The compound interest calculator below can be used to compare or convert the interest rates of different compounding periods. Please use our Interest Calculator to do actual calculations on compound interest.
The compound interest calculator above converts an interest rate from one compounding frequency to another. Enter a rate, tell it how often that rate compounds, and choose the frequency you want it expressed in — the calculator returns the exactly equivalent rate. A 6% rate compounded monthly, for example, is the same deal as a 6.16778% rate compounded annually. Different numbers, identical outcome.
This is the tool you need when two offers are quoted on different terms and you cannot tell which is actually better. Banks, lenders, and credit card issuers all quote rates using different compounding conventions, and a rate is meaningless until you know how often it compounds. Converting everything to a single common frequency is the only honest way to compare.
Note that this calculator converts rates; it does not project balances. To see what a specific sum of money grows to over time, use the Interest Calculator or the Investment Calculator.
Interest is the cost of using borrowed money — the amount a lender receives for advancing funds to a borrower. Interest comes in two fundamentally different flavors, and the distinction between them is one of the most consequential ideas in all of personal finance.
Simple interest is earned only on the principal. If you deposit $1,000 at 6% simple interest, you earn $60 every year, forever. After 10 years you have earned $600, and after 30 years $1,800. The interest never grows, because it is always calculated on that original $1,000 and nothing else.
Compound interest is earned on the principal and on the interest already accumulated. That same $1,000 at 6% compounded annually earns $60 in year one, but in year two it earns 6% of $1,060 — $63.60. In year three it earns 6% of $1,123.60. The interest itself starts earning interest, and the balance curves upward instead of climbing in a straight line. After 30 years you have $5,743.49 rather than $2,800.
That gap — nearly $3,000 on a $1,000 deposit, from nothing more than the choice of interest convention — is the entire reason compounding matters. Albert Einstein is popularly credited with calling compound interest the eighth wonder of the world; the attribution is almost certainly apocryphal, but the sentiment survives because the math genuinely is startling.
Once interest compounds, a second question immediately follows: how often? The stated rate alone is not enough information. A 6% rate compounded once a year and a 6% rate compounded every day are not the same rate, because in the second case the interest starts earning its own interest 365 times instead of once.
Here is what a nominal 6% rate is actually worth at each compounding frequency, expressed as the effective annual rate:
Two things stand out. First, more frequent compounding always produces a higher effective rate — good news if you are saving, bad news if you are borrowing. Second, the gains taper off sharply. Going from annual to monthly compounding buys you a meaningful 0.168 percentage points. Going from daily all the way to continuous compounding — from 365 periods to infinitely many — buys you a mere 0.0005 percentage points. Compounding frequency converges quickly, and past monthly the differences become close to irrelevant for most practical purposes.
Every conversion runs through a common pivot: the effective annual rate. Whatever frequency you start with, the calculator first works out what one full year of growth actually amounts to, then re-expresses that same annual growth in the frequency you asked for.
Step 1 — to the effective annual rate:
EAR = (1 + r / n)n − 1
Step 2 — back out to the target frequency:
output = m × [ (1 + EAR)1/m − 1 ]
Here r is the input rate as a decimal, n is the number of input compounding periods per year, and m is the number of output periods per year. The period counts are 1 for annually, 2 for semiannually, 4 for quarterly, 12 for monthly, 24 for semimonthly, 26 for biweekly, 52 for weekly, and 365 for daily.
Continuous compounding is the limiting case as the number of periods approaches infinity, and it uses the exponential function instead:
To the effective annual rate: EAR = er − 1
Back out to a continuous rate: output = ln(1 + EAR)
Worked through with the default values: a 6% rate compounded monthly gives EAR = (1 + 0.06/12)12 − 1 = 1.00512 − 1 = 0.0616778, or 6.16778% compounded annually. Run it the other way and 6% compounded annually converts to 12 × (1.061/12 − 1) = 5.84106% compounded monthly.
The two labels in the dropdowns — Annually (APY) and Monthly (APR) — point at the single most commercially important application of this calculator.
APR (Annual Percentage Rate) is a nominal rate. It is the periodic rate multiplied by the number of periods in a year, with no allowance for the compounding that happens in between. A credit card charging 1.5% per month advertises an APR of 18%, because 1.5 × 12 = 18. In the United States, the Truth in Lending Act requires lenders to disclose APR, and it also folds in certain fees — which makes it a useful comparison tool for loans, but a systematic understatement of what compounding will actually cost you.
APY (Annual Percentage Yield), also called the effective annual rate, is the honest number. It answers the only question that really matters: if I leave this money alone for one year, what percentage more will I have? APY bakes the compounding in. That 18% APR credit card, compounding monthly, carries an APY of 19.56% — over a point and a half more than the advertised figure. On a $10,000 balance carried for a year, that gap is $156 you did not see coming.
The asymmetry in how these are quoted is not accidental. Under U.S. regulation, deposit accounts must advertise APY (the higher, more attractive number for a saver), while loans advertise APR (the lower, more attractive number for a borrower). Both disclosures are legally correct and both are chosen to flatter. Converting everything to a common frequency before comparing is your defense.
