The most comprehensive free compound interest calculator available. Includes interactive growth charts, year-by-year breakdown, scenario comparison, inflation adjustment, APR/APY converter, and the Rule of 72. Built for students, educators, investors, and anyone who wants to understand how money grows over time.
Your base rate compared against a low and high scenario based on your variance range.
Detailed annual progression showing balance, contributions, interest earned, and real value.
| Year | Age | Opening Balance | Contributions | Interest Earned | Closing Balance | Real Value |
|---|
Convert between Annual Percentage Rate (APR) and Annual Percentage Yield (APY) for any compounding frequency.
Compound interest is the process of earning interest on both the original principal and the accumulated interest from previous periods. Unlike simple interest, which only earns on the initial deposit, compound interest grows exponentially because each period's interest becomes part of the principal for the next calculation.
Albert Einstein is often (apocryphally) credited with calling compound interest "the eighth wonder of the world." Whether or not he said it, the sentiment captures something real: the combination of time, a consistent return rate, and reinvested interest can turn modest savings into substantial wealth, and modest debt into a crushing burden.
The difference is most visible over long time periods. Consider $10,000 invested at 7% per year for 30 years:
| Type | After 10 Years | After 20 Years | After 30 Years |
|---|---|---|---|
| Simple Interest | $17,000 | $24,000 | $31,000 |
| Compound (Annual) | $19,672 | $38,697 | $76,123 |
| Compound (Monthly) | $20,097 | $40,388 | $81,165 |
| Compound (Daily) | $20,137 | $40,551 | $81,645 |
After 30 years, daily compounding produces more than 2.6 times the return of simple interest on the same principal and rate. This is the power of compounding.
Adding regular contributions dramatically accelerates growth. The same $10,000 at 7% for 30 years, with $500 added monthly, grows to approximately $680,000 rather than $81,000. The contributions themselves total $180,000 over 30 years, but the compounding effect on those contributions adds another $420,000 in interest. This is why starting early and contributing consistently is the single most impactful financial habit for long-term wealth building.
This calculator uses three distinct formulas depending on the inputs provided. Understanding these formulas helps you verify results and apply the concepts in other contexts.
$10,000 invested at 7% per year, compounded monthly, for 20 years.
A = 10,000 × (1 + 0.07/12)12×20
A = 10,000 × (1.005833)240
A = 10,000 × 4.0388
A = $40,388 (interest earned: $30,388)
$10,000 initial, $500/month contributions, 7% compounded monthly, 20 years.
PMT per period = $500 (monthly contributions, monthly compounding)
Part 1: 10,000 × (1.005833)240 = $40,388
Part 2: 500 × [(1.005833)240 - 1] / 0.005833 = 500 × 520.93 = $260,464
A = $40,388 + $260,464 = $300,852
Compounding frequency refers to how often interest is calculated and added to your principal. The more frequently interest compounds, the higher your effective annual yield (APY), even if the nominal rate (APR) stays the same.
| Frequency | Periods/Year | APY at 6% APR | $10,000 after 10 years |
|---|---|---|---|
| Annually | 1 | 6.000% | $17,908 |
| Semi-Annually | 2 | 6.090% | $18,061 |
| Quarterly | 4 | 6.136% | $18,140 |
| Monthly | 12 | 6.168% | $18,194 |
| Daily | 365 | 6.183% | $18,220 |
| Continuous | Infinite | 6.184% | $18,221 |
The difference between annual and daily compounding on $10,000 at 6% over 10 years is only $312. The compounding frequency matters, but it matters far less than the interest rate itself and the length of time invested. Chasing a slightly higher compounding frequency while accepting a lower rate is almost always counterproductive.
When comparing financial products, always compare APY (Annual Percentage Yield), not APR (Annual Percentage Rate). APY already accounts for compounding frequency and gives you the true annual return. A savings account advertising 5.9% APR compounded monthly has an APY of 6.06%. Use the APR/APY converter in this calculator to translate between the two.
The Rule of 72 is a mental math shortcut for estimating how long it takes to double an investment at a fixed annual return. Divide 72 by the annual interest rate percentage to get the approximate doubling time in years.
| Annual Return | Rule of 72 Estimate | Exact Doubling Time |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
The Rule of 72 is most accurate for rates between 6% and 10%. For rates outside this range, the Rule of 69.3 (using 69.3 instead of 72) is more precise, particularly for continuous compounding. For quick mental estimates, 72 is preferred because it has more integer divisors, making the arithmetic easier.
The Rule of 72 works equally well for understanding how inflation erodes purchasing power. At 3% inflation, the purchasing power of money halves in approximately 24 years (72 / 3). At 6% inflation, it halves in 12 years. This is why real (inflation-adjusted) returns matter as much as nominal returns.
Time is the most powerful input in compound interest. Consider two investors, both earning 7% annually:
Investor A contributes only $60,000 more in total ($240,000 vs $180,000) but ends up with more than double the final balance. The extra 10 years of compounding is worth approximately $714,000. This is why financial advisors consistently emphasise starting early above all other advice.
For savings accounts, the advertised rate is typically APY (already accounting for compounding). For term deposits, rates are usually quoted as APR. Use the APR/APY converter in this calculator to compare products accurately.
The S&P 500 has returned approximately 10% per year on average since 1926 (approximately 7% after inflation). This calculator can model long-term portfolio growth, though actual investment returns are variable and not guaranteed. The calculator assumes a fixed rate, which is a simplification for illustrative purposes.
Compound interest applies equally to debt. A credit card with 20% APR compounded daily will more than double the balance in approximately 3.5 years if no payments are made. This calculator can model debt growth by setting the principal to the debt amount and contributions to $0 (or negative for repayments).
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