Compound interest formula
The compound interest formula is A = P(1 + r/n)nt, where the balance A grows from the principal P at an annual rate r compounded n times a year for t years.[1][2]
Worked example: $10,000 at 5% compounded monthly for 10 years is 10,000 × (1 + 0.05/12)120 = 10,000 × 1.647009 = $16,470.09, so $6,470.09 of the balance is interest. With simple interest the same deposit would earn only $5,000; the extra $1,470.09 is interest earned on interest.
Regular deposits add a second term, the future value of a series of payments (an annuity).[3] For deposits of PMT at the end of each period:
Compounding frequency: daily vs monthly vs annually
More frequent compounding earns slightly more, but the difference is small next to the rate itself. Here is $10,000 at 5% for 10 years:
| Compounding | Balance | Interest | APY |
|---|---|---|---|
| Annually | $16,288.95 | $6,288.95 | 5.000% |
| Quarterly | $16,436.19 | $6,436.19 | 5.095% |
| Monthly | $16,470.09 | $6,470.09 | 5.116% |
| Daily | $16,486.65 | $6,486.65 | 5.127% |
| Continuously | $16,487.21 | $6,487.21 | 5.127% |
Daily compounding beats monthly by only a few dollars here. That is why U.S. banks must quote the annual percentage yield (APY), which folds the compounding into one comparable number.[4] If an account quotes an APY, choose "Rate is an APY" in the calculator and the frequency stops mattering. The daily compound interest calculator handles daily rates and weekday-only compounding.
Compound interest with monthly contributions
Regular deposits usually matter more than the starting amount. Saving $200 a month at 5% compounded monthly:
| Period | Deposited | Balance (end of month) | Balance (start of month) | Interest |
|---|---|---|---|---|
| 10 years | $24,000 | $31,056.46 | $31,185.86 | $7,056.46 |
| 20 years | $48,000 | $82,206.73 | $82,549.26 | $34,206.73 |
| 30 years | $72,000 | $166,451.73 | $167,145.28 | $94,451.73 |
After 30 years interest makes up more than half of the balance. Depositing at the start of each month adds one extra month of interest on every deposit. To plan the deposit for a specific target, use the savings goal calculator; for a savings account that quotes an APY, the savings calculator.
Goal seek: time, rate or deposit needed
Switch "Solve for" to work backward from a target. Starting with $10,000 and saving $200 a month:
- Time to goal: at 5% compounded monthly you reach $100,000 in 18 years and 10 months.
- Rate needed: to reach $100,000 in 20 years you need 4.34% a year compounded monthly.
- Deposit needed: at 5% for 20 years you need $177.29 a month.
For a quick estimate of doubling time without a calculator, divide 72 by the rate; the rule of 72 calculator shows how close that shortcut gets.
What if the rate is different?
One percentage point of rate changes the result more than most people expect, because the difference compounds too. The calculator shows your plan at two points below and above the rate you enter. For $10,000 plus $200 a month over 10 years, compounded monthly:
- 3%: $41,441.82
- 4%: $44,358.29
- 5%: $47,526.55
- 6%: $50,969.84
- 7%: $54,713.58
The spread between 3% and 7% is $13,271.76 on $34,000 of money put in. Savings and money market rates move with the economy, so treat a long projection as a range, not a promise; for a fixed rate locked in for the term, see the CD calculator.
Inflation and taxes
A balance in future dollars buys less than the same number today. Prices rose 3.7% over the 12 months to September 2026 (CPI-U, Bureau of Labor Statistics).[5] At that rate, the $47,526.55 from the 10-year example with deposits is worth about $33,048.27 in today's dollars. Enter an inflation rate to see this line on the chart.
Interest on bank accounts, CDs and bonds is generally taxable in the year it is credited, and banks report it on Form 1099-INT.[6] In a taxable account, enter your tax rate: the calculator then compounds the after-tax rate, which is how the money actually grows if you pay the tax from the account. Retirement accounts that defer tax should use 0%.
How this calculator works
- Same formula everywhere. The result shown on this page before you type anything was computed with the same code that runs in your browser.