Below the main answer, the calculator lists your input rate expressed at every one of the nine compounding frequencies at once, with your selected output row highlighted. This is often more useful than the single conversion, because it lets you see the whole landscape in one glance and check any offer you encounter without re-running the calculation.
The row spread also gives you an immediate feel for how much compounding frequency actually matters at your rate. At 2%, the entire range from annual to continuous spans about 0.02 percentage points — negligible. At 25%, the same range spans about 3.4 percentage points — very much worth caring about. Compounding frequency matters more the higher the rate, which is precisely why it matters most on credit cards and payday loans, and least on savings accounts.
Annually — interest is added once per year. Common for certificates of deposit, some bonds, and simple loan structures. When a rate compounds annually, the nominal rate and the effective rate are identical, which is why this option is labeled APY.
Semiannually — twice a year. This is the standard convention for U.S. Treasury bonds and most corporate bonds, which pay coupons every six months.
Quarterly — four times a year. Used by many savings accounts, dividend-paying investments, and business loans.
Monthly — twelve times a year, and by far the most common convention in consumer finance. Mortgages, auto loans, credit cards, personal loans, and most savings accounts all compound monthly. This is the frequency APR is usually quoted against.
Semimonthly — twice a month, 24 times a year. Occasionally used for payroll-linked products and some accelerated payment schedules.
Biweekly — every two weeks, 26 times a year. Note that biweekly is not the same as semimonthly: 26 periods versus 24. That extra two periods is exactly why biweekly mortgage payment plans shorten a loan term — you end up making the equivalent of 13 monthly payments a year instead of 12.
Weekly — 52 times a year. Common in some short-term lending and certain international products.
Daily — 365 times a year. Credit cards typically compute interest using a daily periodic rate, as do many high-yield savings accounts and money market accounts. This calculator uses a 365-day year; some institutions use 360 days for certain products, which produces a slightly different result.
Continuously — the theoretical limit of compounding infinitely often. No real bank compounds continuously, but the model is used constantly in quantitative finance because the exponential math is far easier to work with. It also gives you a hard upper bound: no compounding schedule, however aggressive, can exceed the continuous rate.
A handy companion to compound interest math is the Rule of 72: divide 72 by an annual rate of return to estimate how many years it takes money to double. At 6%, money doubles in roughly 12 years. At 9%, about 8 years. At 3%, about 24 years.
The rule is an approximation derived from the logarithmic nature of compounding, and it is remarkably accurate for rates between roughly 4% and 15%. Use the effective annual rate for best results — which is exactly what this calculator produces. The rule works in reverse too: at 3% inflation, prices double roughly every 24 years, which is why the real, inflation-adjusted return on your savings matters more than the headline number.
This calculator computes conversions using exact closed-form mathematics and displays results to five decimal places. That level of precision is more than sufficient for any practical financial decision — a difference in the fifth decimal place of a percentage amounts to a fraction of a cent on a $10,000 balance.
Keep in mind that the compounding convention is only one input into what an account actually pays. Real-world results also depend on the day count basis the institution uses (365 vs. 360 days, actual vs. approximated months), when interest is credited versus when it is calculated, minimum balance requirements, promotional rate periods, and fees. Two accounts with identical stated rates and identical compounding can still pay different amounts.
APR is a nominal rate that ignores intra-year compounding — it is just the periodic rate times the number of periods. APY (the effective annual rate) includes compounding and tells you what you actually earn or pay over a year. APY is always greater than or equal to APR, and they are equal only when interest compounds exactly once per year.
Yes, if you are saving — and always more cost if you are borrowing. But the effect has diminishing returns. Moving from annual to monthly compounding at 6% gains you 0.168 percentage points; moving from daily to continuous gains you only 0.0005.
Continuous compounding is the mathematical limit of compounding infinitely often, computed as er − 1. No bank offers it in practice, but it is used widely in quantitative finance because it simplifies the math, and it serves as the theoretical maximum any compounding schedule can approach.
No. Biweekly means every two weeks, giving 26 periods per year. Semimonthly means twice a month, giving 24. That difference of two periods is the mechanism behind biweekly mortgage payment plans, which effectively squeeze in an extra monthly payment each year.
365 is the standard calendar-year convention and the one used here. Some institutions use a 360-day year (the "banker's year") for certain commercial products, which produces slightly different figures. Check your account terms if the distinction matters for your situation.
Not directly — this calculator converts rates rather than projecting balances. Convert your rate to an effective annual rate here, then use the Interest Calculator or Future Value Calculator to project a balance forward.
The conversion still works mathematically and returns a negative equivalent rate, which can be useful for modeling deflation or negative-yielding bonds. Rates at or below −100% compounded annually are undefined and will return an error.
This Compound Interest Calculator is provided for educational and general informational purposes. It converts stated interest rates between compounding conventions and does not account for fees, taxes, day count variations, minimum balance requirements, or promotional terms that may affect what an account actually pays or costs. Consult your account disclosures and a qualified financial professional before making financial decisions.