Compound Interest Calculator
Enter an opening balance, a rate, a term, how often interest is added and what you pay in along the way. You get back your opening deposit, your contributions, the interest and the closing balance. Most calculators stop there. This one also runs the same deposits through simple interest at the same rate, because compounding only means something next to the alternative. On the defaults it comes to $2,853.16 of a $55,290.66 balance. The other $12,437.50 of interest would have turned up either way.
Your deposit
What is in the account on day one.
The nominal rate, not the APY. We work out the APY below.
Time and compounding
Whole years.
Changes the APY, not the rate you typed.
Contributions
Final value
$55,290.66
After 10 years at 5.00%, compounded monthly.
Rate and time
Compounding is worth $2,853.16 here. The same deposits at the same rate with interest that never compounds reach $52,437.50, so compounding accounts for 18.7% of the $15,290.66 of interest. The rest would have been earned either way.
Year by year
| Year | Start | Paid in | Interest | End |
|---|---|---|---|---|
| 1 | $10,000 | $3,000 | $581.33 | $13,581 |
| 2 | $13,581 | $3,000 | $764.56 | $17,346 |
| 3 | $17,346 | $3,000 | $957.16 | $21,303 |
| 4 | $21,303 | $3,000 | $1,159.62 | $25,463 |
| 5 | $25,463 | $3,000 | $1,372.43 | $29,835 |
| 6 | $29,835 | $3,000 | $1,596.13 | $34,431 |
| 7 | $34,431 | $3,000 | $1,831.28 | $39,263 |
| 8 | $39,263 | $3,000 | $2,078.46 | $44,341 |
| 9 | $44,341 | $3,000 | $2,338.28 | $49,679 |
| 10 | $49,679 | $3,000 | $2,611.40 | $55,291 |
A gross nominal projection at a fixed rate. No tax, inflation, fees or missed deposits. Interest credited to a US deposit account is generally taxable in the year it is credited, so the amount you keep is lower than the figure above.
Worked example
You open an account with $10,000 and add $250 at the end of every month. It pays a nominal 5% a year, compounded monthly, and you leave it alone for ten years. Three questions: what do you end with, how much of that is interest rather than your own money, and how much of the interest is there only because earlier interest earned interest?
You end with $55,290.66. Of that, $10,000 is the opening balance, $30,000 is the 120 monthly deposits and $15,290.66 is interest. A nominal 5% compounded monthly is an APY of 5.1162%, because the twelve additions inside the year each earn for the rest of it. Run the same deposits with interest that never compounds and you get $52,437.50, so compounding is worth the $2,853.16 difference, or 18.7% of the interest. The effect arrives late. Year one earns $581.33. Year ten earns $2,611.40 off the same $250 a month, 4.5 times as much, because the balance doing the earning is four and a half times bigger. Stretch the plan to thirty years and interest becomes $152,742.10 of a $252,742.10 balance: 60.4% of the account is money you never deposited, against 16.2% at the five year mark.
Why the first years feel like nothing is happening
The mechanic is one line. Interest gets added to the balance, and after that the interest earns interest too. It needs a calculator because the curve is not a straight line, and people misjudge it in a consistent direction. Short horizons get over-estimated. Long ones get badly under-estimated.
Run the defaults out and watch how much of the balance is interest instead of deposits. Five years, 16.2%. Ten years, 27.7%. Twenty, 46.1%. Thirty, 60.4%. The only thing changing is the number of years. Somewhere in the third decade the account stops being mostly your own money.
The same thing happens inside a single run. Year one earns $581.33. Year ten earns $2,611.40, off an identical $250 a month. The rate never accelerated. The balance doing the earning just got bigger, which is why the early years feel like nothing is happening, and why starting feels least worthwhile at the point it matters most.
It is also why the comparison has to be against simple interest and not against zero. Same deposits, same rate, no compounding: $52,437.50. With compounding: $55,290.66. The $2,853.16 gap is what compounding bought, a fifth of the $15,290.66 of interest. Pages that hand you the total interest and call it the compounding effect are out by a factor of five.
APY is the number US law defines
You cannot compare two accounts on their nominal rates. 5% compounded monthly and 5% compounded annually are different products wearing the same number. What settles it is the effective annual rate, and in the United States that has a legal definition rather than a conventional one.
Appendix A to 12 CFR Part 1030, Regulation DD under the Truth in Savings Act, gives the general formula as APY = 100 [(1 + Interest/Principal)^(365/Days in term) - 1], where Principal is what was assumed deposited at the start, Interest is the total dollars earned over the term, and Days in term is the actual number of days. For a 365 day term it collapses to APY = 100 (Interest/Principal). The regulation supplies its own example: an institution paying $30.37 on a $1,000 six month certificate over a 182 day period discloses an annual percentage yield of 6.18%. Put those numbers into the simple interest calculator here and it returns 6.1837%, which rounds to the regulation's figure.
