Free effective annual rate calculator
See the rate you really pay or earn. Enter a nominal annual rate and pick how often it compounds — annual, monthly, daily, or continuous. The calculator returns the effective annual rate (EAR), the spread over the nominal rate, and how the result changes with compounding frequency — updated live, as you type.
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Estimates only, based on the values you enter. Not financial advice.
Results are estimates. Consult a professional.
What is the effective annual rate?
The effective annual rate (EAR) is the interest rate you actually earn or pay over a year once compounding is taken into account. A bank can advertise a 12% nominal rate, but if that interest is added monthly, your money grows by 12.68% over the year — because each month's interest itself starts earning interest. That higher, truer figure is the effective annual rate, and it is the number this effective annual rate calculator returns the moment you enter a nominal rate and a compounding frequency.
EAR goes by several names. You will also see it called the effective interest rate, the annual equivalent rate (AER) on UK savings products, or simply the effective rate. They all mean the same thing: the annualised rate that reflects the real effect of compounding, so two products with different nominal rates and compounding schedules can be compared on a level footing.
The effective annual rate formula explained
The formula has two moving parts: the nominal rate divided into equal slices, and the number of times those slices compound in a year. You divide the nominal rate i by the number of periods n to get the rate per period, grow $1 by that periodic rate n times over the year, and subtract the original dollar to leave just the interest.
- Convert the nominal rate to a decimal. A 12% nominal rate becomes 0.12.
- Divide by the periods per year (n). Monthly compounding means n = 12, so the periodic rate is 0.12 ÷ 12 = 0.01 (1% per month).
- Compound across the year. Raise (1 + 0.01) to the 12th power to get 1.126825.
- Subtract 1 and convert back to a percent. 1.126825 − 1 = 0.126825, or an EAR of 12.68%.
For continuous compounding — the theoretical limit where interest is added every instant — the formula collapses to a clean exponential: EAR = e^i − 1. At a 12% nominal rate that gives 12.75%, the ceiling that no finite compounding frequency can quite reach.
A worked example using the effective annual rate calculator
Suppose a lender quotes a 12% nominal annual rate but charges interest monthly. You want to know the true annual cost. Here is exactly how the calculator gets there — set the nominal rate, choose the compounding frequency, then read the EAR.
Step 1 — Enter the nominal rate
Type 12 into the nominal annual rate field. This is the headline, quoted rate — the one before compounding is accounted for. On its own it tells you almost nothing about what you will actually pay.
Step 2 — Choose the compounding frequency
Set the compounding control to Monthly. That tells the calculator n = 12: interest is added twelve times a year, and each addition starts earning interest of its own. This is the single most important choice on the page, because it is what separates the effective rate from the nominal one.
Step 3 — Read the effective annual rate
To put that in dollars: $10,000 borrowed at 12% compounded monthly grows to about $11,268 after a year, not $11,200. The $68 gap is exactly what the effective annual rate captures — and why comparing two loans on their nominal rates alone can mislead you.
Now flip the frequency to see the lesson land. Leave the rate at 12% but switch compounding to daily, and the EAR climbs to 12.747%; switch it to continuous and it reaches 12.750%. Drop it to annual and the EAR falls all the way back to 12.000% — identical to the nominal rate, because there is no intra-year compounding left to capture. The nominal rate never moved; only the compounding did, and the effective rate moved with it.
How EAR rises with compounding frequency
For a fixed nominal rate, the effective annual rate climbs every time you compound more often — from annual, to semiannual, quarterly, monthly, daily, and finally the continuous-compounding ceiling. The table below holds the nominal rate at 12% and shows how the EAR grows as the periods per year increase. The jumps get smaller each step: most of the benefit of compounding is captured by the time you reach monthly.
| Compounding frequency | Periods/year (n) | Effective annual rate |
|---|---|---|
| Annual | 1 | 12.000% |
| Semiannual | 2 | 12.360% |
| Quarterly | 4 | 12.551% |
| Monthly | 12 | 12.683% |
| Daily | 365 | 12.747% |
| Continuous | ∞ | 12.750% |
EAR for a 12% nominal rate at each compounding frequency. Computed with EAR = (1 + 0.12/n)^n − 1, and e^0.12 − 1 for the continuous row.
The pattern of diminishing returns is the key takeaway. Going from annual to semiannual compounding adds 0.36 percentage points; semiannual to quarterly adds only 0.19; quarterly to monthly adds 0.13; and monthly all the way to continuous adds just 0.07 combined. This is why most real-world products compound monthly or daily and rarely bother going finer — past monthly, the extra effective yield is too small to matter to either side. The same shape holds at any nominal rate: the bulk of the compounding benefit is captured early, and the curve flattens toward the continuous ceiling.
EAR vs APR — what is the difference?
