Compound Interest Calculator
Calculate how your savings and investments grow over time with the power of compound interest. See year-by-year breakdowns and visualize your wealth growth.
- Compound interest = "interest on interest" — your earnings generate their own earnings
- More frequent compounding = more growth — daily beats monthly beats yearly
- Time is the biggest factor — start early, even with small amounts
- The Rule of 72: divide 72 by your interest rate to estimate years to double
- Regular contributions dramatically accelerate growth — consistency beats timing
| Year | Principal | Interest | Balance |
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| Year | Initial | Contributions | Interest | Balance |
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CAGR = (Ending Value / Starting Value)^(1/Years) - 1
A = P × e^(r × t)
Where e ≈ 2.71828 (Euler's number)
How Compound Interest Works
Compound interest is the process where interest earned on an investment is reinvested, so that in subsequent periods, interest is earned on both the original principal and the previously accumulated interest. This creates exponential growth over time, often called "interest on interest." The concept is recognized by the U.S. Securities and Exchange Commission (SEC) as a foundational principle of long-term investing.
The basic formula is A = P(1 + r/n)nt, where P is your principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. The more frequently interest compounds, the faster your money grows. For a deeper dive into every variable, see our compound interest formula guide.
Compound Interest by Account Type
Where you hold your money determines how compound interest applies. Different account types offer different rates, tax treatments, and risk levels. The FDIC insures bank deposits up to $250,000, while investment accounts carry market risk but historically higher returns.
| Account Type | Typical Rate | Compounding | $10,000 After 20 Years | Risk Level |
|---|---|---|---|---|
| High-Yield Savings | 4.00% – 5.00% APY | Daily | $21,911 – $26,533 | Very Low (FDIC insured) |
| Certificates of Deposit | 4.25% – 5.25% APY | Daily | $23,050 – $27,862 | Very Low (FDIC insured) |
| U.S. Treasury Bonds | 4.00% – 4.50% | Semi-annually | $21,911 – $24,117 | Very Low |
| S&P 500 Index Fund | ~10% historical avg | Market-driven | $67,275 | High (short-term) |
| 401(k) Account | 7% – 10% avg | Market-driven | $38,697 – $67,275 | Moderate-High |
| Roth IRA | 7% – 10% avg | Market-driven | $38,697 – $67,275 (tax-free) | Moderate-High |
Rates shown are approximate for early 2026. Savings account and CD rates are set by banks and influenced by the Federal Reserve's federal funds rate. Stock market returns reflect long-term historical averages and are not guaranteed.
A Brief History of Compound Interest
Compound interest is not a modern invention. Ancient Mesopotamian clay tablets from around 2400 BCE show early forms of interest-on-interest calculations. The mathematical formula as we know it was formalized in 17th-century Europe, and Jacob Bernoulli's work on continuous compounding in 1683 led to the discovery of the mathematical constant e (approximately 2.71828).
Benjamin Franklin demonstrated compound interest's power in practice. In 1790, he left 1,000 pounds (about $4,400) each to the cities of Boston and Philadelphia, with instructions to invest the money and let it compound for 200 years. By 1990, Boston's fund had grown to $4.5 million and Philadelphia's to $2 million — real-world proof of what compounding does across centuries. Today, the principle of compound interest underpins everything from savings accounts to retirement planning.
Why Compounding Frequency Matters
| Frequency | Periods/Year | $10,000 at 7% for 10 Years |
|---|---|---|
| Annually | 1 | $19,671.51 |
| Quarterly | 4 | $19,897.89 |
| Monthly | 12 | $19,966.17 |
| Daily | 365 | $20,137.53 |
| Continuous | ∞ | $20,137.53 |
The difference between annual and daily compounding on $10,000 at 7% is $466 over 10 years. While meaningful, the jump from daily to continuous compounding is negligible. Most high-yield savings accounts and CDs already compound daily, so you are getting near-optimal frequency. For a full analysis, see our compounding frequency comparison.
Frequently Asked Questions
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (calculated only on the principal), compound interest grows exponentially over time. The concept is explained in detail by the SEC's investor education resources.