So compare APYs, never nominal rates. Any US deposit account has to disclose one, so the comparison is always there for you. If someone quotes a rate without saying how often it compounds, ask, because until you know that you do not yet have a number.
The calculator shows the APY for whichever frequency you pick. Switch the selector and the APY moves while the rate you typed sits still. That is all compounding frequency does.
Frequency is the input that changes the answer least
It is also the one people fiddle with most. Take $10,000 at a nominal 4.50% for one year. Compounded annually it earns $450.00. Semiannually, $455.06. Quarterly, $457.65. Monthly, $459.40. Daily, $460.25. Continuously, the ceiling no real product pays, $460.28.
Annual to daily is $10.25 on $10,000, and daily lands three cents short of the theoretical maximum. Nothing is left past daily. That is why no product compounds more often, and why continuous compounding stays a teaching device.
Rate and term are the levers. Half a point on that same $10,000, 4.50% to 5.00%, is worth $50.00 against the $10.25 the entire frequency range buys. One extra year beats both. If one account compounds daily and the other pays a tenth of a point more, take the tenth of a point.
The continuous option exists to settle that question rather than approximate it. On the defaults it beats monthly by $38.79 over ten years, and that is the most frequency can ever be worth to you. Knowing the ceiling is $38.79 over a decade is useful before anyone sells you a compounding schedule.
The Rule of 72, and where it is wrong
Divide 72 by the rate for roughly the years to double. It is a good approximation and it is wrong predictably, so this calculator prints the exact figure beside it instead of passing the shortcut off as fact.
Exact doubling time is ln(2) divided by ln(1 + effective annual rate). At 1% the rule says 72 years and the truth is 69.66, overstating by 2.34 years. At 2% it says 36 against 35.00. At 4%, 18 against 17.67. At 6%, 12 against 11.90. At 8% it is 9 against 9.006, effectively exact. Above 8% the error changes sign: at 12% the rule says 6 years against 6.12, at 20% it says 3.6 against 3.80. So 72 flatters low rates and shortchanges high ones. It is at its best in the mid single digits, which is where most people use it anyway.
The doubling figure here covers the opening balance and ignores your contributions. Fold fresh deposits into it and you are describing a savings plan, not growth. Mixing the two is how a calculator ends up claiming a savings account doubles your money in four years.
At the FDIC national average savings rate of 0.38%, doubling takes 182 years. That is the argument for chasing the rate rather than the compounding schedule, in one number.
Where a merchant actually runs into this
Most compound interest calculators are built for retirement savers. Merchants arrive here for three other reasons, and each one changes a decision.
A rolling reserve is a lump sum sitting still for a fixed term. A processor holding 10% of your card volume for 180 days is sitting on money you cannot deploy, and under almost every US merchant agreement it earns you nothing while it sits. Drop your reserve balance and holding period into the simple interest calculator at the FDIC money market average of 0.63% and you get the interest you are giving up. On $50,000 held for 180 days, $155.34. It is a small number and it should be. What a reserve costs you is the use of the cash, and $155.34 is not that. Work the figure out once so nobody can wave it around as a stand-in for the real damage.
A merchant cash advance goes the other way. It has no interest rate, only a factor rate, so nothing on this page applies to it and there is nothing to compound. Type a factor rate in here and you get a confident, meaningless number. Use the factor rate to APR converter, which solves for the rate that makes the cash you received equal the stream of daily payments.
The third is dull and real: cash you are holding anyway. Payout timing, settlement float and a reserve you have already agreed to all leave a balance parked somewhere for a known number of days. This page and its simple interest twin price that balance, and the FDIC table below says what the national averages currently are. Between them that is enough to separate a bank offer worth switching for from one worth $12 a year.
This is arithmetic on the figures you entered, not financial advice and not an offer. Your account agreement or loan note is the authority on what you will actually earn or owe.
FDIC national deposit averages effective 17 August 2026, with what $10,000 becomes at each rate on this page's own arithmetic. The FDIC defines the national rate as the average of rates paid by all insured depository institutions and credit unions for which data is available, weighted by each institution's share of domestic deposits. These are averages. Individual institutions pay well above and well below them.
| Fee | National average | APY, compounded monthly | $10,000 after 10 years | Years to double |
|---|---|---|---|---|
| SavingsWhere most balances actually sit. Read the doubling column. | 0.38% | 0.381% | $10,387.25 | 182 years |
| Money market | 0.63% | 0.632% | $10,650.09 | 110 years |
| 12-month CD | 1.71% | 1.723% | $11,863.46 | 41 years |
| 24-month CD | 1.57% | 1.581% | $11,698.76 | 44 years |
| 36-month CD | 1.34% | 1.348% | $11,433.07 | 52 years |
| 48-month CD | 1.27% | 1.277% | $11,353.41 | 55 years |
| 60-month CDLonger is not automatically higher. The 60 month average sits above both the 36 and 48 month averages here. That is the curve on the day it was read, not a rule. | 1.36% | 1.369% | $11,455.94 | 51 years |
Assumptions and limits
- The defaults, $10,000 opening and $250 a month at 5% for ten years, are placeholders picked to make the arithmetic legible. They are not a forecast, and nobody is offering you that rate. Replace all four with your own figures before reading anything into the output.
