Compound Interest Calculator
See how your savings or investments grow over time when interest compounds on itself. Drag the sliders to explore scenarios instantly -- or pick a preset to get started.
Investment Parameters
Growth Over Time
Year-by-year balance showing contributions (teal) vs interest earned (blue) stacked together.
Compounding Frequency Comparison
Side-by-side comparison of your inputs across all compounding frequencies.
Year-by-Year Breakdown
Detailed annual progression of your investment.
| Year | Deposits | Interest | Year Interest | Balance |
|---|
The Compound Interest Formula
The standard formula for compound interest without contributions:
A = P x (1 + r/n)nxt
- A -- future value (what you end up with)
- P -- principal (starting amount)
- r -- annual interest rate as a decimal (6% = 0.06)
- n -- compounding periods per year (12 for monthly)
- t -- time in years
When you add regular contributions (C) made at each compounding period, the future value of the contribution stream is:
FVcontributions = C x [((1 + r/n)nxt - 1) / (r/n)]
The total future value is the sum of both parts.
Compound vs. Simple Interest
Simple interest is calculated only on the original principal: Interest = P x r x t. Compound interest is calculated on the principal plus all previously earned interest.
The gap between them widens dramatically over time:
- 5 years: $10,000 at 8% -- Simple: $14,000 / Compound (monthly): $14,898 -- difference of $898
- 20 years: $10,000 at 8% -- Simple: $26,000 / Compound (monthly): $49,268 -- difference of $23,268
- 30 years: $10,000 at 8% -- Simple: $34,000 / Compound (monthly): $109,357 -- difference of $75,357
How Compounding Frequency Changes the Result
$10,000 at 6% annual rate for 10 years:
- Annually (n=1): $17,908.48
- Quarterly (n=4): $18,140.18
- Monthly (n=12): $18,193.97
- Daily (n=365): $18,220.44
The difference between annual and monthly compounding is $285.49 on a $10,000 deposit. Going from monthly to daily adds another $26.47. More frequent compounding always produces a higher result, but the marginal gain shrinks as frequency increases.
What Is APY?
APY (Annual Percentage Yield) is the effective annual return when compounding is taken into account. If a bank offers 6% compounded monthly, the APY is:
APY = (1 + 0.06/12)12 - 1 = 6.168%
APY lets you compare accounts with different compounding frequencies on equal footing. A 5.9% rate compounded daily (APY 6.077%) beats a 6.0% rate compounded annually (APY 6.0%).
The Rule of 72
The Rule of 72 is a quick mental shortcut to estimate how long it takes to double your money with compound interest. Divide 72 by the annual interest rate to get the approximate number of years.
Years to double ~ 72 / interest rate
This approximation works best for rates between 2% and 15%. For exact results, use the calculator above.
Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only grows on the original amount), compound interest causes your balance to grow at an accelerating rate over time.
What is the compound interest formula?
A = P x (1 + r/n)nxt, where A is the future value, P is the principal, r is the annual interest rate as a decimal, n is compounding periods per year, and t is the number of years.
How does compounding frequency affect growth?
More frequent compounding produces slightly more growth. For example, $10,000 at 6% for 10 years yields $17,908 with annual compounding, $18,194 with monthly compounding, and $18,220 with daily compounding. The difference is most noticeable at higher rates and longer time periods.
What is the difference between compound interest and simple interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously earned interest. Over time, compound interest grows significantly faster because you earn "interest on interest."
What does APY mean?
APY (Annual Percentage Yield) is the effective annual rate of return when compounding is taken into account. It is always equal to or higher than the stated nominal rate. The formula is: APY = (1 + r/n)n - 1.
How do contributions affect compound interest?
Regular contributions dramatically accelerate growth because each new deposit also earns compound interest. Even small consistent additions compound over time -- this is why starting early with regular savings has such a large impact on long-term wealth.
What is the Rule of 72?
The Rule of 72 is a shortcut to estimate how many years it takes to double your money. Divide 72 by the annual interest rate: at 6%, your money doubles in approximately 12 years (72 / 6 = 12). At 8%, it doubles in about 9 years. The rule is most accurate for rates between 2% and 15%.
How much will $10,000 grow in 10 years?
It depends on the interest rate. At 5% compounded monthly, $10,000 grows to $16,470 in 10 years. At 7%, it reaches $20,097. At 10%, it reaches $27,070. The higher the rate and the more frequent the compounding, the larger the final balance. Use the calculator above to model any rate.
How long does it take to double your money with compound interest?