More frequent compounding produces slightly more growth. Daily compounding earns more than monthly, which earns more than annually. However, the difference between daily and continuous compounding is negligible. For savings accounts and CDs, daily compounding is the standard.
The Rule of 72 is a quick way to estimate how long it takes to double your money. Divide 72 by your annual interest rate: at 7%, your money doubles in approximately 72 ÷ 7 ≈ 10.3 years. It is most accurate for rates between 5% and 12%.
APR (Annual Percentage Rate) is the stated interest rate without compounding. APY (Annual Percentage Yield) accounts for compounding and reflects the actual rate you earn. A 5% APR compounded daily produces a 5.13% APY. The Consumer Financial Protection Bureau provides additional guidance on understanding these rates.
Regular monthly contributions dramatically accelerate growth. Each contribution begins earning compound interest immediately, creating multiple streams of compounding. For example, $500/month at 7% for 30 years grows to over $566,000 — with more than $386,000 coming from interest alone. Use our Monthly Contributions tab above to see the impact.
Compound interest works for you on savings and investments, but against you on debt. Credit card debt compounds daily at high rates (18-30%), which is why the CFPB recommends paying off high-interest debt as a priority before investing. See our common compound interest mistakes guide for more.
At a 7% average annual return: investing $500/month from age 25 to 65 yields approximately $1,199,832. Starting at 35 requires roughly $1,000/month to reach the same goal. The earlier you start, the less you need to contribute each month. Use the Goal tab in our calculator to find your exact number based on your starting point and timeline.
Compound interest is earned on high-yield savings accounts, certificates of deposit (CDs), money market accounts, bonds, and through reinvested dividends in stock investments. Tax-advantaged accounts like 401(k)s and Roth IRAs amplify compounding by sheltering your growth from annual taxes. FDIC-insured options carry no risk to your principal up to $250,000 per depositor.
Simple interest is calculated only on the original principal amount, while compound interest is calculated on the principal plus all previously accumulated interest. For example, $10,000 at 7% simple interest earns $700 every year, totaling $24,000 after 20 years. With compound interest (monthly), the same investment grows to $40,387 — a $16,387 difference. Over longer periods, the gap widens dramatically. Read our full simple vs compound interest guide for detailed side-by-side comparisons with charts.
Inflation erodes the purchasing power of your money over time, which means your real (inflation-adjusted) return is lower than your nominal return. If your investment earns 7% annually but inflation is 3%, your real return is roughly 4%. Over 30 years, $100,000 growing at 7% nominally becomes $761,226, but in today's dollars (adjusted for 3% inflation), that is only about $313,725 in purchasing power. To maintain real growth, your investment returns must consistently outpace inflation. The Bureau of Labor Statistics CPI data tracks historical inflation rates, and Federal Reserve interest rate data helps you compare nominal rates across different periods.
Absolutely. Compound interest is a double-edged sword. When you carry debt — especially high-interest credit card debt at 18% to 30% APR — compounding works against you. A $5,000 credit card balance at 22% APR, with only minimum payments, can take over 20 years to pay off and cost more than $10,000 in interest alone. Student loans, auto loans, and mortgages also compound, though typically at lower rates. The Consumer Financial Protection Bureau (CFPB) recommends prioritizing high-interest debt repayment before aggressive investing, because the guaranteed "return" from eliminating a 22% debt usually exceeds potential investment gains.
Learn More About Compound Interest
Our free guides cover every aspect of compound interest, from the basics for beginners to advanced strategies for maximizing growth. Whether you are comparing simple versus compound interest, understanding CAGR, or learning the Rule of 72, our guides provide clear explanations with real numbers.
For additional resources, the SEC's compound interest calculator offers an independent tool, and Investopedia's compound interest overview provides supplementary educational content. The Federal Reserve Economic Data (FRED) database is an excellent source for historical interest rate data.
