Effective Annual Rate Calculator

EAR formula

Related pages

For a consumer-friendly version, use the APY calculator. For balance projections, use the compound interest calculator.

What 8% nominal is actually worth

A nominal rate is a quoted rate. The effective annual rate is what you receive once compounding inside the year is accounted for. The gap is the entire reason this calculator exists — two accounts quoting the same 8% do not pay the same amount.

8% nominal. The final row is the mathematical ceiling: compounding more often than daily adds almost nothing.

Moving from annual to monthly compounding on 8% is worth $30.00 in the first year on $10,000. Moving from monthly to daily adds a further $2.78. The first step matters; the second is nearly noise, which is why “compounded daily” in an advertisement is a weaker selling point than it sounds.

Reading a rate the way a comparison should

The effective rate is the only fair basis for comparing two products, because it removes the compounding convention from the comparison and leaves only the money.

• EAR = (1 + r/n)ⁿ − 1. Nominal rate r as a decimal, n compounding periods per year.
• Working backwards. To receive an effective 8.00% with monthly compounding, the nominal rate needs to be about 7.7208% — noticeably below 8%.
• APY is the same idea. On deposit accounts the effective annual rate is normally published as APY; on borrowing, APR may or may not include compounding depending on jurisdiction. See APY vs APR.
• Fees break the comparison. An account with a higher effective rate and an annual fee can pay less than a lower-rate account without one.

On multi-year horizons the effect accumulates. $10,000 at a 6% nominal rate for ten years finishes at $17,908.48 compounded annually and $18,193.97 compounded monthly — a difference of $285.49 from the convention alone.

Questions about effective annual rate

What is the difference between nominal rate and effective annual rate?

The nominal rate is quoted before compounding within the year. The effective annual rate is what you actually earn once compounding is applied. They are equal only when interest compounds exactly once a year.

Is a higher effective annual rate always better?

For a saver, yes, all else equal — but all else rarely is. Compare after fees, and check whether the rate is introductory, capped by balance, or conditional on deposits.

Why does daily compounding barely beat monthly?

Because the sequence converges. As periods per year increase, the effective rate approaches the continuous limit e^r − 1, which for 8% is 8.3287%. Daily is already within a rounding error of that ceiling.

How do I convert an effective rate back to a nominal one?

Rearrange the formula: nominal = n × ((1 + EAR)^1/n − 1). It is the calculation you need when a provider quotes APY and you want to compare against a nominal rate elsewhere.