- Different schedules. With monthly deposits and daily compounding, each month earns (1 + r/365)365/12 − 1, the exact monthly equivalent of daily compounding. Balances therefore match A = P(1 + r/n)nt at every compounding date.
- Tested. The code is checked against hand-worked results: $10,000 at 5% monthly for 10 years = $16,470.09; $1,000 at 5% continuous for 10 years = $1,648.72.
- Limits. Real accounts round interest to the cent each period and count actual days in each month, so a bank statement can differ by a few cents. Rates on savings accounts change; the calculator assumes the rate you enter holds for the whole period.
Common mistakesEntering an APY as if it were a nominal rate (choose "Rate is an APY"), forgetting that a monthly rate must be multiplied by 12, and comparing accounts by rate instead of APY.
All interest and savings calculators
Interest
- Interest calculatorInterest earned on a sum, simple or compound, every method side by side
- Interest rate calculatorThe rate behind a growth figure or a loan payment
- Simple interest calculatorI = P × r × t, solved for interest, principal, rate or time
- Daily compound interest calculatorCompound a daily rate, weekdays only and partial reinvestment
- How much interest will I earn?Interest per day, month and year on any balance, with tables
- Compound interest formulaA = P(1 + r/n)^nt explained with worked examples
- Compound vs simple interestThe same deposit both ways, year by year
Savings
- Savings calculatorBalance and interest from monthly deposits at an APY
- High yield savings account calculatorYour APY against the FDIC national average, in dollars
- Savings goal calculatorMonthly deposit needed for a target, or time to reach it
- Millionaire calculatorWhen you reach $1 million at your saving rate and return
- Money market calculatorTiered APYs, monthly fees and the minimum balance
CDs and APY
- CD calculatorValue at maturity from APY or rate, any term
- CD early withdrawal penalty calculatorWhat breaking a CD costs, and when it pays
- CD ladder calculatorRungs, blended APY and the ladder against a single CD
- APY calculatorAPR to APY and back, for any compounding
- What is APY?Annual percentage yield vs interest rate vs APR
Treasuries
- T-bill calculatorPrice, investment rate and the state-tax edge over a CD
- Treasury bill ratesLatest auction rates for 4- to 52-week bills
- Treasury bond calculatorPrice or yield to maturity of a Treasury note or bond, with duration
- Savings bond calculatorWhat an EE or I savings bond is worth, with the 20-year doubling guarantee
- I bond calculatorValue of your I bond month by month with the TreasuryDirect rates
- I bond ratesCurrent composite, fixed and inflation rates, and the history
Growth and time value
- Rule of 72 calculatorDoubling time, and how far off the shortcut is
- CAGR calculatorCompound annual growth rate between two values
- Future value calculatorA lump sum and a series of payments, grown forward
- Present value calculatorWhat a future sum or payment stream is worth today
- Dividend calculatorDividend income, yield and the capital an income goal needs
- DRIP calculatorDividends reinvested vs taken as cash, side by side
Frequently asked questions
What is compound interest?
Compound interest is interest calculated on the principal plus the interest already earned. Each period's interest is added to the balance, so the next period earns interest on a larger amount.
How do you calculate compound interest monthly?
Divide the annual rate by 12, add 1, raise it to the number of months and multiply by the principal: A = P(1 + r/12)12t. $10,000 at 5% for 10 years is 10,000 × (1.0041667)120 = $16,470.09.
Is daily compounding much better than monthly?
Only slightly. At 5%, daily compounding gives an APY of 5.127% against 5.116% for monthly. The rate matters far more than the compounding schedule.
How long does it take to double money with compound interest?
About 72 divided by the annual rate in percent: 9 years at 8%, 12 years at 6%. The exact time is ln 2 ÷ ln(1 + r) with annual compounding.
Do deposits at the start of the month earn more?
Yes. A deposit made at the start of a period earns interest for that whole period, so the total is the end-of-period result times (1 + r/n).
What is continuous compounding?
Compounding infinitely often. The formula becomes A = Pert; $1,000 at 5% for 10 years grows to $1,648.72, only a little more than daily compounding.