The Mathematics Behind Compound Interest
Understanding the compound interest formula is essential for making informed financial decisions. The standard formula is:
A = P(1 + r/n)nt
Each variable plays a specific role in determining your final balance:
- A = the future value of the investment, including interest
- P = the principal (initial investment amount)
- r = the annual interest rate (expressed as a decimal, so 7% = 0.07)
- n = the number of times interest is compounded per year (12 for monthly compounding, 365 for daily compounding)
- t = the number of years the money is invested
Worked Example: $10,000 at 7% for 20 Years (Monthly Compounding)
Let us walk through the formula step by step with a practical example. Suppose you invest $10,000 at a 7% annual interest rate, compounded monthly, for 20 years:
- Identify the variables: P = $10,000, r = 0.07, n = 12, t = 20
- Calculate r/n: 0.07 / 12 = 0.005833
- Calculate (1 + r/n): 1 + 0.005833 = 1.005833
- Calculate nt: 12 × 20 = 240 (total compounding periods)
- Raise to the power: 1.005833240 = 4.0387
- Multiply by P: $10,000 × 4.0387 = $40,387.39
Your $10,000 investment grows to $40,387.39 — meaning you earned $30,387.39 in interest alone, more than three times your original deposit. This is the power of compound interest over long time horizons. The SEC's compound interest calculator can be used to verify these calculations independently. For more real-world examples and variations of this formula, see our detailed guide on how compound interest works.
Historical Context: How Interest Rates Have Changed
Interest rates have varied dramatically over the past several decades, influenced by Federal Reserve monetary policy, inflation, and broader economic conditions. Understanding this history helps set realistic expectations for your investment returns. The Federal Reserve publishes selected interest rate data going back decades, and the FRED Federal Funds Rate History provides a comprehensive look at rate trends.
In the early 1980s, the Federal Funds Rate peaked above 20% as the Fed fought double-digit inflation. Savings accounts offered yields of 10% or more. By contrast, the 2010s saw near-zero interest rates following the 2008 financial crisis, with savings accounts yielding less than 0.10%. The 2020s brought another shift: the Fed raised rates aggressively in 2022-2023 to combat post-pandemic inflation, pushing high-yield savings rates above 5% for the first time in nearly two decades.
Historical Average Returns by Asset Class
The table below shows approximate average annual returns across different asset classes and decades. These figures illustrate why long-term investors often favor equities despite their short-term volatility, and why the choice of account type profoundly impacts how compound interest grows your wealth.
| Decade | Savings Accounts | CDs (5-Year) | 10-Year Treasury Bonds | S&P 500 (Stocks) | Real Estate (REIT Index) |
|---|---|---|---|---|---|
| 1980s | 5.0% – 10.0% | 8.0% – 12.0% | 10.0% – 13.0% | 17.6% avg | 9.0% – 12.0% |
| 1990s | 2.0% – 5.0% | 4.0% – 7.0% | 6.0% – 8.0% | 18.2% avg | 7.0% – 10.0% |
| 2000s | 0.5% – 4.0% | 2.0% – 5.0% | 4.0% – 6.0% | −0.9% avg | 6.0% – 10.0% |
| 2010s | 0.01% – 2.0% | 0.5% – 3.0% | 1.5% – 3.0% | 13.6% avg | 8.0% – 12.0% |
| 2020s (to date) | 0.01% – 5.0% | 0.5% – 5.25% | 1.5% – 5.0% | 12.0% avg* | 5.0% – 10.0% |
*2020s stock returns through early 2026; all figures are approximate annualized averages. Sources: FRED, S&P Dow Jones Indices, NAREIT.
The key takeaway is that long-term stock market returns have averaged around 10% annually over the past century, while fixed-income instruments offer lower but more stable returns. When using our compound interest calculator, a rate of 7% is a commonly used estimate for inflation-adjusted stock market growth, while 4-5% is reasonable for current high-yield savings. For a beginner's guide to choosing the right assumptions for your calculations, see our educational resources.
Compound Interest Across Different Account Types
Not all compounding is created equal. The account where you hold your money determines the interest rate, compounding frequency, tax treatment, and level of risk — all of which profoundly affect your long-term growth. Understanding these differences can help you maximize your returns while managing risk appropriately.
Savings Accounts and CDs
High-yield savings accounts and certificates of deposit are the safest places to earn compound interest. They are insured by the FDIC up to $250,000 per depositor per institution. Both typically compound interest daily and credit it monthly. As of early 2026, the best high-yield savings accounts offer 4.0% to 5.0% APY, while 5-year CDs can reach 4.25% to 5.25% APY. The trade-off with CDs is reduced liquidity — you agree to lock up your money for a set term.
