Compound interest calculator
Calculate how any investment grows with compound interest over time. Enter principal, rate, compounding frequency, and duration to see final value and year-by-year growth.
What is compound interest?
Compound interest is the mechanism behind most long-term wealth creation. Unlike simple interest — which pays only on the original principal — compound interest earns interest on interest. Over time, that second-order effect dominates: the longer your horizon and the more frequent the compounding, the larger the gap between simple and compound outcomes becomes.
This calculator lets you pick any compounding frequency (annual, semi-annual, quarterly, monthly, daily, or continuous) and optionally add a monthly contribution. It reports the final amount, total interest earned, and the APY (annual percentage yield) — the true effective annual rate after compounding is applied.
The compound-interest formula
The standard compound interest formula for discrete compounding is A = P(1 + r/n)^(nt), where P is principal, r is the annual rate (as a decimal), n is the compounding frequency per year, and t is time in years. For continuous compounding, the formula becomes A = P × e^(rt).
A = P (1 + r/n)^(nt)
A = P × e^(rt) (continuous)The Rule of 72
To estimate doubling time quickly: 72 ÷ annual rate ≈ years to double. At 6% your money doubles in roughly 12 years; at 9% in 8 years; at 12% in 6 years. It's not exact, but it's close enough to run the numbers in your head.
Common Uses
- Retirement corpus planning: Calculate how much a monthly contribution will grow to over 20–30 years at expected market returns to set a retirement target.
- Education fund projections: Estimate how much you need to invest today to fund a child's college education 15 years from now at a given growth rate.
- Comparing savings accounts: Enter different rates and compounding frequencies to directly compare which bank or investment product delivers more at maturity.
- Loan interest analysis: Understand how compound interest on credit card debt or personal loans grows over time without regular repayments.
- Inflation impact modelling: Model how a fixed sum loses purchasing power over time at the current inflation rate by treating inflation as a "negative" return.
- Business investment ROI: Project returns on a capital investment over multiple years accounting for reinvested profits at a target CAGR.
- FIRE movement planning: Calculate the investment corpus needed to retire early and live off annual returns without drawing down the principal.
- Goal-based investing: Work backwards from a target amount (down payment, travel fund) to determine the monthly investment required today.
FAQ
What is continuous compounding?
Continuous compounding assumes interest is added to the balance at every instant rather than at discrete intervals. It's the mathematical limit as the number of compoundings per year approaches infinity, governed by A = P × e^(rt). In practice, daily compounding is nearly identical to continuous — the difference at 10% over 5 years is less than 0.01%.
What is the difference between APR and APY?
APR is the nominal (stated) annual rate. APY is the effective annual rate after compounding. For example, 12% APR compounded monthly produces an APY of 12.68%. APY is what you actually earn; APR is what gets advertised.
Does compounding frequency really matter?
Higher frequency produces slightly more interest, because interest starts earning interest sooner. The gap is small but real: $10,000 at 10% for 5 years yields $16,105 (annual), $16,453 (monthly), and $16,487 (continuous). Over longer horizons and larger principals, the difference compounds — pun intended.
What is the Rule of 72?
The Rule of 72 is a quick mental shortcut: divide 72 by your annual rate to estimate how many years it takes for money to double. At 8% it's roughly 9 years, at 12% it's 6 years. The rule is accurate within 1% for rates between 6% and 10%, making it great for back-of-envelope estimates.
Does the compound interest calculator store my financial data?
No. All calculations run entirely in your browser. Your investment figures are never sent to a server or stored after you close the page.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the simple annual rate without compounding. APY (Annual Percentage Yield) reflects the effective rate after compounding — it is always higher than APR when interest compounds more than once per year.
By the Numbers
- An investment growing at 7% annually doubles every 10.3 years — derived from the Rule of 72
- Warren Buffett earned over 99% of his net worth after age 52, a direct result of long-term compounding
- The S&P 500 has delivered an average annual return of approximately 10.5% (nominal) over the past 50 years
- At a 3% annual inflation rate, purchasing power is cut in half in approximately 23 years