Compound Interest Calculator
Compounding means the interest you earn starts earning interest of its own. Enter an initial investment, monthly contribution, expected return, and time horizon to see year-by-year compound growth.
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Educational purposes only.
This calculator illustrates the concept of compound interest with hypothetical returns. Actual investment returns vary and are not guaranteed. Past performance does not indicate future results.
Educational purposes only. These calculators illustrate concepts and do not constitute investment advice. Read our disclaimer
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</p>What is Compound Interest?
Compound interest is interest calculated on both the original amount and on the interest already added to it. Because each period earns interest on a slightly larger balance than the last, the balance grows by a rising amount each period rather than a fixed one.
The formula
A = P(1 + r/n)^(nt)- A = final balance
- P = starting principal
- r = annual interest rate, as a decimal
- n = compounding periods per year
- t = number of years
Take $10,000 at 7% compounded monthly for 20 years. Here r/n is 0.07 ÷ 12, or about 0.005833, and nt is 12 × 20 = 240 periods. That gives 10,000 × (1.005833)^240, which works out to roughly $40,387. The $30,387 difference is interest, and about $16,400 of that is interest earned on earlier interest rather than on the original $10,000.
Simple interest vs compound interest
Simple interest is calculated only on the starting amount. $10,000 at 7% simple interest earns $700 every year, forever: after 20 years that is $14,000 of interest and a $24,000 balance.
Compound interest recalculates against the running balance. Year one still earns $700, but year two earns 7% of $10,700, and so on. The gap between the two widens slowly at first and then sharply, because the difference itself compounds.
How often the recalculation happens matters less than people expect. Compounding more frequently means interest starts earning interest sooner, so the balance ends higher, but the effect shrinks as frequency rises. On $10,000 at 7% for 20 years, annual compounding gives about $38,697 and monthly about $40,387, a difference of roughly $1,690. Moving from monthly to daily adds only about $160 more, and continuous compounding, the theoretical ceiling, gives about $40,552.
| Years | Simple interest | Compounded annually | Difference |
|---|---|---|---|
| 5 | $13,500 | $14,026 | $526 |
| 10 | $17,000 | $19,672 | $2,672 |
| 20 | $24,000 | $38,697 | $14,697 |
| 30 | $31,000 | $76,123 | $45,123 |
Illustrative arithmetic at a fixed rate. Real returns vary year to year, and past performance does not indicate future results.
How regular contributions change the picture
Adding money on a schedule changes what the total is made of. Each contribution compounds only for the time remaining, so a deposit made in year one does far more arithmetic work than an identical deposit made in year nineteen.
The split between "money you put in" and "interest" therefore shifts over long periods. Over a short horizon most of the balance is contributions. Over a long one, the interest portion can exceed them, because the early deposits have had more periods to compound.
Estimating doubling time in your head
Dividing 72 by the interest rate gives a close approximation of how many years a balance takes to double. At 7%, 72 ÷ 7 ≈ 10.3 years; the exact figure is 10.24. The number 72 is used because it sits near 100 × ln(2) ≈ 69.3 while being far easier to divide in your head. The shortcut holds to within a few months for rates between roughly 6% and 10%, and drifts further at the extremes.
What this calculator does not account for
- The rate is constant. Real investment returns vary year to year, and a sequence averaging 7% will not produce the same result as a steady 7%.
- Contributions are treated as arriving on a perfectly regular schedule.
- No taxes, fees or fund expense ratios are deducted. An expense ratio reduces the effective rate every year it is charged.
- Inflation is not applied. The final figure is in nominal dollars, not what those dollars will buy.
Use the Rule of 72 for a one-step estimate of doubling time; use this calculator when you need the full year-by-year balance with contributions. Rule of 72 Calculator
How It Works
Enter your starting amount
Type in how much you have to invest now (initial investment) and how much you plan to add each month.
Set your expected return
Choose an annual return rate and compounding frequency. 7% is a common long-term estimate for a diversified stock portfolio.
Choose your time horizon
Enter how many years you plan to invest. Longer time horizons show dramatically more growth due to compounding.
See your projected growth
View your final balance, total interest earned, and a year-by-year chart showing how your money grows over time.
Frequently Asked Questions
Compound interest is interest earned on both your initial principal and the accumulated interest from previous periods. Unlike simple interest (which only earns on the principal), compound interest creates a snowball effect where your money grows faster over time.
More frequent compounding produces slightly higher returns because interest starts earning interest sooner. Daily compounding earns more than monthly, which earns more than annually. However, the differences are relatively small — the biggest factors are your contribution amount, rate of return, and time horizon.
The S&P 500 has historically returned roughly 10% annually before inflation (about 7% after inflation). For a conservative estimate, 6-7% is commonly used. Bond-heavy portfolios might assume 4-5%. The right number depends on your investment mix and risk tolerance. Past returns do not guarantee future results.
A common guideline is 15-20% of pre-tax income for retirement, though smaller amounts still compound. As an illustration, $100/month at 7% for 30 years works out to just over $120,000. The calculator lets you experiment with different contribution amounts to find what works for your budget.
Time matters more than any other input because growth is exponential, not linear. In early years, interest earned is modest. But as your balance grows, each year's interest becomes larger and larger. This is why starting early, even with small amounts, can outperform starting later with larger amounts.
This calculator shows nominal (pre-tax, pre-inflation) returns. To approximate after-inflation returns, use a lower rate (e.g., 7% instead of 10%). Tax impact depends on account type: tax-advantaged accounts (401k, IRA, Roth IRA) grow tax-free or tax-deferred, while taxable accounts owe taxes on gains annually.
The Rule of 72 is a quick way to estimate how long it takes to double your money. Divide 72 by your annual return percentage. At 7% return: 72 ÷ 7 ≈ 10.3 years to double. At 10%: 72 ÷ 10 ≈ 7.2 years. This only applies to the initial investment without additional contributions.