EAR and APR are the two rates you will meet most often, and they answer different questions. The annual percentage rate (APR) is a nominal rate that bundles in fees but does not compound — it assumes you pay interest off each period. The effective annual rate (EAR) ignores fees but captures compounding, so it shows the true rate at which a balance grows. EAR is the better tool for comparing how compounding differs between products; APR is the better tool for comparing the fee-inclusive cost of loans.
| APR (annual percentage rate) | EAR (effective annual rate) | |
|---|---|---|
| Includes compounding? | No | Yes |
| Includes fees? | Often yes | No |
| Always ≥ nominal rate? | Equal to nominal | Yes (≥ nominal) |
| Best for | Comparing loan cost with fees | Comparing true compounding |
APR and EAR each tell only part of the story. For a true apples-to-apples comparison, look at both.
Because APR does not compound, EAR is always equal to or greater than the matching APR — they are identical only when interest compounds exactly once a year. To convert in the other direction, see the APR calculator, the APY calculator (APY is EAR for savings products), and the compound interest calculator.
A worked contrast makes the gap concrete. A credit card with a 24% APR compounded monthly carries an effective annual rate of 26.82% — nearly three percentage points above the quoted APR, purely from monthly compounding on an unpaid balance. The APR is what appears in the cardholder agreement; the EAR is what actually accrues if you carry the balance for a year. When you compare two cards, comparing their APRs is fine only if they compound on the same schedule; the moment the schedules differ, EAR is the only fair comparison.
Why the effective annual rate matters
The effective annual rate exists to make different products directly comparable. Two loans can quote near-identical nominal rates yet cost different amounts because one compounds quarterly and the other weekly. EAR strips out that difference by restating every rate on the same annual, compounded basis — so the lowest EAR is genuinely the cheapest loan, and the highest EAR is genuinely the best-yielding deposit.
- Comparing loans and credit cards. A card quoting 36% nominal compounded monthly actually charges an EAR of 42.58% — a difference no borrower should ignore.
- Comparing savings and CDs. A higher compounding frequency raises the effective yield, so a slightly lower nominal rate can still win on EAR.
- Reading the fine print. Lenders quote the lower nominal rate; savings providers advertise the higher effective (AER) rate. Knowing both keeps you from being misled by either.
There is a reason lenders prefer to advertise the nominal rate rather than the EAR: it looks smaller. The Corporate Finance Institute notes that banks quote the lower stated rate on loans to make borrowing appear cheaper, while promoting the higher effective rate on deposits to make saving look more attractive. The effective annual rate is how you see through both.
How to calculate the effective annual rate by hand
You do not need this calculator to find EAR — the arithmetic is short enough for any scientific calculator. Take a 6% nominal rate compounded quarterly as an example.
- Periodic rate: 6% ÷ 4 periods = 1.5% = 0.015 per quarter.
- Grow $1 across the year: (1 + 0.015)^4 = 1.06136.
- Subtract the principal: 1.06136 − 1 = 0.06136.
- Convert to a percent: the EAR is 6.136%.
The same three operations — divide, raise to the power, subtract one — work for any frequency. In a spreadsheet the formula is =(1 + rate/n)^n − 1, or you can use the built-in =EFFECT(nominal_rate, n) function in Excel and Google Sheets, which does exactly this.
Why don't banks use the effective annual rate?
Whether a provider quotes the nominal or the effective rate usually comes down to which one looks better. On loans and credit cards, the nominal (stated) rate is lower than the EAR, so lenders advertise the nominal figure to make borrowing seem cheaper. On savings accounts and CDs, the effective rate is higher than the nominal rate, so banks promote the effective (AER) figure to make the return look stronger.
Neither is dishonest on its own — both are accurate descriptions of the same product — but they are not directly comparable. The fix is always to restate every offer as an effective annual rate before you choose, which is what this calculator does in one step.
Formula sources and methodology
All figures on this page are computed with the standard effective-rate identity EAR = (1 + i/n)^n − 1, and EAR = e^i − 1 for continuous compounding. The 12% and 36% monthly examples match the worked illustrations published by the Corporate Finance Institute; the formula and continuous-compounding case match CalculatorSoup and Omni Calculator. Everything runs in your browser — no rate you enter is sent anywhere.
Corporate Finance Institute — Effective Annual Interest Rate (EAR).CalculatorSoup — Effective Annual Rate (EAR) Calculator.Frequently asked questions about the free effective annual rate calculator
About this effective annual rate calculator
This effective annual rate calculator runs entirely in your browser. Every rate you enter stays on your device — nothing is sent to a server, logged, or shared. It applies the standard EAR = (1 + i/n)^n − 1 formula (and e^i − 1 for continuous compounding), recomputing instantly as you change the nominal rate or compounding frequency.
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