Retirement Accounts: 401(k)s and Roth IRAs
Tax-advantaged retirement accounts like 401(k)s and Roth IRAs supercharge compounding by deferring or eliminating taxes on your investment gains. In a traditional 401(k), contributions are tax-deductible and growth is tax-deferred until withdrawal. In a Roth IRA, contributions are made with after-tax dollars, but all growth and qualified withdrawals are completely tax-free. The CFPB's retirement savings tools can help you understand how these accounts fit into your overall financial plan.
Stock Market and Index Funds
Investing in stocks or stock index funds provides compound growth through both price appreciation and reinvested dividends. While the S&P 500 has historically returned roughly 10% annually (about 7% after inflation), returns are volatile in any given year. The compounding effect in the stock market comes from keeping investments working through market cycles rather than from a fixed interest rate. Dollar-cost averaging — investing a fixed amount at regular intervals — pairs well with long-term compounding strategies.
Side-by-Side Comparison
The table below compares how $10,000 grows across different account types over 10, 20, and 30 years, assuming typical returns and monthly compounding where applicable:
| Account Type | Assumed Annual Return | Tax Treatment | $10K after 10 Years | $10K after 20 Years | $10K after 30 Years |
|---|---|---|---|---|---|
| High-Yield Savings | 4.5% APY | Taxable annually | $15,530 | $24,117 | $37,453 |
| 5-Year CD (rolled over) | 4.75% APY | Taxable annually | $15,905 | $25,291 | $40,237 |
| U.S. Treasury Bonds | 4.25% | State tax-exempt | $15,230 | $23,183 | $35,286 |
| 401(k) — Stocks | 7.0% | Tax-deferred | $20,097 | $40,387 | $81,165 |
| Roth IRA — Stocks | 7.0% | Tax-free growth | $20,097 | $40,387 | $81,165 |
| S&P 500 Index Fund | 10.0% | Capital gains tax | $27,070 | $73,281 | $198,374 |
Note: Returns are approximate and assume reinvestment of all earnings. Tax effects on final withdrawal amounts are not reflected in the taxable account figures. Actual results will vary based on specific rates, fees, and market conditions. For personalized calculations, use the calculator above or the SEC's compound interest calculator.
The Power of Starting Early
Of all the factors that influence compound interest — rate of return, contribution amount, compounding frequency — time is the most powerful. The reason is mathematical: compound interest grows exponentially, not linearly, which means each additional year adds more absolute growth than the year before. This is why starting early, even with modest amounts, creates such a dramatic advantage over time.
Consider three investors, each contributing $500 per month at a 7% average annual return (compounded monthly), but starting at different ages:
| Milestone | Starting at Age 25 | Starting at Age 35 | Starting at Age 45 |
|---|---|---|---|
| Monthly contribution | $500 | $500 | $500 |
| Years of investing | 40 years | 30 years | 20 years |
| Total contributed | $240,000 | $180,000 | $120,000 |
| Balance at Age 35 | $86,541 | $0 (not started) | $0 (not started) |
| Balance at Age 45 | $262,481 | $86,541 | $0 (not started) |
| Balance at Age 55 | $621,079 | $262,481 | $86,541 |
| Balance at Age 65 | $1,320,571 | $621,079 | $262,481 |
| Total interest earned | $1,080,571 | $441,079 | $142,481 |
| Interest as % of total | 81.8% | 71.1% | 54.3% |
The investor who starts at age 25 contributes only $60,000 more than the one who starts at age 35 ($240,000 vs $180,000), yet ends up with more than twice the final balance ($1,320,571 vs $621,079). The extra 10 years of compounding generates an additional $699,492. Meanwhile, the investor starting at age 45 — despite contributing $120,000 — accumulates less than 20% of what the age-25 investor achieves.
This is why financial advisors universally recommend beginning to invest as early as possible. Even if you can only afford $100 or $200 per month in your twenties, those early contributions have the longest runway for compounding and contribute disproportionately to your final balance. The CFPB's retirement savings tools can help you model different starting points and contribution levels. For additional strategies on getting started, read our beginner's guide and tips on how to maximize your returns through consistent investing.