Compound interest calculator

The math: future value of a lump sum plus ordinary annuity. FV = P·(1+r/n)^n·t + PMT·((1+r/n)^n·t − 1)/(r/n), where P is starting principal, r is annual rate, n is compounds/year, t is years, and PMT is the per-period contribution. End-of-period contributions (the conservative assumption).

Nominal vs effective:the "7% annual" you enter is a nominal rate. At monthly compounding it produces a slightly higher effective annual yield (APY ≈ 7.23%). That's the standard convention for savings accounts and broker statements. If your account quotes APY directly, you can enter that value with annual compounding for a closer match.

The 7% default isn't a promise.S&P 500 long-run returns have averaged ~10% nominal / ~7% real (after ~3% inflation) over 90+ years. But individual 30-year windows have ranged from ~3% real to ~10% real. Run the calculator at both 5% and 9% — the spread is the uncertainty band on your retirement, and it's wider than people think.

Inflation isn't modeled separately.A future-value figure of $610k in 30 years is in nominal dollars; at ~3% inflation that's roughly $251k in today's purchasing power. To model in real terms, enter the inflation-adjusted return rate (subtract expected inflation from nominal return — about 7% nominal − 3% inflation = 4% real).

Taxes aren't modeled either. Inside a Roth IRA or Roth 401(k) the future-value figure is what you actually get to spend. Inside a traditional 401(k) or IRA, every dollar withdrawn is taxed at your ordinary-income rate. Inside a taxable brokerage, qualified dividends and long-term gains are taxed annually — drag of ~0.3-0.8% per year depending on bracket and turnover.

Starting early dwarfs starting big.$200/mo for 40 years ($96k contributed) ends up materially larger at 7% than $400/mo for 20 years ($96k contributed) — same dollars in, but the early-starter's contributions get more years of compounding. This is the "decade of your 20s is worth more than your 40s" effect, and it's the argument for funding even a small Roth IRA early.

The Rule of 72approximates the time to double a lump sum as 72 ÷ annual-rate-in-percent. At 6% money doubles in ~12 years; at 9% in ~8 years. It's a heuristic — accurate within ~1% for rates in the 6-10% range, less so at extremes. Useful as a sanity check on any future-value calculator (including this one).

This isn't a retirement planner. It assumes a constant rate and constant contribution. Real returns are lumpy (sequence- of-returns risk matters when drawing down), and contributions usually rise with income. Use this to build intuition; use a Monte Carlo retirement tool when planning actual drawdown.