Compound Interest Calculator

Future value of a present sum: FV = P × (1 + r/n)^(n×t), where P is principal, r is annual rate, n is compounding periods per year, t is years. With monthly compounding (n=12), $10,000 at 7% over 30 years becomes 10000 × (1 + 0.07/12)^(12×30) = 10000 × 8.1163 = $81,164. Annual compounding (n=1) gives slightly less — $76,123 — because monthly compounding lets earlier interest earn its own interest sooner.

With regular contributions, add the future value of an annuity: FV_annuity = PMT × ((1 + r/n)^(n×t) − 1) / (r/n). At $500/month contributions plus the $10k principal, the 30-year total at 7% is $81,164 + $611,728 = $692,892. The contributions ($500 × 360 = $180,000) earned $432,892 in interest — more than 2× what you put in.

• Rule of 72 — divide 72 by the annual rate to estimate doubling time. At 6%, money doubles in 12 years. At 9%, in 8 years. Accurate enough for mental math at rates between 4-10%.
• Rule of 114 — triples in 114/rate years.
• Rule of 144 — quadruples in 144/rate years.
• Inflation hedge — real return = nominal return − inflation. A 7% return at 3% inflation is a real return of 4%, not 7%. For retirement planning, always model in real (inflation-adjusted) terms; nominal projections look impressive but cannot buy more bread.

Continuous compounding gives FV = P × e^(rt) — the theoretical maximum. For r=7%, t=30 years: e^(0.07×30) = 8.1662, so $10k → $81,662. Compare to monthly compounding result of $81,164 — only $498 difference (0.6%). Annual compounding gives $76,123 — about 6% less.

Practical takeaway: monthly vs daily vs continuous compounding rarely matters for retirement-horizon decisions. Annual vs monthly matters at low rates and long horizons. The much bigger lever is the rate itself; argue about asset allocation, not compounding frequency.

• You are deciding how much to save for retirement and want to see what specific contribution rates project to at 65.
• You are comparing two savings products with different rates and compounding schedules and want to see the actual after-N-years difference.
• You are weighing "pay down debt" vs "invest" — compare guaranteed rate-of-return from paying off a 6% mortgage against expected market return.
• You are teaching a kid (or yourself) why starting early matters, with concrete numbers instead of abstract arguments.

• It will not predict actual market returns. The 7% historical S&P 500 average is real (with dividends, before inflation) but past performance does not guarantee future returns. Model multiple scenarios — low (4%), expected (7%), optimistic (10%) — to bound your assumptions.
• It will not account for sequence-of-returns risk. The order of returns matters at retirement (drawing down during a crash is much worse than after one). For retirement-stress-testing, use Monte Carlo tools.
• It will not include taxes. Tax-advantaged accounts (401k, IRA, ISA, RRSP) compound without annual tax drag; taxable brokerage accounts lose 0-2%/year to dividend and capital gains taxes. Account-type matters as much as rate.