Long-term growth of recurring savings.
Compound interest is the engine that turns small, regular savings into a meaningful sum over years and decades. Albert Einstein is widely (probably falsely) credited with calling it the eighth wonder of the world; what he or someone else clearly meant is that compounding produces effects that human intuition consistently underestimates. Anyone planning for retirement, a child's education, a future down payment, or simply trying to understand what a bank deposit will be worth in ten years needs this calculation. It is also at the core of student loans, credit-card debt, and bond pricing, just running in the other direction — the same formula that grows your savings at a 7 % rate also grows the balance on a 22 % credit card. The reason most people misjudge the result is that they expect a linear curve and the reality is exponential: the account balance grows slowly for the first few years and then suddenly accelerates. The calculation here lets you see the exact trajectory for any combination of starting amount, monthly contribution, rate, and horizon.
Compound growth with regular contributions blends two formulas. For an initial principal P growing at an annual rate r over n years, with no further deposits, the future value is:
FV = P × (1 + r)ⁿ
If you also contribute a fixed amount C at the end of each period (most commonly each year, but also each month), the future value of those contributions is:
FVₐ = C × ((1 + r)ⁿ − 1) / r
The total future value is the sum FV + FVₐ. For monthly compounding and monthly contributions, divide r by 12 and use 12n as the exponent. Total deposits made are P + C × n (or P + C × 12n for monthly), and total interest earned is the difference between FV + FVₐ and total deposits.
Four inputs: Initial deposit (the starting capital), Monthly contribution (set to zero if you want pure principal growth), Annual interest rate (the nominal rate; for stocks, a long-run U.S. equity assumption is 7 % real or about 10 % nominal), and Years (the time horizon). The results panel returns the final balance, the total deposited (so you can see how much of the result came from your money versus the interest), and the total interest earned.
You deposit $5,000 today and add $300 every month into an account that returns 7 % per year, compounded monthly. Over 30 years, the (1 + r/12)¹²ⁿ term works out to about 8.116. The initial $5,000 grows to roughly $40,580. The contribution stream of $300 × 360 months = $108,000 grows to about $367,000 thanks to compounding. The final balance is about $407,500. Of that, you contributed $113,000 ($5,000 + $108,000); the remaining $294,500 — roughly 2.6 times what you put in — is pure interest. Push the horizon to 40 years instead of 30 and the final balance jumps to about $796,000, more than double, despite contributing only $36,000 more. That ten-year extension matters so much because compounding works on the entire balance you've already built.
First, conflating nominal and real returns. A 7 % nominal stock return at 3 % inflation is a real return of about 4 %; ignore inflation and you'll badly overestimate your future purchasing power. Second, ignoring fees. A 1 % annual fee compounded over 30 years can reduce a final balance by 25 % or more — yes, just one percentage point. Third, forgetting taxes. Interest in a taxable account is taxed each year; in a Roth IRA or 401(k), it is not. The "growth" the formula shows is pre-tax in most cases. Fourth, treating an average return as guaranteed. Stock-market returns are an average over decades; in any given year they range from disastrous (-30 %) to exuberant (+30 %). Fifth, the most expensive trap of all: compounding on the wrong side. Carrying a $5,000 credit-card balance at 22 % APR and paying only the minimum is the same formula working against you, doubling your debt in about three and a half years if untouched.
The compound interest formula has a few important relatives. The rule of 72 is a back-of-envelope shortcut: years to double ≈ 72 / rate (in percent). At 7 %, your money roughly doubles every 10.3 years; at 10 %, every 7.2 years. Continuous compounding (the limit as the period gets infinitely small) replaces (1 + r/n)ⁿ with eʳᵗ, where e is Euler's number — relevant for some bonds and mathematical models, less so for retail savings. Inflation-adjusted compounding subtracts the inflation rate before applying the formula, to reason in today's dollars. Geometric vs. arithmetic mean returns: a portfolio that gains 50 % then loses 50 % does not end up flat (it ends at 75 % of where it started), because compounding is multiplicative. This is why a single bad year matters more than a single good year of equal magnitude. Compounding is also the mathematical foundation of the time value of money more generally — every dollar today is worth more than a dollar tomorrow because today's dollar can earn interest.
Read the full guide →