higher returns. Daily compounding earns slightly more than monthly, which earns more than yearly. For example, $10,000 at 5% for 10 years yields $16,288.95 (annually), $16,436.19 (monthly), and $16,486.65 (daily).
What is the Rule of 72?
The Rule of 72 is a quick mental math shortcut to estimate how long it takes to double your money. Divide 72 by the annual interest rate. At 6% interest, your money doubles in approximately 72 ÷ 6 = 12 years.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the stated interest rate without compounding. APY (Annual Percentage Yield) includes the effect of compounding. APY is always equal to or higher than APR. A 5% APR compounded monthly equals a 5.116% APY.
How much will $10,000 grow in 20 years at 7%?
With annual compounding, $10,000 at 7% for 20 years grows to $38,696.84. With monthly compounding, it grows to $40,387.39. This demonstrates the power of compound interest over long time horizons.
Does compound interest work on debt too?
Yes, compound interest works on debt as well. Credit card balances, student loans, and mortgages all accrue compound interest. This is why paying only minimums on credit cards can result in paying much more than the original balance.
When should I start investing to maximize compound interest?
As early as possible. A 25-year-old investing $200/month at 7% will have about $525,000 by age 65. A 35-year-old investing the same amount will only have about $244,000. Starting 10 years earlier more than doubles the result.
What is continuous compounding?
Continuous compounding is the theoretical limit of compounding frequency, where interest is calculated and added to the principal infinitely often. The formula is A = Pe^(rt). In practice, daily compounding is very close to continuous compounding.
How do taxes affect compound interest?
Taxes can significantly reduce compound interest gains. In a taxable account, you pay taxes on interest earned each year, reducing the amount that compounds. Tax-advantaged accounts like 401(k)s and IRAs allow full compounding until withdrawal.