How this works
Compound interest is interest paid on interest already earned, so your balance grows faster every year. Add regular monthly contributions and the effect snowballs — small, steady deposits over decades end up dwarfing the original principal. Enter your starting amount, your expected annual return, your time horizon, and an optional monthly contribution. The result shows the future balance, total interest, and how much of it came from your contributions versus growth.
The single most important variable is time, not rate. The Rule of 72 is the back-of-envelope shortcut: divide 72 by your rate of return to get the number of years it takes for money to double. At 4% (typical savings account), money doubles every 18 years. At 7% (long-run stock market average), every ~10 years. At 10% (S&P 500 nominal historical), every ~7 years. Across a 40-year working life at 7%, money doubles four times — meaning $10,000 invested at 25 becomes $160,000 by 65 with no additional contributions. That same $10,000 invested at 45 has only one doubling left, ending at $40,000. The lost two doublings cost more than the next 20 years of disciplined saving could replace.
This is why retirement-planning math feels so unforgiving: every year you delay, you lose a doubling at the end of the chain, where the dollar amounts are largest. A common worked example: Saver A invests $5,000/year from age 25 to 35 ($50,000 total) and then stops. Saver B invests $5,000/year from age 35 to 65 ($150,000 total — three times more). At a 7% return, both finish at roughly the same balance around age 65 (~$540,000). Saver A invested less and finished with roughly the same amount because the early money had more doublings ahead of it. The corollary: if you can invest only one of "more money later" or "less money sooner", sooner almost always wins for any horizon longer than ~15 years.
The formula
FV = future value (final balance). P = starting principal. r = annual rate as a decimal (7% → 0.07). n = compounding periods per year (1 annual, 12 monthly, 365 daily). t = time in years. C = contribution per period (monthly contributions are converted to match the chosen frequency). When contributions are zero, only the first term applies.
Example calculation
- You start with $10,000, contribute $200/month, and earn 7% per year compounded monthly for 10 years.
- After 10 years your $10k starting amount alone grows to about $20,096 — already roughly doubled.
- Add the monthly contributions and the final balance is roughly $54,800. Total contributions: $24,000. Interest: ~$20,800.
Frequently asked questions
Does compounding frequency really matter?
A bit, but less than you'd think. On $10k at 7% over 10 years, annual compounding gives ~$19,672, monthly gives ~$20,097, and daily gives ~$20,136. The jump from annual to monthly matters; from monthly to daily is barely noticeable. Rate and time are far more powerful than frequency.
What rate of return should I assume?
Historical long-run averages: ~10% nominal / ~7% real (after inflation) for a diversified global stock portfolio, ~3–5% nominal for bonds, ~4–5% for a balanced 60/40 portfolio. For a high-yield savings account, use the current APY (typically 4–5% in 2024). For long-horizon planning, 6–7% is a reasonable middle ground.
Is the result before or after inflation?
It's nominal — i.e. before inflation. To see the real (purchasing-power) value of your future balance, subtract expected inflation from the rate of return. If you expect 7% returns and 3% inflation, run the calculator at 4% to see the result in today's dollars.
Why does Einstein supposedly call compounding "the eighth wonder of the world"?
The quote is almost certainly apocryphal, but the underlying math is real. Linear growth — adding the same amount each year — feels intuitive. Exponential growth doesn't: doubling time at 7% is roughly 10 years (the Rule of 72: 72/rate ≈ doubling time). Over a 40-year career, money compounds 4 times, turning $10k into $160k with no contributions at all.
How does the Rule of 72 actually work?
Rule of 72: doubling time ≈ 72 ÷ rate. At 6%, money doubles every 12 years; at 8%, every 9 years; at 12%, every 6 years. The same rule works in reverse — at what rate must your money grow to double in N years? 72 ÷ N. To double in 8 years, you need 9% returns. The number 72 is convenient because it has lots of small divisors (2, 3, 4, 6, 8, 9, 12), making mental arithmetic easy. The exact mathematical answer is ln(2)/ln(1+r) which gives 70.0–70.5 for low rates and 73 at 25% — so the rule slightly underestimates doubling time at low rates and slightly overestimates at high rates. For everything between 4% and 15% it's accurate to within half a year, which is plenty for ballpark planning.
What's the difference between APR and APY?
APR (Annual Percentage Rate) is the simple, non-compounded annual rate. APY (Annual Percentage Yield) is what you actually earn after compounding within the year. They're identical only when compounding is annual. For a 6% APR with monthly compounding, the APY is (1 + 0.06/12)^12 − 1 = 6.17%. Banks usually quote savings products in APY (the bigger, more flattering number) and loans in APR (the smaller, more flattering number). Always compare apples to apples: convert both to APY for savings/investments, both to APR for loans, or use a calculator that handles either form.
Is compound interest taxable?
In most jurisdictions, yes — interest and investment gains are taxed in the year they're earned, even if you reinvest them. In the US, interest from savings accounts and bonds is taxed as ordinary income (10–37% federal); long-term capital gains and qualified dividends from stocks are taxed at 0%, 15%, or 20%. Tax-advantaged accounts shelter the compounding from this drag: 401(k)s and traditional IRAs defer tax until withdrawal, Roth IRAs and Roth 401(k)s pay tax upfront and grow tax-free forever. Over 30 years, sheltering investments in a Roth account vs. a taxable brokerage at the same return often delivers 25–35% more after-tax wealth, purely because the compounding is uninterrupted. The calculator shows pre-tax growth; if you're modelling a taxable account, reduce your assumed return by your effective tax rate.