Use the Rule of 72: divide 72 by the annual interest rate. At 6%, your money doubles in approximately 12 years (72 / 6 = 12). At 8%, it doubles in about 9 years. At 10%, about 7.2 years. This approximation works best for rates between 2% and 15%.
How do I calculate compound interest monthly?
Use the formula A = P x (1 + r/12)^(12xt), where P is the principal, r is the annual rate as a decimal, and t is the number of years. For example, $10,000 at 6% for 10 years compounded monthly: A = 10,000 x (1 + 0.005)^120 = $18,193.97. The key is dividing the annual rate by 12 and multiplying the exponent by 12.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal rate -- the stated rate before compounding effects. APY (Annual Percentage Yield) is the effective rate after compounding. A 6% APR compounded monthly gives a 6.168% APY. When comparing savings accounts, always compare APY because it reflects what you actually earn. When comparing loan costs, APR is the standard disclosure.
Does this calculator store my data?
No. All calculations run entirely in your browser using JavaScript. No data is sent to any server.
Related Tools
- Simple Interest Calculator -- compare with non-compounding growth
- Savings Goal Calculator -- find how long it takes to reach a target amount
- Investment Return Calculator -- model returns with contributions
- Inflation Calculator -- see how inflation affects future purchasing power
- Loan Calculator -- calculate monthly loan payments
- How Compound Interest Works -- in-depth guide with formula walkthrough, worked examples, and common mistakes
Privacy & Limitations
- Client-side only. No data is sent to any server. No cookies, no tracking of values entered. All calculations run in your browser using JavaScript.
- Assumes a fixed interest rate. Real-world investments experience variable rates. This calculator models a constant annual rate for estimation purposes.
- Does not account for taxes or fees. Investment returns are often subject to capital gains tax, management fees, or inflation. Actual net growth will be lower than the result shown.
- Not financial advice. This tool is educational. It demonstrates how compound interest works mathematically. Consult a qualified financial professional for investment decisions.
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Compound Interest Calculator FAQ
What is compound interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only grows on the original amount), compound interest causes your balance to grow at an accelerating rate over time.
What is the compound interest formula?
The formula is A = P × (1 + r/n)^(n×t), where A is the future value, P is the principal, r is the annual interest rate (decimal), n is the number of compounding periods per year, and t is the number of years.
How does compounding frequency affect growth?
More frequent compounding produces slightly more growth. For example, $10,000 at 6% for 10 years yields $17,908 with annual compounding, $18,167 with monthly compounding, and $18,197 with daily compounding. The difference is most noticeable at higher rates and longer time periods.
What is the difference between compound interest and simple interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously earned interest. Over time, compound interest grows significantly faster because you earn interest on your interest.
What does APY mean?
APY (Annual Percentage Yield) is the effective annual rate of return when compounding is taken into account. It is always equal to or higher than the stated nominal rate. APY = (1 + r/n)^n - 1, where r is the nominal rate and n is compounding periods per year.
How do contributions affect compound interest?
Regular contributions dramatically accelerate growth because each new deposit also earns compound interest. Even small consistent additions can make a large difference over long periods -- this is the principle behind retirement savings plans.
What is the Rule of 72?
The Rule of 72 is a shortcut to estimate how many years it takes to double your money with compound interest. Divide 72 by the annual interest rate. At 6%, money doubles in approximately 12 years (72 / 6 = 12). At 8%, it doubles in about 9 years. The rule is most accurate for rates between 2% and 15%.
How much will $10,000 grow in 10 years?
It depends on the interest rate. At 5% compounded monthly, $10,000 grows to $16,470 in 10 years. At 7%, it reaches $20,097. At 10%, it reaches $27,070. The higher the rate and the more frequent the compounding, the larger the final balance.
How long does it take to double your money with compound interest?
Use the Rule of 72: divide 72 by the annual interest rate. At 6%, your money doubles in approximately 12 years (72 / 6 = 12). At 8%, it doubles in about 9 years. At 10%, about 7.2 years. This approximation assumes compound interest and works best for rates between 2% and 15%.
How do I calculate compound interest monthly?
To calculate compound interest with monthly compounding, use the formula A = P x (1 + r/12)^(12xt), where P is the principal, r is the annual rate as a decimal, and t is years. For example, $10,000 at 6% for 10 years compounded monthly: A = 10,000 x (1 + 0.005)^120 = $18,193.97.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding. A 6% APR compounded monthly gives a 6.168% APY. When comparing savings accounts, always compare APY. When comparing loan costs, APR is the standard disclosure.
Does this calculator store my data?
No. All calculations run entirely in your browser. No data is sent to any server, and nothing is stored.