Compound interest calculator

Compound interest is interest earned on interest. $10,000 at 5% a year earns $500 in the first year and $525 in the second, because the second year's interest is paid on $10,500. After 10 years it has grown to $16,289 compounded yearly, against $15,000 with simple interest, which is paid only on the original deposit.

The SEC's Investor.gov puts it the same way with $100 at 5%: $105 after a year, $110.25 after two, more than $162 after 10 years and almost $340 after 25, with nothing more added. The longer money compounds, the more of the balance is interest rather than deposits.

For a single deposit, the balance after t years is:

A = P(1 + r/n)^nt

• A is the ending balance.
• P is the starting amount, the principal.
• r is the yearly interest rate as a decimal: 5% is 0.05.
• n is how many times interest compounds each year: 1 yearly, 4 quarterly, 12 monthly, 365 daily.
• t is the number of years.

Worked example: $10,000 at 5% compounded monthly for 10 years. The monthly rate is 0.05 ÷ 12 ≈ 0.0041667 and there are 12 × 10 = 120 compounding periods, so A = 10,000 × 1.0041667¹²⁰ = 10,000 × 1.6470 = $16,470.09. Of that, $6,470.09 is interest.

Regular additions each grow by the same rule from the day they land. Added at the end of every period, they sum to PMT × ((1 + i)^N − 1) ÷ i, where PMT is each addition, i the rate per period and N the number of additions. The calculator works it out month by month instead, which also handles yearly additions and a contribution that rises each year.

At 7% a year, $10,000 grows to $19,672 in 10 years, $38,697 in 20 and $76,123 in 30, compounded yearly. At 4% it reaches $14,802 in 10 years; at 10%, $25,937.

Saved at the end of each month at 7%, compounded monthly, $500 a month grows to $86,542 in 10 years, $260,463 in 20 and $609,985 in 30. Of that 30-year total, $180,000 is your own money and $429,985 is interest.

Time does most of the work. At 8%, 40 years of $500 a month puts in twice as much as 20 years but ends with more than 5 times the balance, because the early deposits have decades longer to earn interest on their interest.

Use the APY your account pays, or a long-run average return for investments. In the FDIC's national rates published September 21, 2026, the average savings account paid 0.37%, a money market account 0.63% and a 12-month CD 1.73%. The S&P 500 returned about 10.7% a year from 1957 to 2026 with dividends reinvested, but stock returns swing from year to year and are never guaranteed.

Deposit rates are the FDIC's national averages published September 21, 2026, weighted by each bank's and credit union's share of deposits. Rates differ widely from one bank to the next, so use the APY your own account pays. The S&P 500 figure is its average yearly return with dividends reinvested, from Robert Shiller's market data; it is about 6.8% a year after inflation, and any single year can be far above or below it.

Divide 72 by the yearly interest rate to estimate how many years money takes to double. At 8%, money doubles in about 9 years (exactly 9.01 years); at 4%, about 18. At the 0.37% national average for savings, it takes about 188 years. The rule is closest near 8% and runs a little long at low rates.

The SEC's example is 9%: 72 ÷ 9 = 8, so money doubles about every 8 years. The rule also works backward: to double in 10 years you need about 7.2% a year.

Only a little. $10,000 at 5% for 10 years grows to $16,289 compounded yearly, $16,470 monthly and $16,487 daily, so daily compounding adds $198 over a decade. The rate matters far more: at 6% compounded yearly, the same $10,000 reaches $17,908.

Going from yearly to monthly compounding is most of the gain; monthly to daily adds only $17 on $10,000 over 10 years. When comparing accounts, compare APYs: they already include compounding, so a higher APY always earns more.

An APR, like a savings account's stated interest rate, is a simple yearly rate that leaves out compounding; APY, the annual percentage yield, counts it. 5% compounded monthly is a 5.12% APY, and 5% compounded daily is 5.13%. Banks must advertise savings rates as an APY under Regulation DD. Card interest compounds the same way: the 21.19% average credit card APR, charged daily, adds up to about 23.6% over a year on a balance left unpaid.

Under Regulation DD, the APY measures the total interest an account pays based on its interest rate and how often it compounds, expressed as a yearly rate over 365 days. Advertised savings rates must be stated as an APY. On credit cards, the CFPB explains that issuers often charge a daily rate, the APR divided by 360 or 365, and add each day's interest to the balance, so it compounds daily. The average APR is the Federal Reserve's G.19 figure for August 2026.

To turn an APY into results here, enter it as the rate and pick yearly compounding. To use a rate that isn't an APY, enter it with the account's own compounding.

• Interest compounds at your chosen frequency. Money added between compounding dates is treated as earning the account's yield from the day it lands.
• Monthly additions land at the end of each month; yearly additions at the end of each year.
• A yearly increase raises the addition once a year: at 3%, $500 a month becomes $515 a month in year two.
• Total contributed is your starting amount plus every addition. Interest earned is the ending balance minus that.
• Doubling time uses the rule of 72 on your rate, with the exact time at your compounding alongside. It ignores additions.