How compound interest works: A = P(1 + r/n)ⁿᵗ
Compound interest is the mechanism by which the interest earned on an investment is automatically reinvested, so that in the next period it also earns interest of its own. This "snowball" effect is why investing early and staying invested for many years has such a large impact on the final result, even with modest contributions.
The classic compound interest formula for a single lump sum is:
A = P × (1 + r/n)n×t
where A is the final accumulated value, P is the initial principal, r is the annual interest rate (as a decimal), n is the number of times interest compounds per year (12 for monthly, 1 for annual), and t is the number of years invested. When regular contributions are added on top of the initial deposit, this result is combined with the future value of an annuity: each contribution compounds interest for the time remaining until the end of the horizon, so earlier contributions generate more accumulated interest than later ones.
This calculator applies that exact logic month by month (if you choose monthly contributions) or year by year (if you choose annual), adding the interest earned on the accumulated balance each period and the new contribution, then charting how much of the final balance comes from your own contributions versus compound interest.
The Rule of 72: estimate how fast your money doubles
The Rule of 72 is a popular mental shortcut among investors to quickly estimate, without a calculator, how many years it takes an investment to double at a constant annual compound return. The formula is simple:
Years to double ≈ 72 / annual return (%)
For example, at a 4% annual return, your money would double in about 72 / 4 = 18 years; at a 9% annual return, in about 72 / 9 = 8 years. This rule works especially well for returns between 6% and 10% per year, and loses some accuracy outside that range, but it's extremely useful for quickly comparing investment scenarios without logarithms or spreadsheets.
US capital gains tax basics
In the US, profits from selling investments held in a regular (taxable) brokerage account are subject to capital gains tax. Long-term capital gains — on assets held for more than one year — are taxed federally at 0%, 15%, or 20%, depending on your total taxable income. Short-term capital gains — on assets held one year or less — are taxed as ordinary income at your regular federal tax bracket, which is usually much higher.
This is one reason many investors prioritize tax-advantaged accounts like a 401(k) (often with an employer match) or an IRA (Traditional or Roth) for long-term investing: contributions and growth inside these accounts can be tax-deferred or even tax-free, compared to a standard taxable brokerage account. Keep in mind this calculator shows your pre-tax, gross balance — it does not subtract any capital gains tax you may owe when you eventually sell. Always consult a tax professional for guidance specific to your situation.