How to use this compound interest calculator
- Enter your initial investment, the amount you start with. It can be $0 if you are only making regular deposits.
- Add a regular contribution and how often you make it: weekly, every two weeks (handy if you save from each paycheck), monthly, quarterly or yearly. Choose “None” for a one-time lump sum.
- Enter the annual interest rate and compounding frequency. For a savings account or CD, use the rate and compounding schedule in the account disclosure, or enter the APY and choose “Annually.” For stocks, remember returns are not fixed: the S&P 500’s compound average was about 10% a year from 1928 through 2025 with dividends reinvested (NYU Stern data), with large swings from year to year.
- Set the time period in years and months. Open “Contribution timing & yearly increase” to deposit at the start of each period or raise your deposits every year. Results, the chart and the table update as you type, and “Copy link” saves your scenario.
What is compound interest?
Compound interest is interest earned on your original money and on the interest it has already earned. Each time interest is added to the balance, the next round of interest is figured on a slightly bigger number, so growth speeds up over time. Simple interest, by contrast, is paid only on the original principal.
Here is $10,000 at 5% a year with no further deposits. After 30 years, compounding (monthly) earns $34,677 of interest versus $15,000 with simple interest, 2.3 times as much:
| Years | With simple interest | With compound interest | Extra from compounding |
|---|---|---|---|
| 5 years | $12,500 | $12,834 | $334 |
| 10 years | $15,000 | $16,470 | $1,470 |
| 20 years | $20,000 | $27,126 | $7,126 |
| 30 years | $25,000 | $44,677 | $19,677 |
Compound interest formula
For a single deposit, the balance after t years is:
A = P × (1 + r/n)^(n × t)
- A
- balance after t years
- P
- principal (initial investment)
- r
- annual interest rate as a decimal (5% = 0.05)
- n
- compounding periods per year (12 for monthly, 365 for daily)
- t
- number of years
Regular deposits made at the end of each compounding period add the future value of an annuity:
FV = PMT × ((1 + r/n)^(n × t) − 1) ÷ (r/n)
- FV
- future value of the deposits
- PMT
- deposit per period
Deposits at the start of each period earn one more period of interest, so multiply FV by (1 + r/n). When deposits and compounding happen on different schedules, the calculator converts the rate to an equivalent rate per deposit period, (1 + r/n)n/p − 1, where p is the number of deposits per year.
Worked example
Take the default inputs: P = $10,000, PMT = $200 a month, r = 0.05, n = 12 and t = 10. The growth factor is (1 + 0.05/12)120 = 1.647009, so the initial investment grows to $10,000 × 1.647009 = $16,470.09. The deposits grow to $200 × (1.647009 − 1) ÷ 0.004167 = $31,056.46. Together that is $47,526.55, the same result the calculator shows. Making each deposit at the start of the month instead raises it to $47,655.95.
How much will $10,000 grow?
Value of a one-time $10,000 investment compounded annually, with no further deposits. At 7%, the money roughly doubles every decade: $19,672 after 10 years and $76,123 after 30.
| Time | 3% | 5% | 7% | 10% |
|---|---|---|---|---|
| 5 years | $11,593 | $12,763 | $14,026 | $16,105 |
| 10 years | $13,439 | $16,289 | $19,672 | $25,937 |
| 20 years | $18,061 | $26,533 | $38,697 | $67,275 |
| 30 years | $24,273 | $43,219 | $76,123 | $174,494 |
The rate you earn matters, too. The FDIC’s national average savings rate was 0.37% as of September 21, 2026; at that rate, $10,000 would grow to only about $10,376 in 10 years, while the same deposit at 5% reaches $16,289. Comparing rates before you open an account pays off.
Does compounding frequency matter?
More frequent compounding earns a little more, but the gains shrink quickly. For $10,000 at 5% over 10 years, moving from annual to monthly compounding adds $181.15; moving from monthly to daily adds just $16.55, and even continuous compounding adds only $0.56 more than daily.
| Compounding | APY | Balance after 10 years |
|---|---|---|
| Annually | 5.000% | $16,288.95 |
| Semi-annually | 5.062% | $16,386.16 |
| Quarterly | 5.095% | $16,436.19 |
| Monthly | 5.116% | $16,470.09 |
| Daily (365 / yr) | 5.127% | $16,486.65 |
| Continuously | 5.127% | $16,487.21 |
The calculator starts at monthly compounding because it lines up with the most common saving habit, a deposit every month. Banks must tell you how often interest is compounded and credited on a deposit account (Regulation DD, § 1030.4), so switch the setting to match your account.
APY vs. APR: what’s the difference?
