Compound Interest Calculator
See how your money grows with compound interest over time.
| Year | Balance | Contributions | Interest |
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What Is Compound Interest?
Compound interest is interest calculated on both your original principal and the interest already earned in previous periods. Simple interest only earns on the principal. That tiny distinction — "interest on interest" — is what turns small savings into serious wealth over 20–40 years. Investor.gov, the SEC's official investor resource, calls it the single most powerful concept in personal finance.
The mechanic is simple: every compounding period (a day, month, quarter, or year), the interest earned is added back to the balance, and next period's interest is calculated on the new, larger balance. Because the balance grows every period, so does the interest earned — producing an exponential curve instead of a straight line.
Compound interest works in both directions. On your savings it's a gift. On credit card debt at 22% APR compounding daily, it's the reason a $5,000 balance can cost $9,000+ in interest at minimum payments. This calculator models the growth side.
The Three Compound Interest Formulas
A— final amount (future value)P— principal (initial deposit)r— annual interest rate (decimal, e.g. 0.07 for 7%)n— compounding periods per year (1, 4, 12, 365)t— time in yearse— Euler's number ≈ 2.71828
The standard formula assumes interest compounds once a year. The frequency-based formula is the one most calculators (including this one) actually use — plug in n = 12 for monthly, 365 for daily. Continuous compounding is the theoretical limit as n → ∞; in practice, the difference between daily and continuous is less than 0.2% even over decades.
Worked Example — Maria Invests $10,000 at 7%
Why Starting Early Beats Starting Big
The single most important variable in compound interest is time. Here is the classic age-20-vs-age-30 comparison, assuming a 7% annual return compounded monthly:
| Investor | Starts at | Contributes until | Total contributed | Value at 65 |
|---|---|---|---|---|
| Ana (early) | Age 20 | Age 30 (10 yrs, $500/mo) | $60,000 | $554,000 |
| Ben (late) | Age 30 | Age 65 (35 yrs, $500/mo) | $210,000 | $857,000 |
| Claire (both) | Age 20 | Age 65 (45 yrs, $500/mo) | $270,000 | $1,411,000 |
Ana contributes less than one-third of what Ben contributes ($60K vs $210K) and still ends up with 65% of his balance — because her 10 early years got 35–45 years of additional compounding. Claire, who does both, ends up with roughly the sum of the two, proving that early contributions don't just add to late ones — they multiply.
Rules of Thumb
Divide 72 by the annual return to estimate how many years it takes your money to double. At 6% → 12 years. At 8% → 9 years. At 10% → 7.2 years. It's an approximation (exact formula is ln(2) ÷ ln(1+r)) but accurate to within 0.5 years for rates between 6% and 10%.
Divide 115 by the annual return to estimate how long until your money triples. At 7% → 16.4 years. At 10% → 11.5 years. Combine with the Rule of 72 and you get a fast mental model: at 7.2% return, money doubles in 10 years and triples in 16.
The long-run US inflation rate per BLS CPI-U data is roughly 3%. Subtract that from nominal returns to get "real" purchasing power growth: 7% nominal → ≈4% real. A 40-year $10,000 investment at 7% nominal is worth about $149,000 nominal but only ≈$48,000 in today's dollars.
How to Use This Calculator
- Enter your initial investment (principal) — the amount you're starting with today. Enter 0 if you're starting from scratch and only adding monthly.
- Enter your monthly contribution — how much you plan to add each month. For a Roth IRA, the 2026 contribution limit is $7,000/year ($583/month); for a 401(k) it's $23,500/year ($1,958/month).
- Enter your annual interest rate. Conservative (HYSA): 4–5%. Bonds: 4–5%. US stocks (long-run): 7% real / 10% nominal. Aggressive: 10%+.
- Choose a compounding frequency. Monthly is the most realistic for retirement accounts. Daily is typical for HYSAs.
- Set the investment period in years. For retirement, use your years until age 65. For college savings, use years until the child turns 18.
- Read the results panel — future value, total contributions, and interest earned. Scan the year-by-year table to see when interest starts outpacing contributions (usually around year 10–15).
- Try the Rule of 72 — set contribution = 0 and adjust period until the future value doubles. The period you land on should be approximately 72 ÷ rate.
Methodology & Assumptions
- Applies the standard formula
A = P(1 + r/n)^(n·t)with the compounding frequency you select (daily, monthly, quarterly, semi-annually, or annually). - Monthly contributions are added at the end of each compounding period (ordinary annuity). Beginning-of-period contributions would yield slightly higher results.
- Rate input is a nominal annual rate (APR), not APY. The effective yield (APY) is higher and depends on the frequency you select.
