Compound Interest Calculator

What compound interest actually is

Simple interest pays a flat percentage of your starting principal, year after year. Compound interest pays a percentage of whatever you have now — including the interest you earned last year, and the year before, and so on. After enough cycles, the interest you earn on past interest dwarfs the interest on the original principal.

This is the mechanism behind every long-term wealth-building argument in personal finance. It's also why the early years of saving feel like nothing is happening: with no past interest to compound on, the curve is essentially linear. Around year 10–15 (at 7% real returns), the slope starts to bend visibly. By year 25–30, the curve is nearly vertical.

The formula

The compound interest formula with periodic contributions:

FV = P · (1 + r/n)^(n·t) + PMT · [((1 + r/n)^(n·t) − 1) / (r/n)]

where

• P = starting principal
• PMT = contribution per compounding period
• r = nominal annual rate
• n = compounding periods per year
• t = years

The first term is what the starting principal grows to on its own. The second term is the future value of an ordinary annuity — what your stream of contributions grows to. Both grow as (1 + r/n)^(n·t), which is the geometric kernel of everything compounding.

Time, not rate, is the lever. Doubling the rate roughly doubles your money. Doubling the time can quadruple it.

Rule of 72

A back-of-envelope shortcut: your money doubles in roughly 72 ÷ rate years. At 6% it doubles in 12 years; at 9% in 8; at 12% in 6. The exact formula is ln(2) / ln(1 + r) — for 7%, that gives 10.24 years vs. the rule's 10.29. Close enough for a coffee-shop estimate.

The rule is most accurate around 8%. At 2% it slightly overestimates; at 20% it underestimates. For anything in the range investors actually care about (4–12%), it's reliable within a few months.

Compounding frequency: how much it actually matters

More frequent compounding gives slightly higher final balances — but the gap is smaller than most people guess. At a 6% nominal rate compounded over 30 years on a $10,000 principal with no contributions:

The jump from annual to monthly is meaningful ($2,800 over 30 years). From monthly to daily is rounding noise. Banks advertise "daily compounding" because it sounds aggressive; in practice it's worth ~$260 on a $10k account vs monthly. The bigger lever is always the rate and the horizon.

What this calculator doesn't model

• Inflation. If you use a nominal rate (like 10% for stocks), the final dollars are also nominal — future dollars worth less than today's. Use a real rate (7% for stocks) to get an answer in today's purchasing power.
• Taxes. Interest in taxable accounts is taxed annually; capital gains in brokerage accounts are taxed on sale. Tax-advantaged accounts (Roth, traditional 401(k), HSA) defer or eliminate this. The model assumes tax-free compounding.
• Variable returns. Real markets don't return a constant 7%. Volatility introduces sequence-of-returns risk during withdrawal — see the FIRE-number guide for how to account for it.
• Fees. A 1% annual expense ratio compounds the same way returns do — backwards. Over 30 years it can shave 25–30% off your terminal value at a 7% gross return.
• Real-life contribution patterns. The model assumes constant monthly deposits. Job changes, raises, market dips when you're tempted to skip contributions — none of that is in the smooth curve.