Under the Truth in Savings Act’s Regulation DD, a deposit account’s interest rate is the annual rate that does not reflect compounding, while the annual percentage yield (APY) reflects both the rate and how often it compounds over a 365-day year. The formula is APY = (1 + r/n)n − 1, so 5% compounded monthly is an APY of 5.116%. Because APY already includes compounding, it is the fair way to compare savings accounts and CDs.
APR is the yearly rate quoted on loans and credit cards. Compounding works against you there: many card issuers charge a daily periodic rate (the APR divided by 360 or 365) and add each day’s interest to the balance, according to the CFPB. At the Federal Reserve’s latest average of 22.15% at commercial banks for card accounts assessed interest, a balance with no payments or new charges would grow by about 24.8% in a year with daily compounding (APR ÷ 365). See how fast a balance can shrink with our credit card payoff calculator.
The Rule of 72: how long to double your money
To estimate how many years it takes an investment to double, divide 72 by the annual rate of return. At 5%, that gives 14.4 years; the exact answer with annual compounding, ln(2) ÷ ln(1 + r), is 14.21 years. The shortcut works best in the middle of the range:
| Annual return | Rule of 72 | Exact (compounded annually) | Difference |
|---|---|---|---|
| 2% | 36.0 years | 35.00 years | +1.00 |
| 3% | 24.0 years | 23.45 years | +0.55 |
| 4% | 18.0 years | 17.67 years | +0.33 |
| 5% | 14.4 years | 14.21 years | +0.19 |
| 6% | 12.0 years | 11.90 years | +0.10 |
| 7% | 10.3 years | 10.24 years | +0.04 |
| 8% | 9.0 years | 9.01 years | −0.01 |
| 9% | 8.0 years | 8.04 years | −0.04 |
| 10% | 7.2 years | 7.27 years | −0.07 |
| 12% | 6.0 years | 6.12 years | −0.12 |
How to make compound interest work for you
- Start early. Investing $200 a month at a 7% average annual return grows to $494,308 over 40 years but $233,891 over 30 years. The extra 10 years add $24,000 of deposits and $236,418 of additional growth.
- Raise your contributions. Increasing that $200 by 3% a year lifts the 30-year total from $233,891 to $320,959.
- Use tax-advantaged accounts. Interest in a regular savings account is taxed every year, which slows compounding. Retirement accounts let earnings grow without yearly tax; see our 401(k) calculator and retirement calculator.
- Pay off high-interest debt first. Every dollar that pays down a credit card saves interest at the card’s APR, which is usually far more than a savings account or CD pays.
- Account for inflation. A future balance buys less than the same dollars today. Check the effect with our inflation calculator, or model different returns with the investment calculator.
Frequently asked questions
How do I calculate compound interest?
Use A = P(1 + r/n)nt, where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. For $10,000 at 5% compounded monthly for 10 years, A = $10,000 × (1 + 0.05/12)120 = $16,470.09. Regular deposits add a second term from the annuity formula, which this calculator handles for you.
How much will $10,000 be worth in 10 years?
With annual compounding and no further deposits, $10,000 grows to $16,289 at 5% a year, $19,672 at 7% and $25,937 at 10%. Savings account rates can change over time and stock market returns vary from year to year, so treat any long-term projection as an estimate rather than a promise.
What is the difference between APY and APR?
APY (annual percentage yield) includes the effect of compounding over a year; the plain interest rate does not. Federal Regulation DD requires banks to state both in deposit account disclosures. For example, 5% compounded monthly is an APY of 5.116%. APR is the yearly rate quoted on loans and credit cards, and it generally does not show the effect of compounding.
Is daily compounding better than monthly?
Daily compounding pays slightly more, but the difference is small. $10,000 at 5% for 10 years grows to $16,486.65 with daily compounding versus $16,470.09 with monthly compounding, a gap of $16.55. The interest rate and how long you leave the money invested matter far more than the compounding schedule.
What is the Rule of 72?
The Rule of 72 estimates how many years it takes money to double: divide 72 by the annual interest rate. At 8%, that is 72 ÷ 8 = 9 years, and the exact answer with annual compounding is 9.01 years. The shortcut is closest for rates between about 6% and 10% and drifts further off at very low or very high rates.
How much do I need to save each month to have $1 million?
Assuming a 7% average annual return and deposits at the end of each month, you would need about $855 a month for 30 years or $405 a month for 40 years, starting from $0. A lower return or a shorter time frame raises the amount a lot. Returns are not guaranteed, so revisit the numbers every year with this calculator.
Is compound interest taxable?
Yes. The IRS treats interest from bank accounts, money market accounts and CDs as taxable income, and banks send Form 1099-INT when they pay you $10 or more. You must report all taxable interest even without a form. Inside a traditional IRA, earnings are taxed only when withdrawn, and qualified Roth IRA withdrawals are tax-free, so more of the growth keeps compounding.