Compound interest is interest calculated on both your original principal and on interest that has already been added to your balance, so your money grows at an accelerating rate over time rather than a constant one. This is different from simple interest, which is always calculated only on the original principal, compound interest is why long-term investing rewards patience so heavily: the growth curve gets visibly steeper the longer money is left untouched.

For the same nominal annual interest rate, more frequent compounding produces a higher effective annual return, since interest is credited and starts earning its own interest sooner. The difference between annual and daily compounding is usually small for typical rates (a fraction of a percent in effective annual yield), but it grows more noticeable at higher interest rates or over very long time horizons.

Continuous compounding is the mathematical limit of compounding frequency as the number of compounding periods per year approaches infinity, calculated using the formula A = P × e^(rt), where e is Euler’s number (approximately 2.71828). While no real bank account compounds literally continuously, it’s used in academic finance and options pricing (including the Black-Scholes model) as a clean theoretical upper bound on how much compounding frequency alone can boost returns.

Contributing at the beginning of each period lets that deposit earn interest for the entire period instead of arriving too late to earn anything that period, which compounds into a larger final balance over many years, though the difference for any single month is small. If your paycheck or savings plan naturally deposits money at a specific time, use that setting to get the most accurate projection of your actual timeline.

Regular contributions, even modest ones, often end up contributing more to your final balance than the growth of your original principal alone, especially over multi-decade horizons, because each new contribution gets its own compounding runway. Try running the calculator with and without a monthly contribution on the same principal and time period to see just how large the gap becomes, it’s often a bigger lever than trying to find a slightly higher interest rate.

For interest-bearing accounts with a fixed, known rate (savings accounts, CDs, bonds held to maturity), yes, this calculator uses the exact standard compound interest formulas and produces bank-grade precision. For market-linked investments like stock index funds, actual annual returns vary significantly year to year rather than following a smooth fixed rate, so treat any single ‘expected return’ figure for stocks as a simplifying long-term average, not a guarantee.

No, this calculator projects gross growth before any taxes owed on interest, dividends, or capital gains, which vary by account type (taxable, tax-deferred, or tax-free) and jurisdiction. Interest earned in a taxable account is often taxed annually as ordinary income even if you don’t withdraw it, which reduces your effective compounding rate compared to a tax-advantaged account where growth compounds untaxed until withdrawal.

The Rule of 72 is a quick mental shortcut estimating how many years it takes an investment to double: divide 72 by the annual interest rate percentage. At 6% annual interest, that’s 72 ÷ 6 = 12 years to double, reasonably close to this calculator’s more precise result. It’s a handy sanity check, but this calculator’s month-by-month simulation with your exact compounding frequency and contributions will always be more accurate for actual planning.