📈 Compound Interest Calculator: See Your Money Grow Over Time
By ToolNimba Editorial Team · Reviewed by ToolNimba Editorial Review, personal finance content · Updated 2026-06-20
This calculator gives an estimate only and is not financial advice. It assumes a fixed rate and regular compounding with no extra deposits, fees, or taxes unless you add them. Real returns vary, and savings or investment products can carry risk or change their rate. Confirm the figures with your provider and speak to a qualified adviser before making decisions.
This compound interest calculator shows how a starting amount grows when interest is added back and then earns interest of its own. Enter your principal, the annual interest rate, the number of years, and how often interest compounds (annually, semiannually, quarterly, monthly, or daily). You will see the final balance and the total interest earned straight away, so you can compare scenarios in seconds.
What is the Compound Interest Calculator?
Compound interest is interest earned on both your original money and on the interest already added to it. Unlike simple interest, which is only ever charged on the starting principal, compounding lets each round of interest join the balance and earn more interest in the next period. Over a few years the difference is small, but over decades it becomes the main driver of growth, which is why it is often called the most powerful force in saving.
The core formula is A = P(1 + r/n)^(n*t), where P is the principal, r is the annual rate as a decimal, n is the number of times interest compounds per year, and t is the number of years. The final amount A includes your principal back, so the interest earned is simply A minus P. The more often interest compounds, the more you earn, because interest starts working sooner. Monthly compounding beats annual, and daily edges out monthly, though the gap between frequent options is usually small.
Most real-world saving is not a single lump sum, so many people add regular deposits. To include a fixed contribution PMT made every period, add the future value of that series: FV = PMT (((1 + r/n)^(nt) - 1) / (r/n)). The total ending balance is the compounded principal plus this contribution growth. This is the maths behind a 401(k), an ISA, or any monthly savings plan, and it is why steady contributions often build more wealth than the starting deposit alone.
At the extreme of frequent compounding sits continuous compounding, where interest is added in every instant. As n grows without limit, the formula approaches A = P e^(rt), using Euler's number e (about 2.71828). Continuous compounding is the theoretical ceiling: on $1,000 at 5% for 10 years it gives $1,648.72, only a few cents above daily compounding, which shows how quickly the benefit of more frequent compounding flattens out.
Two things make the biggest difference: time and rate. Because the exponent (n*t) sits at the heart of the formula, adding years has an outsized effect late in the term, when the balance is largest. This is why starting early matters so much and why a modest rate left untouched for thirty years can outgrow a higher rate left for ten. A fast mental check is the Rule of 72: divide 72 by the rate to estimate the years needed to double your money, so 6% doubles in roughly twelve years.
The same maths works against you on debt. A credit card balance left unpaid compounds in exactly the same way, just in the lender's favour, and many cards compound daily. To compare products fairly, look at the annual percentage yield (APY) on savings and the annual percentage rate (APR) with compounding on debt, because both fold the compounding frequency into a single annualised number you can line up side by side.
When to use it
- Estimating how much a savings account or fixed deposit will be worth at the end of its term.
- Comparing two accounts that quote the same rate but compound at different frequencies.
- Projecting the long-run growth of a lump-sum investment so you can plan for a goal.
- Modelling a monthly savings plan, ISA, or 401(k) where you add a fixed amount every period.
- Working out how much interest a credit card or loan balance can pile up if it is left to compound.
- Reverse planning a target, such as the rate or years needed to reach a retirement or house deposit goal.
How to use the Compound Interest Calculator
- Enter your principal, the starting amount of money.
- Type the annual interest rate as a percentage (for example 5 for 5%).
- Set the number of years the money will be invested or saved.
- Choose how often interest compounds: annually, semiannually, quarterly, monthly, or daily.
- Add a regular contribution if you plan to deposit a fixed amount each period.
- Read off the final amount and the total interest earned, then adjust inputs to compare scenarios.
Formula & method
Worked examples
$1,000 invested at 5% for 10 years, compounded monthly.
- r = 5 / 100 = 0.05, n = 12, t = 10
- r/n = 0.05 / 12 = 0.0041667
- n*t = 12 * 10 = 120
- A = 1000 * (1.0041667)^120 = 1000 * 1.64701 = $1,647.01
- interest = 1647.01 - 1000 = $647.01
Result: Final amount $1,647.01, total interest $647.01
$5,000 at 4% for 5 years, compounded quarterly.
- r = 0.04, n = 4, t = 5
- r/n = 0.04 / 4 = 0.01
- n*t = 4 * 5 = 20
- A = 5000 * (1.01)^20 = 5000 * 1.22019 = $6,100.95
- interest = 6100.95 - 5000 = $1,100.95
Result: Final amount $6,100.95, total interest $1,100.95
$1,000 start plus $100 added every month at 6% for 10 years, compounded monthly.
