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Calculate effective annual rate (EAR) from nominal rate and compounding frequency — see EAR, APY and periodic rate.
Calculate effective annual rate (EAR) from nominal rate and compounding frequency — see EAR, APY and periodic rate.
Enter values above and click Calculate — results will appear here with the formula explained.
The effective annual rate translates any nominal rate plus compounding frequency into the true yearly cost: 6% nominal compounded monthly is (1+0.06/12)^12−1 = 6.1678% EAR, while the same 6% compounded quarterly is 6.136%. The gap looks trivial until balances and years scale it — on $100,000 over 10 years it's roughly $350 of difference for 'the same' rate.
APR versus EAR versus APY is the terminology triangle: APR is the nominal rate lenders quote (often excluding fees despite the name), EAR is the mathematically true annual cost including compounding, and APY is EAR's name on deposit products. US Truth in Lending APR includes most fees, making it closer to EAR than a bare nominal — but across borders and products, only EAR compares apples to apples.
Compounding frequency has a ceiling: as m grows, EAR converges to continuous compounding e^nominal − 1 (6.1837% at 6% nominal). Daily versus monthly differs by ~0.015 points — real money at institutional scale, rounding noise for households. What matters for consumers is never frequency itself but EAR equivalence across offers.
Where EAR decides: comparing a 5.9% monthly-compounding loan against a 6.0% annual-compounding one (the 5.9% wins at 6.054% EAR vs 6.0%... actually loses — run both here), choosing savings accounts (APY is the whole comparison), and unmasking 'low rate' credit offers whose fees push APR far above the EAR shown. Any comparison skipping EAR compares labels, not costs.
Fees belong in the rate: a 6% loan with 2 points over 5 years costs roughly 6.4%+ effective. This calculator isolates pure compounding math — add fees to the nominal mentally or via APR disclosures for all-in truth. For YMYL borrowing, compare EAR first, APR second, monthly payment last.
Calculate effective annual rate (EAR) from nominal rate and compounding frequency — see EAR, APY and periodic rate. Formula: EAR = (1 + nominal/m)^m -1 where m=compounding frequency. Example: With 6% nominal monthly: EAR 6.1678%; quarterly: 6.136%; daily: 6.1831%; continuous: 6.1837%.
The effective annual rate translates any nominal rate plus compounding frequency into the true yearly cost: 6% nominal compounded monthly is (1+0.06/12)^12−1 = 6.1678% EAR, while the same 6% compounded quarterly is 6.136%. The gap looks trivial until balances and years scale it — on $100,000 over 10 years it's roughly $350 of difference for 'the same' rate.
APR versus EAR versus APY is the terminology triangle: APR is the nominal rate lenders quote (often excluding fees despite the name), EAR is the mathematically true annual cost including compounding, and APY is EAR's name on deposit products. US Truth in Lending APR includes most fees, making it closer to EAR than a bare nominal — but across borders and products, only EAR compares apples to apples.
Compounding frequency has a ceiling: as m grows, EAR converges to continuous compounding e^nominal − 1 (6.1837% at 6% nominal). Daily versus monthly differs by ~0.015 points — real money at institutional scale, rounding noise for households. What matters for consumers is never frequency itself but EAR equivalence across offers.
Where EAR decides: comparing a 5.9% monthly-compounding loan against a 6.0% annual-compounding one (the 5.9% wins at 6.054% EAR vs 6.0%... actually loses — run both here), choosing savings accounts (APY is the whole comparison), and unmasking 'low rate' credit offers whose fees push APR far above the EAR shown. Any comparison skipping EAR compares labels, not costs.
Fees belong in the rate: a 6% loan with 2 points over 5 years costs roughly 6.4%+ effective. This calculator isolates pure compounding math — add fees to the nominal mentally or via APR disclosures for all-in truth. For YMYL borrowing, compare EAR first, APR second, monthly payment last.
With 6% nominal monthly: EAR 6.1678%; quarterly: 6.136%; daily: 6.1831%; continuous: 6.1837%. On $100,000 over 10 years, monthly versus quarterly compounding differs by about $350 — small per year, visible per decade.
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
Last reviewed: September 2026 · Report an error