Compound Interest Calculator
See how investments grow with the power of compounding over time.
About the Compound Interest Calculator
This compound interest calculator shows how an investment grows when interest is reinvested rather than withdrawn. Enter your initial principal, the annual interest rate, the time horizon, and the compounding frequency (annually, semi-annually, quarterly, monthly, or daily), and the tool returns the future value, total interest earned, and the effective annual rate (EAR).
Compound interest is the most powerful force in personal finance — Einstein is often (perhaps apocryphally) quoted as calling it the 'eighth wonder of the world.' The mechanism is simple: each period, interest is earned not just on the original principal but also on all previously-earned interest. Over long horizons, the effect becomes dramatic. $10,000 invested at 7% annual for 30 years becomes $76,123 — of which $66,123 is interest.
The calculator also exposes the effective annual rate (EAR), which converts any compounding frequency into an equivalent annual rate. This is the honest number to use when comparing accounts that compound at different frequencies. A 7% nominal rate compounded monthly yields a 7.2295% EAR; the same rate compounded daily yields 7.2501%.
How It Works
The future value of a lump sum under compound interest is:
FV = P * (1 + r/n)^(n*t)Where:
- P = principal (initial investment)
- r = annual interest rate (as a decimal)
- n = number of compounding periods per year
- t = number of years
The effective annual rate (EAR) is what you actually earn in a year, accounting for intra-year compounding:
EAR = (1 + r/n)^n - 1For example, 7% nominal compounded monthly gives EAR = (1 + 0.07/12)^12 - 1 = 0.072295 = 7.2295%. The more frequently interest is compounded, the higher the EAR — though the gains diminish quickly. Moving from annual to monthly compounding adds about 23 basis points at 7%; moving from monthly to daily adds only 2 more basis points.
This calculator models a single lump-sum investment. For periodic contributions (e.g., $200/month), use our Savings Goal Calculator or Retirement Calculator.
Worked Examples
Suppose you invest $10,000 at 7% annual interest, compounded monthly, for 10 years.
- Periodic rate: 0.07 / 12 = 0.005583
- Total periods: 12 * 10 = 120
- Future value: 10,000 * (1.005583)^120 = 10,000 * 1.9422 = $19,422.03
- Total interest: $19,422.03 - $10,000 = $9,422.03
- EAR: (1 + 0.07/12)^12 - 1 = 7.2295%
Compare the same investment compounded annually: FV = 10,000 * (1.07)^10 = $19,671.51. The annual compounding actually wins here because the periodic rate is higher per period — but only because the nominal rate is the same. If two banks offer the same EAR, the compounding frequency does not matter.
Over 30 years at 7%, $10,000 grows to $76,123 (monthly compounding). Double the rate to 14% and you get $502,760 — a 6.6x multiple instead of 7.6x. The power of compounding is much more sensitive to the rate than to the term, which is why high-interest debt is so dangerous in reverse.
When to Use This Tool
Use this compound interest calculator when:
- Projecting how a CD, savings account, or bond investment grows over time
- Comparing two savings accounts with different compounding frequencies
- Estimating the long-term growth of a lump-sum inheritance, bonus, or settlement
- Teaching children or students about the magic of compounding
- Comparing the impact of a 1% fee on a long-term investment portfolio
- Estimating future value of a fixed annuity payout reinvested
- Visualizing why starting to invest early matters so much (10 extra years can double the result)
For retirement planning with monthly contributions, use our Retirement Calculator. For SIP-style investing, the Savings Goal Calculator handles periodic deposits.
Limitations & Disclaimer
This calculator models a single lump-sum investment at a fixed nominal rate with periodic compounding. It does not handle periodic contributions, withdrawals, variable rates, tiered interest, taxes on interest earned, inflation adjustments, or fees. The effective annual rate (EAR) assumes reinvestment of all interest at the same rate. Real-world returns on stocks, bonds, and mutual funds are variable and not guaranteed; do not extrapolate a fixed compound-interest result to equity investments. This is an educational tool, not investment advice. See our disclaimer for full terms.
Frequently Asked Questions
What is the difference between APR and APY?
APR (annual percentage rate) is the nominal rate — the simple annual rate without compounding. APY (annual percentage yield), also called effective annual rate (EAR), is what you actually earn after intra-year compounding. A 7% APR compounded monthly gives a 7.2295% APY. Always compare accounts by APY, not APR.
Does compounding daily make a big difference vs monthly?
Very little. At a 7% nominal rate, monthly compounding gives 7.2295% EAR; daily gives 7.2501% EAR. The difference is about 2 basis points per year — $2 on $10,000. Banks often advertise daily compounding as a feature, but the math barely moves. Don't let it sway your choice of account.
How does inflation affect my return?
Inflation erodes purchasing power. If you earn 7% nominal and inflation runs 3%, your real return is approximately 7% - 3% = 4% (more precisely, (1.07 / 1.03) - 1 = 3.88%). Use our <a href='/tools/inflation-calculator.php'>Inflation Calculator</a> to compute real returns over time.
What is the Rule of 72?
The Rule of 72 is a mental-math shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 7%, 72/7 = 10.3 years. At 10%, 7.2 years. At 12%, 6 years. It is approximate but surprisingly accurate for rates between 4% and 15%.
Can this calculator handle continuous compounding?
Not directly — the highest frequency offered is daily (365x). Continuous compounding uses the formula FV = P * e^(r*t), where e is Euler's number (~2.71828). At practical interest rates, continuous and daily compounding differ by less than 1 basis point, so daily is effectively the limit.
Why does my bank's number differ slightly from this calculator?
Banks may use different day-count conventions (actual/365 vs 30/360), round intermediate calculations, or apply tiered interest rates that change at certain balance thresholds. This calculator uses the mathematically exact textbook formula; small differences of a few cents per year are normal and not errors.
Last updated: July 21, 2026 · Author: HT99 Tools Editorial Team · Reviewed by: HT99 Tools Editorial Team