Compound Interest Calculator
Watch your money grow with compound interest, monthly contributions, and any compounding frequency.
Growth Summary
Year-by-Year Breakdown
| Year | Start Balance | Contributions | Interest | End Balance |
|---|
What is a Compound Interest Calculator?
A compound interest calculator shows how an initial sum of money grows over time when the interest it earns is reinvested rather than withdrawn. Because each period's interest is added to the balance, you begin earning interest on your interest, so growth accelerates over time. That is the key difference from simple interest, which is calculated only on the original principal.
This free compound interest calculator goes further than the basic formula: it lets you add regular monthly contributions, choose from six compounding frequencies, and inspect a year-by-year breakdown of contributions, interest, and balance. Use it to model a retirement nest egg, a college fund, or any long-term investment where returns are reinvested.
The Compound Interest Formula
The future value of a single deposit is given by the compound interest formula: A = P(1 + r/n)^(nt)
- A — the final amount (future value) after the investment period
- P — the principal: your initial deposit or investment
- r — the annual interest rate expressed as a decimal (7% becomes 0.07)
- n — the number of compounding periods per year: 1 for annual, 2 for semiannual, 4 for quarterly, 12 for monthly, 365 for daily
- t — the time the money stays invested, in years
For continuous compounding — the theoretical limit as n grows without bound — the formula becomes A = Pe^(rt), where e ≈ 2.71828. When you add monthly contributions, each deposit compounds separately for the time it remains invested, which this calculator handles for you.
Worked Example: $10,000 at 7% for 20 Years
Suppose you invest $10,000 at a 7% annual rate for 20 years and make no further contributions. With annual compounding, n = 1 and the calculation is:
A = 10,000 × (1 + 0.07/1)^(1×20) = 10,000 × 1.07^20 ≈ 10,000 × 3.869685 ≈ $38,696.84
Change only the compounding frequency and the result shifts. The table shows the same $10,000 at 7% for 20 years under every supported frequency.
| Frequency | Periods per Year (n) | Final Balance | Interest Earned | Effective Annual Rate |
|---|---|---|---|---|
| Annual | 1 | $38,696.84 | $28,696.84 | 7.00% |
| Semiannual | 2 | $39,592.60 | $29,592.60 | 7.12% |
| Quarterly | 4 | $40,063.92 | $30,063.92 | 7.19% |
| Monthly | 12 | $40,387.39 | $30,387.39 | 7.23% |
| Daily | 365 | $40,546.56 | $30,546.56 | 7.25% |
| Continuous | ∞ | $40,552.00 | $30,552.00 | 7.25% |
The gains diminish quickly: moving from annual to monthly compounding adds $1,690.55, but daily beats monthly by only $159.17, and continuous adds just $5.44 more. The interest rate and the time you stay invested matter far more than the compounding frequency.
How to Use
- Enter your starting principal — the amount you have today.
- Input the expected annual rate of return and set the duration in years with the slider.
- Select how often interest compounds, from annually to continuously.
- Optionally add a monthly contribution to see how steady investing amplifies compounding.
- Click Calculate to view your final balance, total interest, growth multiple, and a year-by-year breakdown.
The Rule of 72
The Rule of 72 is a mental-math shortcut for estimating how long compounding takes to double your money: divide 72 by the annual rate of return to get the approximate number of years. The rule is most accurate near 8%; the exact formula is ln(2) ÷ ln(1 + r). The table below compares the two.
| Annual Return | Rule of 72 Estimate | Exact Doubling Time |
|---|---|---|
| 2% | 36.0 years | 35.00 years |
| 3% | 24.0 years | 23.45 years |
| 4% | 18.0 years | 17.67 years |
| 5% | 14.4 years | 14.21 years |
| 6% | 12.0 years | 11.90 years |
| 7% | 10.3 years | 10.24 years |
| 8% | 9.0 years | 9.01 years |
| 9% | 8.0 years | 8.04 years |
| 10% | 7.2 years | 7.27 years |
| 12% | 6.0 years | 6.12 years |
Doubling time compounds too. At a 7% return, one doubling takes about 10.3 years, so over 41 years your money doubles roughly four times — turning $10,000 into about $160,000 without adding another cent.
Real vs. Nominal Returns: Accounting for Inflation
Every figure above is a nominal return — it ignores inflation, and each future dollar buys less than a dollar today. The inflation-adjusted, or real, rate of return is approximately the nominal rate minus inflation; the precise formula is (1 + nominal) ÷ (1 + inflation) − 1.
At a 7% nominal return with 3% inflation, the real rate is about 3.88%. Re-run the worked example at that rate and $10,000 becomes roughly $21,425.50 in today's purchasing power after 20 years, rather than the nominal $38,696.84. For long-range planning, enter a conservative real rate into the calculator so inflation does not flatter your projections.
Frequently Asked Questions
What is compounding frequency?
Compounding frequency is how often earned interest is credited to your balance and starts earning interest itself. More frequent compounding produces a slightly higher effective annual rate: at a 7% nominal rate, annual compounding yields exactly 7%, while daily compounding yields about 7.25%.
How much difference does monthly contribution make?
A large one. Invest $10,000 at 7% compounded monthly for 20 years and you end with $40,387.39. Add $500 every month and the balance grows to about $302,370 — of which only $130,000 is money you paid in. Regular contributions harness compounding on every deposit, not just the first one.
What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal, so the balance grows by the same dollar amount every period. Compound interest is calculated on the principal plus all accumulated interest, so growth accelerates. At 7% over 20 years, $10,000 earns $14,000 in simple interest (a final balance of $24,000) but $28,696.84 with annual compounding — more than double.
What does continuous compounding mean?
Continuous compounding is the theoretical limit where interest is compounded infinitely often, calculated with the formula A = Pe^(rt) using the mathematical constant e. In practice it barely differs from daily compounding: on $10,000 at 7% for 20 years, continuous compounding returns $40,552.00 versus $40,546.56 for daily — a gap of just $5.44.
Is daily compounding much better than monthly?
Not dramatically. On $10,000 at 7% for 20 years, daily compounding returns $40,546.56 compared with $40,387.39 for monthly — a difference of $159.17 over two decades. The interest rate and the time horizon have a far bigger impact on your final balance than the compounding frequency.
Does this calculator account for inflation and taxes?
No — results are nominal, pre-tax projections. To approximate an inflation-adjusted outcome, subtract your expected inflation rate from the return rate before calculating (7% nominal with 3% inflation gives a real rate near 4%). Taxes depend on your account type and jurisdiction; a tax-advantaged account such as a 401(k) or IRA lets compounding work on the full balance.
Is this calculator accurate for stocks?
The calculator assumes a fixed annual return, while real stock returns vary from year to year — sometimes sharply. Treat the output as a long-term projection based on an average return, not a guarantee. Sequence-of-returns risk means actual results will differ even when the long-run average matches your input.