Effective annual rate

Before you rely on it

What to check

Convert in both directions before concluding. Their quote and yours.

The common error

Where people go wrong with effective annual rate

Assuming the quoted rate is the effective one. On anything compounding more often than annually it is not, and the gap widens as the rate rises.

Worked through

Effective annual rate in plain numbers

A savings account advertises 12% compounded monthly. Each month earns 1%, so after a year $1,000 grows to $1,000 × 1.01¹², which is $1,126.83; the effective annual rate is 12.683%, not 12%. Now flip it around: a credit card with an 18% stated rate compounded monthly costs 1.5% a month, and the year's effective rate is 1.015¹² − 1, or 19.56%; the same nominal-to-effective conversion works for both, but it helps the saver and hurts the borrower. It puts different compounding schedules on one scale so you can compare fairly.

Easily confused

Effective annual rate and its neighbours

The effective annual rate is the same idea as APY on deposits, and it is not the same as APR. APR stays close to the stated rate and adds fees. The nominal rate ignores compounding. EAR includes compounding within the year. Continuous compounding gives the limiting EAR, e raised to the rate minus one. When the compounding is annual, EAR equals the nominal rate, and use EAR to compare things with different compounding, and APR to compare loans with similar structures.

In real decisions

Where effective annual rate turns up

Anyone comparing savings accounts, CDs, bonds or loans across different compounding schedules uses EAR. Finance textbooks use it to convert rates; lenders in some jurisdictions must state it; it is helpful for calculating what a credit card balance really costs over a year or what an account will pay. Analysts convert quoted rates to EAR before discounting cash flows, so that all rates share a basis.

Know the edges

Where effective annual rate stops being reliable

EAR assumes the rate stays constant for the year and that interest compounds as stated. Fees and taxes are not included. For variable-rate products, it reflects only the current rate, and small differences from frequency can be smaller than differences from fees and account rules. Always check terms behind the number, and prefer offers where the fee-adjusted cost is clear.

Quick answers

What people ask about effective annual rate

Is EAR the same as APY? For deposits, essentially yes. Both express the yearly result after compounding. APY is the regulated term for savings products. EAR is the general name used in finance.

How do I convert a nominal rate to EAR? Divide the rate by the number of compounding periods, add 1, raise it to the number of periods, and subtract 1. A 12% nominal rate compounded monthly gives 12.68%.

Why does EAR matter for loans? It shows what a credit card or loan really costs after compounding. An 18% stated rate compounded monthly costs 19.56% a year.

Can the EAR be lower than the nominal rate? No. With compounding more than once a year, the effective rate is higher. With annual compounding, they are equal.

Is EAR the same as the cost of a loan? It shows the effect of compounding but not fees. APR includes some fees. Use both to compare offers.