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Effective Annual Rate Calculator

EAR calculator. Free online Effective Annual Rate Calculator. Calculate effective annual rate online — fast, accurate, mobile-friendly, no signup needed.

EAR
6.1678%

Derivation

  1. ├── 01Givenr = 6, n = 12
  2. ├── 02Formula100 × ((1+t / 100 / a)^(a)-1)
  3. └── 03Compute EAR6.167781
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§01What is

Understanding the Effective Annual Rate Calculator

The Effective Annual Rate Calculator computes EAR from 2 inputs: apr (%), compounds/year. EAR calculator.

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The Effective Annual Rate Calculator sits in that toolkit — it EAR calculator. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

100 × ((1+t / 100 / a)^(a)-1)

Where

r
APR (%)
n
Compounds/year
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: APR (%) = 6, Compounds/year = 12.

  1. 01Start by noting the input — APR (%): 6.
  2. 02Start by noting the input — Compounds/year: 12.
  3. 03Substitute these values into the formula: 100 × ((1+t / 100 / a)^(a)-1)
  4. 04Compute EAR: the calculator returns 6.16778.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Effective Annual Rate Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

APR (%) halved

r = 3 (from 6)

Keep every other input at its default and halve the apr (%). See how ear responds.

  1. 01New APR (%): 3
  2. 02Baseline EAR: 6.16778
  3. 03New EAR: 3.0416
  4. 04EAR decreases by 50.7% → use this sensitivity to plan for real-world variation.
02 · PATTERN

APR (%) doubled

r = 12 (from 6)

Keep every other input at its default and double the apr (%). See how ear responds.

  1. 01New APR (%): 12
  2. 02Baseline EAR: 6.16778
  3. 03New EAR: 12.6825
  4. 04EAR increases by 105.6% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Compounds/year halved

n = 6 (from 12)

Keep every other input at its default and halve the compounds/year. See how ear responds.

  1. 01New Compounds/year: 6
  2. 02Baseline EAR: 6.16778
  3. 03New EAR: 6.15202
  4. 04EAR decreases by 0.3% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Compounds/year doubled

n = 24 (from 12)

Keep every other input at its default and double the compounds/year. See how ear responds.

  1. 01New Compounds/year: 24
  2. 02Baseline EAR: 6.16778
  3. 03New EAR: 6.1757
  4. 04EAR increases by 0.1% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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