- Does not model taxes, fees, or inflation — the results are pre-tax nominal dollars. For after-tax or inflation-adjusted projections, subtract your marginal tax rate and/or a 3% inflation assumption from the rate.
- All math runs in your browser; no data leaves your device.
Glossary
- Principal (P)
- The initial amount deposited or invested. Does not include later contributions.
- Compounding period
- How often interest is added to the balance. Common: daily (365), monthly (12), quarterly (4), annually (1).
- APR (Annual Percentage Rate)
- The nominal yearly rate, ignoring intra-year compounding. This calculator takes APR as input.
- APY / EAR (Annual Percentage Yield / Effective Annual Rate)
- The effective rate after compounding. APY = (1 + APR/n)^n − 1. Always ≥ APR.
- Future Value (FV)
- The amount your investment grows to at the end of the period. This is the main result.
- Present Value (PV)
- The current worth of a future sum, discounted back at a given rate. Useful for reverse calculations.
- Rule of 72
- Mental math shortcut: years to double ≈ 72 ÷ rate. At 8%, money doubles in about 9 years.
- Continuous compounding
- The theoretical limit as n → ∞. Formula: A = P·e^(rt). Used in academic and derivatives math.
- Nominal vs real return
- Nominal = the headline rate. Real = nominal minus inflation. $40K of nominal future dollars buys less than $40K today.
- Ordinary annuity
- Regular contributions made at the end of each period. This calculator uses ordinary-annuity math.
Frequently Asked Questions
Compound interest is interest calculated on both the original principal and the accumulated interest from previous periods. Unlike simple interest (which only pays on the principal), compound interest grows your balance exponentially. The formula is A = P(1 + r/n)^(nt). Investor.gov calls it "interest on your interest" — the single most powerful concept in personal finance.
Divide 72 by the annual return rate to estimate how many years it takes your money to double. At 8% → 9 years. At 6% → 12 years. At 10% → 7.2 years. The exact formula is ln(2) ÷ ln(1+r), but the Rule of 72 is accurate to within 0.5 years for rates between 6% and 10%.
Yes, but far less than most people expect. $10,000 at 7% for 20 years: annual = $38,697, monthly = $40,388, daily = $40,495, continuous = $40,552. The annual → monthly jump is meaningful (+$1,691); daily → continuous is a rounding error ($57). Rate and time matter much more than frequency.
APR is the nominal rate ignoring intra-year compounding; APY is the effective rate with compounding included. APY ≥ APR always. 6% APR compounded monthly → APY = (1 + 0.06/12)^12 − 1 = 6.168%. US banks must display APY on deposits and APR on loans per the Truth in Savings Act. This calculator takes APR as input.
Enormously. $10,000 at 7% for 30 years grows to ~$76,123. Add $200/month to the same investment and you get ~$320,000 — over 4× more. At $500/month, ~$683,000. The combination of compound growth plus regular contributions is the single most-identified wealth-building pattern in the Fed Survey of Consumer Finances.
Four steps. (1) Convert rate to decimal: 7% → 0.07. (2) Divide by compounding periods: 0.07 ÷ 12 = 0.005833. (3) Raise (1 + periodic rate) to the power of (n × t): (1.005833)^240 = 4.0387. (4) Multiply by principal: $10,000 × 4.0387 = $40,387. For continuous use A = Pe^(rt): $10,000 × e^(0.07 × 20) = $40,552.
In a taxable account — yes, as ordinary income, reported on a 1099-INT/1099-DIV. In a Roth IRA or Roth 401(k) — qualified withdrawals are tax-free, so compounding is tax-free. In a Traditional IRA/401(k) — tax-deferred; you pay ordinary income tax on withdrawals. HSAs offer triple-tax-advantaged compounding (deductible in, tax-free growth, tax-free qualified withdrawals).
At 7% annual compounding: $38,697. Monthly: $40,388. Daily: $40,495. Add $500/month and the total jumps to ~$300,000 because the monthly contributions get their own 20 years of compounding. 7% is roughly the long-run real return of the S&P 500; nominal is closer to 10%.
Continuous compounding is the theoretical limit where interest is added infinitely often. The formula is A = Pe^(rt), where e ≈ 2.71828 is Euler's number. It's used in derivatives pricing and academic finance. In practice, the difference between daily and continuous is tiny: $10,000 at 7% for 20 years gives $40,552 continuous vs $40,495 daily (0.14% more).
Subtract long-run inflation (roughly 3% per BLS CPI-U) from your nominal return to get the "real" rate. A 7% nominal return becomes ≈4% real. $10,000 at 4% real for 20 years = $21,911 — that's the future value in today's purchasing power, not $40,388 of future dollars.