EAR Calculator - Effective Annual Rate
Enter a nominal (stated) interest rate and select how often interest compounds to get the true Effective Annual Rate (EAR). The EAR shows what a loan or investment actually costs or earns over a full year once compounding is counted. Supports annual, semi-annual, quarterly, monthly, semi-monthly, bi-weekly, weekly, daily (365 or 360), and continuous compounding. Results update instantly.
What is the Effective Annual Rate (EAR)?
The Effective Annual Rate (EAR), also called the Annual Equivalent Rate (AER) or effective interest rate, is the true annual return or cost of a financial product once the effect of intra-year compounding is included. When a bank or lender quotes a nominal rate of, say, 12%, that number alone does not tell you how much you actually earn or owe, because interest earned in one period is itself re-invested and earns more interest in the next. The EAR captures all of that. The distinction matters in practice: a 12% nominal rate compounded monthly gives an EAR of about 12.68%, not 12%. The difference compounds over years and can represent thousands of dollars on a large loan or savings balance. Any time you compare two financial products with different compounding schedules, use EAR rather than the nominal rate for an apples-to-apples comparison.
The EAR formula and how it works
For discrete compounding, the formula is: EAR = (1 + r / n)^n - 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For annual compounding (n = 1) EAR equals the nominal rate exactly. As n increases, EAR rises but at a diminishing rate. For continuous compounding, the formula simplifies to EAR = e^r - 1, where e is Euler's number (approximately 2.71828). This represents the mathematical upper bound: no discrete compounding schedule can exceed it. At a 12% nominal rate, daily compounding gives EAR = 12.7475% while continuous compounding gives 12.7497%, a difference of just 0.002 percentage points. The periodic rate, sometimes called the rate per period, is r / n. A 12% rate compounded monthly means 1% is applied to the balance each month. The effect of repeatedly multiplying by (1 + 0.01) twelve times is what produces the EAR.
EAR vs. APR vs. APY: what is the difference?
These three terms often cause confusion because they are related but not interchangeable. The Annual Percentage Rate (APR) is a regulatory disclosure figure used in the US for loans: it includes certain fees alongside the interest rate but uses simple (not compound) arithmetic, so it can understate the true cost of credit. The Annual Percentage Yield (APY), used for savings and deposit accounts, is essentially the same calculation as EAR - it tells you the effective rate after compounding. EAR is the general finance and academic term, APY is the consumer deposit-account version of the same idea. When comparing a savings account advertising 5.00% APY with a loan at 5.00% APR, the loan is cheaper on an equivalent basis, because the APR does not reflect compounding costs the way APY/EAR does. Always match like with like: compare EAR to EAR or APY to APY.
When to use an EAR calculator
Use EAR any time you want to compare rates across different compounding schedules. Common use cases include: comparing credit card offers (many compound daily); evaluating mortgage options with different compounding conventions; assessing savings account or CD offers where banks advertise both nominal and APY; understanding the true cost of a payday loan or short-term consumer credit product; and academic or professional finance work involving bond pricing, derivatives, or corporate valuation. The EAR is also the correct input when discounting cash flows: a nominal rate with monthly compounding cannot simply be divided by twelve for monthly discounting without first converting to a periodic rate implied by the EAR.
EAR vs. nominal rate by compounding frequency (at 12% nominal)
| Compounding frequency | Periods/year | EAR |
|---|---|---|
| Annual | 1 | 12.0000% |
| Semi-annual | 2 | 12.3600% |
| Quarterly | 4 | 12.5509% |
| Monthly | 12 | 12.6825% |
| Semi-monthly | 24 | 12.7160% |
| Bi-weekly | 26 | 12.7179% |
| Weekly | 52 | 12.7341% |
| Daily (365) | 365 | 12.7475% |
| Daily (360) | 360 | 12.7474% |
| Continuous | inf | 12.7497% |
Compounding the same 12% nominal rate more frequently increases the effective annual rate. Continuous compounding is the mathematical upper bound.
Frequently asked questions
What is the difference between EAR and nominal rate?
The nominal rate (also called the stated or advertised rate) is the annual rate before compounding is applied. The EAR is the rate you actually experience after accounting for how many times per year interest is compounded. For annual compounding they are equal. For any more frequent compounding, EAR is always higher than the nominal rate, because you earn (or owe) interest on previously accumulated interest.
How do I calculate EAR from a monthly rate?
If you know the monthly rate m, the EAR is (1 + m)^12 - 1. For example, a credit card charging 1.5% per month has an EAR of (1.015)^12 - 1 = 0.1956, or 19.56%. Equivalently, a 18% nominal rate compounded monthly gives a periodic rate of 18 / 12 = 1.5% per month, yielding the same EAR.
Is EAR the same as APY?
Yes, for practical purposes they are the same calculation. APY (Annual Percentage Yield) is the term used in US consumer banking regulations for deposit accounts, while EAR is the general finance term. Both measure the effective rate after compounding over one year. The main difference is that APY is a regulated disclosure, while EAR is the underlying mathematical concept.
What does continuous compounding mean?
Continuous compounding is the theoretical limit in which interest is compounded an infinite number of times per year. The formula is EAR = e^r - 1, where e is Euler's number. In practice, no bank compounds continuously, but the concept is important in derivatives pricing (Black-Scholes and similar models) and in measuring instantaneous rates of return. Daily compounding comes very close to continuous compounding in practice.
How does compounding frequency affect the total interest paid on a loan?
The more frequently interest compounds, the higher the EAR, and therefore the more interest you pay on a loan (or earn on a savings account) for the same nominal rate. A $10,000 loan at 12% nominal costs about $1,200 in simple interest over one year, but if compounded monthly it costs about $1,268 - the extra $68 is the cost of compounding. Over longer loan terms and higher balances, this difference becomes substantial.