Effective Annual Rate (EAR) Calculator
Convert a nominal annual rate and compounding frequency into the real Effective Annual Rate (EAR).
Input Data
Results
At a glance:The Effective Annual Rate (EAR) — also called the effective annual interest rate or annual equivalent rate — is the real annual rate after compounding, so that different compounding frequencies can be compared fairly. The nominal annual rate is only the 'labelled' rate; the more often interest is compounded, the higher the real rate. Formula: EAR = (1 + nominal rate ÷ m)^m − 1, where m is the number of compounding periods per year. With continuous compounding, EAR = e^nominal rate − 1. EAR is mathematically identical to the Annual Percentage Yield (APY); the terms differ only by context — EAR commonly for borrowing/comparison, APY for deposits.
Formula
EAR = (1 + nominal rate ÷ m)^m − 1, m = compounding periods per year.
Continuous: EAR = e^nominal rate − 1.
$$$EAR = \\left(1+\\dfrac{r}{m}\\right)^{m}-1$$$$$$EAR = e^{r}-1$$$$$(12%)$\\left(1+\\frac{0.12}{12}\\right)^{12}-1\\approx12.68\\%$$$How to Use
- Enter the nominal annual rate quoted by the bank or product.
- Choose the compounding frequency each year (or continuous).
- The real Effective Annual Rate (EAR) and periodic rate show instantly.
FAQ
Why convert to the Effective Annual Rate (EAR)?
Two loans or deposits with the same nominal rate but different compounding frequencies have different real costs or returns. Converting to EAR puts them on a fair, comparable annual basis.
Does more frequent compounding always raise the EAR?
Yes, but with diminishing returns. The jump from annual to monthly is the most visible; the gap from daily to continuous is tiny. Continuous compounding is the theoretical upper limit of compounding frequency.
What is the difference between EAR, APY and APR?
EAR (Effective Annual Rate) and APY (Annual Percentage Yield) are mathematically identical — both equal (1 + r/m)^m − 1, the real annual rate after compounding — differing only in usage: APY is common for deposits/savings (you receive interest), EAR for broader financial analysis. APR (Annual Percentage Rate) is usually the nominal quoted rate before compounding. When comparing products with different compounding frequencies, always convert to EAR/APY for a fair comparison. This calculator's EAR can be read as the equivalent APY.
How is the EAR for continuous compounding calculated, and is it very different from daily?
Continuous compounding uses EAR = e^r − 1, where r is the nominal rate and e ≈ 2.71828. It is the limit as the compounding frequency tends to infinity. At a nominal 12%, continuous EAR ≈ 12.7497%, while daily compounding (m = 365) gives ≈ 12.7475% — a difference of only about 0.0022 percentage points. Daily compounding already nearly reaches the continuous limit, so in practice daily compounding is enough; continuous compounding is mainly used in academic finance such as option pricing.
How do EAR, simple interest, compound interest and daily interest relate?
They are all facets of 'how interest is calculated'. Simple interest charges only on the original principal; compound interest reinvests each period's interest (interest on interest), giving a higher return over time. Because compounding frequency varies, EAR standardises the real annual rate so products can be compared. Daily interest usually uses simple interest (daily rate = annual ÷ 365), but if interest is reinvested daily it becomes daily compounding, whose EAR is (1 + annual/365)^365 − 1, slightly above simple daily interest × 365. For any deposit or loan, the fairest benchmark is the EAR (or the actual annual rate including fees). Pair this tool with our Compound Interest, Simple Interest and APY calculators.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.