The formula
How to calculate effective interest rate
The effective annual rate is what a nominal rate is actually worth once compounding is taken into account. It is the number that lets you compare a savings account paying 6% monthly against one paying 6.1% annually without guessing.
Savings accounts publish this as the AER; loans and credit cards publish the same arithmetic as the EAR. Both answer the question "if this compounded exactly once a year instead, what rate would leave me in the same place?"
What to enter:
- Nominal annual rate (%) — the headline rate, before compounding
- Compounds per year
The result updates on every keystroke. The URL updates too, which makes the filled-in version easy to bookmark or send to someone else.
The order the fields are filled in makes no difference to the result — the calculator recomputes the whole formula from whatever is currently in every field, not step by step. That means it is safe to adjust one number, watch the result change, and adjust it back, without worrying about resetting anything first.
Why effective interest rate matters
The formula behind effective interest rate is standard and has not changed in decades; what changes is the situation it gets applied to. Two households can run the identical calculation and land on very different conclusions once their own numbers — income, rate, term, balance — are dropped in, which is why a generic textbook example is less useful than a calculator you can adjust to match your own circumstances.
This tends to come up when comparing two concrete alternatives — two lenders, two savings products, two ways of structuring the same decision — rather than in the abstract. Run both scenarios through the same calculator with the same assumptions and the comparison becomes fair, because the only thing changing between the two results is the number you are actually trying to test.
This kind of calculation rarely stands entirely alone. A effective interest rate figure usually feeds into a wider decision — how it compares with a competing offer, whether it fits inside a monthly budget, what it does to a longer-term plan — and the value of having it as an exact number rather than a rough guess is that those follow-on comparisons stop being guesswork too. Once one figure in a decision is precise, it is worth making the effort to get the others precise as well, rather than mixing an exact calculation with several estimates and treating the result as equally reliable.
In practice, most people arrive at a page like this one having already tried a version of the calculation by hand or in a spreadsheet, and use the calculator here to confirm it rather than replace it. That is a reasonable way to use it — the two should agree to the last decimal place if the same inputs and the same formula are used, and if they do not, the formula shown above is the one to check your own working against first.
Worked example
Take the figures the calculator starts with:
- Nominal annual rate: 6 %
- Compounds per year: 12
That gives:
- Effective annual rate: 6.1678 %
- Uplift over nominal: 0.1678 percentage points
- Rate per period: 0.5 %
These figures are only the calculator's own starting values, included so the working is visible rather than hidden inside the tool above. Replace them with your own numbers and the same arithmetic applies — nothing about the method changes, only the inputs feeding it.
Reading the result
The gap between nominal and effective widens with both the rate and the frequency. At 3% monthly the uplift is about 0.04 percentage points — noise. At 20% monthly, typical of a credit card, it is nearly 2 points, and at the rates charged by short-term lenders the effective figure can be several times the nominal one.
Where this goes wrong. AER is not APR. APR on a loan folds in mandatory fees as well as compounding, so a loan can carry a 6% nominal rate, a 6.17% EAR and a 7.4% APR all at once. Compare like with like, and for borrowing use APR.
A useful check on any unfamiliar result is to compare it against a rough mental estimate first — round the inputs to convenient numbers and see whether the calculator's answer lands in roughly the same territory. A wildly different figure usually means one of the fields was entered in the wrong unit, most often a percentage typed as a whole number where a decimal was expected, or the reverse.
Yes. AER (annual equivalent rate) is the UK savings term for it, EAR (effective annual rate) is the borrowing term, and effective annual yield is the same calculation again. All three assume interest is left in the account to compound.
Because interest is usually credited monthly, and the monthly rate has to come from somewhere. The nominal rate divided by twelve is what actually lands in the account each month; the AER is the annualised consequence of leaving those payments alone.
The headline figure is effective annual rate. With 6 % nominal annual rate and 12 compounds per year, that comes to 6.1678 %. Change any field and the figure moves with it.
Whenever one of the underlying figures changes — a new interest rate, a different balance, an updated term — since the result only reflects what is currently in the fields. There is no need to keep a separate record of past results; the web address for a filled-in version already carries the figures used to produce it.
Not unless a tax rate or a fee is explicitly one of the inputs above. Where it is not, the figure shown is a gross calculation, and any tax due depends on your personal circumstances and current tax rules, which are worth checking separately.
The arithmetic itself is exact — the calculator applies the formula shown above precisely, with no rounding until the final figure is displayed. The uncertainty, where it exists, is entirely in the inputs: an estimated rate or an approximate balance carries that same approximation through to the result.