- r/n = 0.06 / 12 = 0.005, n*t = 120
- Principal grows: 1000 * (1.005)^120 = 1000 * 1.81940 = $1,819.40
- Contributions grow: 100 * ((1.005)^120 - 1) / 0.005 = 100 * 163.879 = $16,387.93
- Total = 1819.40 + 16387.93 = $18,207.33
- You deposited 1000 + (100 * 120) = $13,000, so interest = $5,207.33
Result: Final amount $18,207.33, total interest $5,207.33
$1,000 at 5% for 10 years: how compounding frequency changes the result
| Compounding | n (per year) | Final amount | Interest earned |
|---|---|---|---|
| Annually | 1 | $1,628.89 | $628.89 |
| Semiannually | 2 | $1,638.62 | $638.62 |
| Quarterly | 4 | $1,643.62 | $643.62 |
| Monthly | 12 | $1,647.01 | $647.01 |
| Daily | 365 | $1,648.66 | $648.66 |
| Continuous | infinite | $1,648.72 | $648.72 |
Growth of $1,000 at 5% compounded annually, over time
| Years | Final amount | Interest earned |
|---|---|---|
| 1 | $1,050.00 | $50.00 |
| 5 | $1,276.28 | $276.28 |
| 10 | $1,628.89 | $628.89 |
| 20 | $2,653.30 | $1,653.30 |
| 30 | $4,321.94 | $3,321.94 |
| 40 | $7,039.99 | $6,039.99 |
Rule of 72: approximate years to double your money
| Annual rate | Years to double (72 / rate) | Exact years (annual compounding) |
|---|---|---|
| 2% | 36.0 | 35.0 |
| 4% | 18.0 | 17.7 |
| 6% | 12.0 | 11.9 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
Common mistakes to avoid
- Confusing compound interest with simple interest. Simple interest is charged only on the original principal, so $1,000 at 5% earns a flat $50 every year. Compound interest earns on the growing balance, so the yearly gain rises over time. Always check which one a product quotes.
- Entering the rate as a decimal instead of a percent. This calculator expects the rate as a percentage, so type 5 for 5%, not 0.05. Entering 0.05 would model a rate of 0.05%, which gives almost no growth.
- Ignoring the compounding frequency. Two accounts can quote the same headline rate yet pay different amounts because one compounds monthly and the other annually. The effective return (APY) bakes in the frequency, so compare on that, not the nominal rate alone.
- Leaving out regular contributions. A lump-sum projection understates most savings plans. If you add money every month, include the contribution so the future value of that series is counted. The deposits, not just the starting amount, often do most of the heavy lifting.
- Forgetting that fees, tax, and inflation eat into the result. This tool shows gross growth before account fees, tax on interest, or inflation. Your real spending power can be noticeably lower, so treat the figure as a ceiling rather than a guarantee.
- Assuming the rate stays fixed forever. Savings rates float, and investment returns are never guaranteed year to year. The calculator uses one fixed rate for simplicity, so run a few rates to see a realistic range rather than a single certain number.
Glossary
- Principal
- The starting amount of money you invest or borrow, before any interest is added.
- Compounding
- Adding earned interest back to the balance so it earns further interest. The more often this happens, the faster the balance grows.
- Nominal rate
- The stated annual interest rate before accounting for how often it compounds.
- APY (annual percentage yield)
- The effective yearly return once compounding is included. It lets you compare accounts with different compounding frequencies fairly.
- APR (annual percentage rate)
- The annualised cost of borrowing. With compounding it reflects how often interest is added to a debt, which matters on credit cards that compound daily.
- Continuous compounding
- The limit of compounding infinitely often, calculated with A = P times e to the power r times t. It sets the ceiling on how much frequent compounding can add.
- CAGR (compound annual growth rate)
- The single yearly rate that would grow a starting value to an ending value over a period, found with (ending / starting)^(1 / years) minus 1.
- Rule of 72
- A shortcut that estimates the years to double money by dividing 72 by the annual percentage rate. At 6% that is about twelve years.
Frequently asked questions
What is compound interest?
Compound interest is interest earned on both your original principal and on the interest already added to it. Because each round of interest earns more interest, your balance grows faster over time than with simple interest.
What is the compound interest formula?
The formula is A = P(1 + r/n)^(n*t), where P is the principal, r is the annual rate as a decimal, n is the number of times interest compounds per year, and t is the number of years. The interest earned is A minus P.
How do I calculate compound interest?
Divide the annual rate by the number of compounds per year, add 1, raise it to the power of the compounds per year times the number of years, then multiply by the principal. For example $1,000 at 5% for 10 years compounded monthly grows to $1,647.01.
How do I include monthly contributions?
Add the future value of your deposits to the compounded principal. Use FV = PMT * (((1 + r/n)^(n*t) - 1) / (r/n)), where PMT is the amount added each period. For example $100 a month for 10 years at 6% compounded monthly grows the contributions to about $16,388 on their own.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal, so the yearly gain is constant. Compound interest is calculated on the principal plus accumulated interest, so the yearly gain grows. Over long periods compounding produces far more.
Does compounding more often earn more money?
Yes, more frequent compounding earns slightly more because interest starts working sooner. Daily beats monthly, which beats annually, but the gap narrows quickly. On $1,000 at 5% for 10 years, annual gives $1,628.89, daily gives $1,648.66, and continuous gives $1,648.72.
What is continuous compounding?
Continuous compounding is the limit of compounding infinitely often, calculated with A = P * e^(r*t) using Euler's number e (about 2.71828). It is the theoretical maximum, but it barely beats daily compounding in practice, adding only a few cents on a typical balance.
How long does it take to double my money?
A quick estimate is the Rule of 72: divide 72 by the annual rate. At 6% money roughly doubles in 72 / 6 = 12 years. It is an approximation, so use the calculator for an exact figure.
What is the difference between CAGR and compound interest?
Compound interest projects a future balance from a known rate. CAGR works backwards: given a starting and ending value, it finds the single annual rate that connects them, using (ending / starting)^(1 / years) minus 1. Use CAGR to measure past performance and compound interest to forecast.
Does this calculator account for taxes, fees, and inflation?
No, it shows gross growth before tax on interest, account fees, or inflation. Your real, after-tax buying power will be lower, so treat the result as an optimistic ceiling and check tax rules and fees with your provider.
Sources
- Compound interest calculator , U.S. Securities and Exchange Commission (Investor.gov)
- What is compound interest? , U.S. Consumer Financial Protection Bureau