How this instrument works
The effective annual rate is what a nominal rate actually becomes once compounding within the year is folded in. A loan, a credit line, a bond, or a corporate discount rate can each be quoted at what looks like the same nominal percentage while compounding on entirely different schedules — annually, monthly, daily — and those schedules are not cosmetic. EAR converts any nominal rate and its compounding frequency into one comparable annual figure, which is why analysts reach for it whenever two financing quotes or two yields need to sit side by side.
The formula is shaped by how nominal rates are written and applied: a rate quoted per year is sliced into n equal periods, so one period earns i ⁄ n. Multiplying by (1 + i ⁄ n) advances the balance one period, and raising that factor to the power n stacks every period across the year; subtracting 1 strips the original balance back out, leaving pure growth. More periods means each slice compounds on interest already added earlier in the same year, so EAR rises with compounding frequency even though the nominal rate never moves — the 12% loan compounded monthly in the worked example below is genuinely a 12.6825% loan, not a rounding quirk.
EAR converts one nominal rate at a time; it does not average a rate that changes mid-term, fold in origination fees or points, or account for tax on interest earned or paid. A corporate treasurer uses it to put a term loan, a revolving credit line and a bond issue on one comparable annual basis before choosing between them; a borrower shopping two lenders uses it to catch a lender whose lower headline rate compounds often enough to cost more than a higher headline rate that compounds once a year. The number this instrument returns is the true annual rate implied by the contract terms you entered — nothing about which contract is the better one to sign.
- Enter the quoted rate into Nominal annual rate, % — type 12 for twelve percent, not 0.12.
- Set Compounding to match how often the rate is applied: Annually, Semi-annually, Quarterly, Monthly, or Daily.
- Read Effective annual rate (EAR), % — the true annual rate once that compounding schedule is included.
- Re-run the instrument with a second quote's rate and compounding, then compare the two EAR figures directly rather than the two nominal ones.
Worked example — 12% compounded monthly
Set Nominal annual rate, % to 12 and Compounding to Monthly, so n = 12. Each of the twelve periods applies i ⁄ n = 0.12 ⁄ 12 = 0.01, or one percent, to a balance that already includes every prior period's interest. Compounding that factor twelve times gives (1.01)¹² − 1 = 0.126825030132, so Effective annual rate (EAR), % reads 12.6825030132 — a contract advertised as '12% APR, compounded monthly' is quietly a 12.6825% obligation, not a 12% one.
Now compare that against a competing quote of 12.5% compounded annually on an otherwise identical loan: with n = 1 there is no compounding gap, so its EAR is exactly 12.5%. Despite the higher headline number, 12.5% compounded annually is the cheaper loan — its 12.5% EAR sits below the 12.6825% EAR the 12% monthly quote actually carries. Ranking the two offers by their nominal rates alone would have picked the more expensive one; running both through this formula does not.
Questions
How is EAR different from APR?
APR is the nominal rate a lender quotes; it does not, by itself, tell you how often that rate compounds within the year. EAR does. A business line of credit advertised at 18% APR compounded monthly carries an EAR of 19.5618% — the 1.5618 percentage points sit entirely in compounding the APR figure never discloses. Two loans with identical APR but different compounding periods have different real costs, which is exactly what EAR is built to expose.
Is EAR the same calculation as APY?
Same formula, different job. APY is the specific figure U.S. banks are required to publish on savings accounts and CDs; EAR is the general finance term for the identical calculation applied wherever a rate compounds — loan quotes, credit lines, bond yields, or a discount rate used in a valuation. A CFO converting a term loan's rate for a financing comparison calls the number EAR; a bank marketing a CD calls the same arithmetic APY.
Can two rates that both say '9%' cost different amounts?
Yes, whenever they compound differently. A bond paying 9% compounded semi-annually carries an EAR of 9.2025%; a loan quoted 9% compounded monthly carries an EAR of 9.3807%. Both show '9%' on the page, but the loan compounds six times more often within the year, so it accrues more than the bond yields — the two 9% figures are not the same number until each is converted through this formula.
Does EAR include fees, points, or taxes?
No. EAR converts a nominal rate and a compounding frequency into one annual figure and nothing else — an 8% loan compounded monthly returns an EAR of 8.30% here regardless of a 2% origination fee charged on top, tax owed on interest earned, or a rate that resets partway through the term. Add those costs separately; this instrument answers one question only, which is what the stated rate becomes once compounding is included.
What happens if I type 0.08 instead of 8?
You get 0.0800% instead of 8.30% — a hundredfold error that reads as a plausible tiny yield rather than an obvious typo. Nominal annual rate, % expects whole percentage points, so eight percent is entered as 8; the division by 100 already happens inside the formula. If a result looks two orders of magnitude too small, that field is almost always why.
References
- U.S. Small Business Administration — Loans
- Consumer Financial Protection Bureau — Consumer Tools
- Federal Reserve — Selected Interest Rates (H.15)
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.