Compound Interest Calculator

Compound interest is interest earned on both the original principal and on interest that has already accrued. It is the fundamental mechanism behind long-term wealth building — Albert Einstein reportedly called it the eighth wonder of the world, and Warren Buffett has attributed much of his fortune to letting compound interest run for six decades. The mechanism is straightforward: at the end of each compounding period, the interest earned in that period is added to the principal, so the next period's interest is calculated on a slightly larger base. Over long horizons the effect is dramatic.

Contrast compound interest with simple interest. Simple interest earns the same fixed amount every period, because the interest calculation is always based on the original principal. A $10,000 deposit at 5% simple interest for 30 years earns exactly $500 per year, totalling $15,000 in interest. The same deposit at 5% compound interest, compounded annually, grows to roughly $43,219 — of which $33,219 is interest. The difference of $18,219 is entirely due to interest earning interest.

Real-world savings accounts, certificates of deposit, bonds, retirement accounts, and mortgages all use compound interest. The specific compounding frequency (annual, quarterly, monthly, daily, or continuous) affects the final balance but is rarely the dominant factor; the interest rate and the length of the horizon do most of the work.

The formula for future value with periodic compounding is a rearrangement of exponential growth, applied once per compounding period rather than continuously.

For a given nominal annual rate, more frequent compounding produces a slightly higher final balance, because interest is added back to the principal sooner. The differences between annual and monthly compounding are meaningful; the differences between monthly and daily compounding are almost always negligible. The table below shows the future value of $10,000 held for 10 years at a nominal 5% annual rate, under different compounding schedules.

As the number of compounding periods per year grows without bound, the discrete formula approaches an exponential limit. This is continuous compounding, and it uses the natural constant e (approximately 2.71828). Continuous compounding is used in derivatives pricing, Fed interest-rate modelling, and physics-style growth calculations, but almost never in retail banking products.

Most real-world savers deposit a fixed amount each month rather than a single lump sum. The formula extends by adding the future value of an ordinary annuity — a series of equal periodic payments. This calculator uses the same formula the SEC Investor.gov compound interest calculator uses; both assume contributions are made at the END of each period (an "ordinary annuity" or "annuity in arrears").

The Rule of 72 is a mental-arithmetic shortcut for estimating how long it takes an investment to double at a given interest rate. Divide 72 by the annual rate expressed as a whole number: at 6%, an investment doubles in roughly 72 ÷ 6 = 12 years; at 8%, in 72 ÷ 8 = 9 years. The rule is derived from the natural-log-of-2 identity (ln 2 ≈ 0.693) with a small adjustment that makes the divisor land on 72 rather than 69.3 — 72 is more mentally tractable because it has many small factors (2, 3, 4, 6, 8, 9, 12).

The rule is remarkably accurate for interest rates between 4% and 12% (error under 1%). Above 15% or below 2% the error grows enough to matter for planning; the exact "years to double" is ln(2) ÷ ln(1 + r) rather than 72/r. As a sanity check for a projection or a quick evaluation of an offered rate, though, the Rule of 72 is one of the most useful shortcuts in personal finance.

The compound-interest calculator projects nominal (before-inflation) balances. Over long horizons, inflation erodes purchasing power meaningfully. Roughly, a nominal return of r under inflation i produces a real return of approximately r - i (the Fisher equation gives the exact relation: (1 + real) = (1 + nominal) ÷ (1 + inflation)).

At a nominal 6% return with 3% inflation, the real return is closer to 2.91%, not 3%. Over 30 years the compounded difference becomes enormous: $1 at 6% grows to $5.74; at 2.91% it grows only to $2.36. For retirement planning and long-horizon savings goals, use the real return (nominal minus expected inflation) rather than the raw quoted rate. The US Bureau of Labor Statistics reports current inflation figures monthly through the Consumer Price Index (CPI).

US banks are required by the Truth in Savings Act (Regulation DD, 12 CFR Part 1030) to disclose the Annual Percentage Yield (APY) on savings accounts, money-market accounts, and certificates of deposit. APY is the effective annual return after compounding is applied, computed with the standard compound-interest formula. This is the number you compare when shopping banks — not the "nominal rate" or "interest rate", which don't account for compounding frequency.

If Bank A offers a 4.90% nominal rate compounded daily and Bank B offers 5.00% compounded annually, the daily-compounded account has an APY of about 5.02%, meaning Bank A's stated 4.90% is actually the higher effective yield. Regulation DD exists precisely so that consumers can make this comparison without doing the math themselves.

Tax-advantaged retirement accounts (401(k), Traditional IRA, Roth IRA) let compound interest work without the annual drag of taxation. In a taxable brokerage account, the interest earned each year is taxed at ordinary-income rates the year it is earned, which reduces the compounding base. In a Traditional 401(k) or IRA, interest compounds untaxed until withdrawal in retirement. In a Roth IRA, contributions are taxed up-front and both interest and growth are tax-free forever.

For 2026, the IRS employee deferral limit for 401(k) contributions is $23,500, with a $7,500 catch-up allowance for savers aged 50 and older, for a combined limit of $31,000. The IRA contribution limit is $7,000, with a $1,000 catch-up. Employer matching contributions do not count against the employee deferral cap — they fall under a separate combined-limit ceiling of $70,000 for 2026 (employee deferrals + employer contributions + after-tax contributions).

The tax-deferred compounding advantage is quantitatively significant. A $500-per-month contribution over 30 years at 7% nominal return compounds to about $611,000 in a taxable account (after annual tax drag at 24%) and $589,000 in a Roth IRA — with the crucial difference that every dollar in the Roth can be withdrawn tax-free, whereas the taxable balance has embedded gains that will be taxed on realisation. Structuring compound-interest growth inside the right account structure is often as important as the underlying interest rate. See the Retirement Calculator to model these tradeoffs across a full lifetime.

"Money doubles every 10 years at 7%": approximately true (Rule of 72 gives 72/7 = 10.3 years), but only if you neither add nor withdraw anything and the rate stays constant. Real-world portfolios have volatility, contributions, and withdrawals, so applying the doubling shortcut to a live account is misleading.

"Monthly compounding is much better than annual": in the table above the difference over 10 years at 5% is $181 on $10,000 — less than 2% of principal. The dominant driver of long-term return is the rate itself and the length of the horizon, not the compounding frequency.

"5% APR and 5% APY are the same": no. APR (Annual Percentage Rate) is a nominal rate that ignores compounding, mostly used for loans. APY (Annual Percentage Yield) is the effective annual return after compounding. When comparing savings products, use APY. When comparing loans, use APR — plus origination fees, which APR by law includes in the US.

"Compound interest only matters after 30 years": at 8% return, $10,000 grows to $21,589 in 10 years and $46,610 in 20 years. Even a decade of compounding roughly doubles a lump sum at typical equity returns. The bigger-is-better rhetoric around long horizons is real, but even short horizons show meaningful compound growth.