Effective Annual Rate (EAR) Calculator
Convert a stated nominal interest rate into the true annual rate once compounding is included. Use it to compare loans or savings accounts that compound at different frequencies.
Last updated: May 2026
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About this calculator
The effective annual rate (EAR), also called the annual equivalent rate or APY, is the real rate of interest you earn or pay over a year once compounding is taken into account. The formula is EAR = (1 + i/m)^m − 1, where i is the Nominal Annual Rate (the quoted or 'stated' rate) as a decimal and m is the number of Compounding Periods per year. The intuition is that interest charged or earned partway through the year itself starts earning interest, so the true annual rate is always at least as high as the nominal rate — and strictly higher whenever m is greater than 1. The more frequently interest compounds, the larger the gap: monthly compounding beats annual, daily beats monthly, and continuous compounding (the limit as m → ∞) gives EAR = e^i − 1. Edge cases: with m = 1 the EAR equals the nominal rate exactly; as m grows the EAR rises but with diminishing increments, approaching the continuous-compounding ceiling. This is why lenders often advertise a low nominal rate while the figure that actually governs your cost is the EAR. Regulators require an APY (savings) or APR (loans) disclosure precisely so consumers can compare products on an equal footing rather than being misled by compounding frequency.
How to use
Example 1 — a credit card quoting 12% compounded monthly. Enter Nominal Annual Rate = 12 and Compounding Periods per Year = 12. EAR = (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 = 0.126825, or 12.68%. Verify: monthly compounding adds about 0.68 percentage points over the headline 12%, so your real annual cost is higher than the sticker rate. Example 2 — a savings account paying 5% compounded daily. Enter 5 and 365. EAR = (1 + 0.05/365)^365 − 1 ≈ 0.051267, or 5.13%. Verify: daily compounding lifts the 5% nominal rate to about 5.13%, close to the continuous-compounding limit of e^0.05 − 1 = 5.127%. The two examples show that compounding frequency works for you on savings and against you on debt.
Frequently asked questions
What is the difference between nominal rate, APR, and APY?
The nominal rate is the simple stated rate before compounding effects; APY (annual percentage yield) is the effective rate you actually earn on savings once compounding is included — the same thing this calculator computes. APR (annual percentage rate) on loans is trickier: it includes certain fees but, in many jurisdictions, is quoted as a nominal rate that ignores intra-year compounding, so the true cost (the EAR) can be higher than the APR. The practical rule is to compare savings products by APY and loans by their effective rate, not the headline number. Mixing these up is the single most common rate-comparison mistake. When in doubt, convert everything to EAR so you are comparing like with like.
Why does more frequent compounding increase the effective rate?
Because each time interest is added to the balance, the next interest calculation is applied to a slightly larger amount — interest earns interest. With annual compounding that only happens once; with monthly compounding it happens twelve times, each building on the last. The effect grows with frequency but with diminishing returns: the jump from annual to monthly is far larger than the jump from daily to continuous. In the limit of infinitely frequent compounding, the EAR reaches e^i − 1, a hard ceiling. That is why a savings account advertising 'daily compounding' is only marginally better than monthly at the same nominal rate.
How do I convert the effective rate back to a nominal rate?
Reverse the formula: the nominal rate i = m × ((1 + EAR)^(1/m) − 1), where m is your compounding frequency. For instance, to find the monthly-compounded nominal rate that produces a 12.68% EAR, you would compute 12 × ((1.1268)^(1/12) − 1) ≈ 12%. This is useful when a product quotes an APY and you need the periodic rate for a payment schedule. Be careful to match the m you use in the conversion to the actual compounding frequency, or the numbers will not line up. Going back and forth between nominal and effective rates is a routine but error-prone step in finance.
When should I NOT use the effective annual rate?
EAR assumes a fixed nominal rate and a constant compounding frequency, so it is the wrong tool for variable-rate loans or accounts whose rate resets, where the effective cost changes over time. It also ignores fees, points, and other charges — for loans, those belong in an APR calculation, and a low EAR can still hide an expensive product once fees are added. Do not use EAR to compare investments with uncertain returns, since it describes a contractual interest rate, not a risky expected return. Finally, for very short holding periods the annualized figure can exaggerate the rate you will actually experience. Use EAR specifically to compare the compounding cost or yield of fixed-rate, interest-bearing products.
Is APY the same as the effective annual rate?
Yes — APY (annual percentage yield) and EAR are the same calculation, just labeled differently depending on context. Banks use 'APY' when advertising deposit accounts because regulations require a standardized, compounding-inclusive yield so savers can compare accounts fairly. Economists and textbooks tend to say 'effective annual rate.' Both answer the same question: given a nominal rate and how often it compounds, what is the true rate over one year? So if you see APY on a savings account, you can plug its underlying nominal rate and compounding frequency into this calculator and reproduce it exactly. In short, the two terms are interchangeable names for the same compounding-adjusted rate.