Compound Interest Calculator
Project the future value of a lump-sum investment when interest is reinvested each year using A = P · (1 + r)ᵗ. The simplest compounding model — assumes annual compounding, a constant rate, and no additional contributions or withdrawals.
Last updated: May 2026
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About this calculator
The discrete compound-interest formula is A = P · (1 + r/100)ᵗ, where P is the initial principal, r is the annual interest rate expressed as a percentage (entered as e.g. 5 for 5%, not 0.05), t is the number of years, and A is the value after t years. Each year the balance is multiplied by (1 + r/100); after t years the cumulative multiplier is (1 + r/100)ᵗ. This calculator uses annual compounding only — once per year. For more frequent compounding (monthly, daily) use the generalised form A = P · (1 + r/(100·n))^(n·t), which produces a slightly larger result for the same nominal rate. The continuous-compounding limit (n → ∞) gives A = P · e^(rt/100), the absolute upper bound for a given rate. Variables: principal P ≥ 0; rate r can be positive (growth), zero (no change), or negative (loss, must satisfy r > -100 to keep the balance non-negative); time t ≥ 0. Edge cases: r = 0 gives A = P (no change); r = -100 gives A = 0 after one period (total wipeout); for very long horizons even small rates produce dramatic growth — at 7% over 50 years, $1 grows to about $29.46 (the rule of 72 says doubling takes ~10.3 years, and 50/10.3 ≈ 4.85 doublings, so 2^4.85 ≈ 28.9, close enough). The formula assumes the rate is constant for the whole period — a critical assumption that almost never holds for real investments. For variable rates, multiply the per-period factors together: A = P · ∏ (1 + rᵢ/100). For lump-sum-plus-contribution growth (a savings plan), use a future-value-of-annuity formula instead.
How to use
Example 1 — Long-horizon investment. You invest $10,000 at 5% annual interest for 10 years, untouched. Enter Principal = 10000, Rate = 5, Time = 10. A = 10000 · (1.05)¹⁰ ≈ 10000 · 1.62889 ≈ $16,288.95. ✓ The original $10,000 has grown by 62.9% in pure compounding interest, even though the rate is "only" 5% per year. With simple (non-compound) interest the same investment would have grown to just $15,000. Example 2 — Inflation projection. Inflation has averaged 3% per year and you want to know what a $50,000 salary today will need to grow to in 20 years just to maintain purchasing power. Enter Principal = 50000, Rate = 3, Time = 20. A = 50000 · (1.03)²⁰ ≈ 50000 · 1.80611 ≈ $90,305.56. ✓ So you need almost $90k in 2046 to match $50k in 2026 — a sobering anchor for retirement planning, salary negotiations, and any decision involving long-term real (vs nominal) values.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal: I = P · r · t. The balance grows linearly, by a constant amount each year. Compound interest is calculated on the principal plus all previously accrued interest, so each year's interest is slightly larger than the last and the balance grows exponentially. Over one year the two are identical; over a decade compounding produces a small advantage; over 30+ years the gap becomes enormous. At 7% for 30 years, simple interest doubles your money to about 3.1× principal, while compound interest grows it to about 7.6× principal. Almost all real-world savings accounts, mortgages, credit cards, and investment returns use compound interest in some form. Simple interest persists mainly in short-term consumer loans and academic examples.
Does compounding frequency change the result?
Yes — more frequent compounding produces a larger final balance for the same nominal rate, but with sharply diminishing returns. Annual compounding of 5% gives 1.0500× per year; monthly compounding of the same 5% nominal rate (5%/12 per month, compounded 12 times) gives 1.0512×; daily compounding gives 1.0513×; continuous compounding gives 1.0513× (essentially the same). Going from annual to monthly captures most of the benefit; going from monthly to daily adds almost nothing. The advertised APY (annual percentage yield) bakes the compounding frequency into a single comparable number — when comparing accounts, always look at APY rather than the stated nominal rate. This calculator uses annual compounding only; for monthly/daily/continuous variants use a generalised compound-interest tool.
What is the rule of 72 and does it work?
The rule of 72 is a mental shortcut for estimating how long it takes a compounding investment to double: divide 72 by the rate (as a whole-number percentage). At 6% your money doubles every ~12 years; at 8% every ~9 years; at 12% every ~6 years. The rule is accurate to within ~0.5% for rates between 4% and 12% because ln(2) ≈ 0.693 and 0.72 is close enough for mental arithmetic. It is wonderfully useful for sanity-checking retirement plans: if you are 35, expect 7% real returns, and your money doubles every ~10.3 years, then $50,000 invested today will be roughly $200,000 by age 55 and $400,000 by age 65 — without adding a dollar. The rule degrades for very high rates (above 15–20%) where the exact formula t = ln(2)/ln(1 + r) diverges noticeably from 72/r.
What are the most common mistakes people make with compound interest?
The first is starting late. Because growth is exponential, the last decade of a 40-year investment horizon often produces more in dollar terms than the first 20 years combined — small contributions in your 20s outweigh much larger contributions in your 40s. The second is confusing nominal rate with APY; a "7% rate compounded monthly" is actually about 7.23% APY, and ignoring this consistently underestimates growth. The third is ignoring inflation: a 6% nominal return during 3% inflation is really 3% in purchasing power, and only the real return matters for long-term planning. The fourth is forgetting taxes and fees, both of which compound just as ruthlessly against you as interest compounds for you (a 1% expense ratio over 30 years can eat 25%+ of your final balance). The fifth is treating the formula as exact when in reality investment returns are noisy — actual outcomes can deviate by 50% or more from the projected value due to sequence-of-returns risk.
When should I not use this calculator?
Skip it if you plan to make regular contributions or withdrawals — it assumes a single lump-sum deposit that just sits and compounds, so it will materially understate the balance of an account you keep adding to; use a future-value-of-annuity or savings-goal calculator instead. It is wrong for loans you actively pay down, because each payment reduces principal and changes the interest base; use a loan-amortization or mortgage payment calculator. Do not use it for variable-rate accounts where the rate changes over time — the formula assumes a constant rate. It cannot model investment returns that are not pure interest (stock dividends, capital gains, volatility), which fluctuate year to year — use a Monte Carlo retirement simulator for those. Finally, do not use the annual-compounding form when you actually need monthly or continuous compounding; the answer differs by 1–3% over typical horizons and that matters in finance.