- The rate is treated as fixed and known for the whole term, and every deposit is assumed to arrive in full and on time. Real accounts reprice, real savers skip months, and neither is modelled. A ten year projection at a rate nobody has committed to for ten years illustrates the arithmetic, not the future.
- The compounding frequency and the contribution frequency are independent, because in practice they are: daily compounding with monthly deposits is the normal case. The maths converts the nominal rate to an effective annual rate first, then to a rate per contribution period. That is exact for any pairing, rather than an approximation that only holds when the two happen to match.
- Contribution timing is a switch, and it moves the answer. Deposits at the end of each period, the default, earn nothing in the period they arrive. Deposits at the start earn for the full period. On the defaults that is $161.75 over ten years. Small, but it decides which of two calculators agrees with your statement.
- Nothing here models tax, inflation, fees or early withdrawal penalties, and all four are real. Interest on a US deposit account is generally taxable in the year it is credited, so the after-tax figure is lower than the number shown, and an inflation-adjusted figure is lower again. Treat the output as a gross nominal balance.
- The FDIC averages in the table above are national averages published by the FDIC, effective 17 August 2026. The FDIC republishes them monthly, so re-check the source before quoting them. The derived columns beside them are computed by this page, not published by the FDIC.
Frequently asked questions
- What is the compound interest formula?
- For a lump sum it is A = P(1 + r/n)^(nt), where P is the opening balance, r is the nominal annual rate as a decimal, n is the number of compounding periods a year, and t is the number of years. $10,000 at 5% compounded monthly for ten years is 10,000 x (1 + 0.05/12)^120 = $16,470.09. Regular deposits need a second term, the future value of an annuity. This calculator handles the two frequencies separately instead of assuming your deposits land exactly when interest is credited: it works out the effective annual rate, converts that to a rate per deposit period, then steps through the term. That gives the same answer as the closed form when the frequencies match, and the right answer when they do not.
- How much difference does compounding frequency really make?
- Much less than the term or the rate. On $10,000 at a nominal 4.50% for one year, annual compounding earns $450.00, quarterly earns $457.65, monthly earns $459.40 and daily earns $460.25. Continuous compounding, the mathematical ceiling that no product pays, earns $460.28, so daily lands within three cents of the maximum possible. The whole annual-to-daily range is $10.25 on $10,000. A tenth of a percentage point on the rate beats any change in frequency, which is why comparing APYs settles the question and comparing compounding schedules does not.
- What is the difference between compound interest and simple interest?
- Simple interest is paid only on the money you deposited. Compound interest is paid on the deposits and on the interest already credited. Over short terms the gap is close to nothing: $25,000 at 9% for 30 days earns $184.93 either way, to the cent. Over long terms it takes over. On this page's defaults, ten years of $250 a month on a $10,000 opening balance ends at $55,290.66 compounded against $52,437.50 simple, a gap of $2,853.16. Watch the proportion, because it gets misstated constantly. Total interest is $15,290.66, and compounding accounts for $2,853.16 of it. The other $12,437.50 would have been earned anyway.
- How long does it take to double your money?
- The exact figure is ln(2) divided by ln(1 + the effective annual rate). The Rule of 72 approximates it by dividing 72 by the rate, and this calculator prints both so you can see the error. The rule is nearly perfect at 8%, where it says 9 years against a true 9.006. Below that it overstates: at 1% it says 72 years against 69.66. Above that it understates: at 20% it says 3.6 years against 3.80. For a sense of scale on real deposit rates, the FDIC national average savings rate of 0.38% doubles money in 182 years. The doubling figure here covers the opening balance only and leaves your contributions out, because a doubling time that counts fresh deposits is describing a savings plan rather than growth.
- Should contributions be set at the start or the end of the period?
- Match whichever your account actually does. If you do not know, use the end of the period, which is the default here and the more conservative of the two. A deposit at the start earns interest for that whole period, an annuity due in the language of the formula. A deposit at the end earns nothing until the next one. On the defaults the difference is $161.75 over ten years on a $55,290.66 balance, so it will not change a decision, but it will decide whether this calculator agrees with your bank statement, and that is usually why anyone is checking.
- Does this calculator account for tax and inflation?
- No, and both matter more than most of the inputs it does model. Interest credited to a US deposit account is generally taxable in the year it is credited, so the balance you keep is smaller than the balance shown, and how much smaller depends on your marginal rate rather than on anything here. Inflation is a second, separate reduction in what the balance buys. The output is a gross nominal projection. Use it to compare two options on identical assumptions, not to predict a future amount of spendable money.
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