Rate Conversion (APR and EAR)

Translate between a nominal annual rate (APR) and the effective annual rate (EAR) it actually produces once compounding is applied. A 12% APR compounded monthly is a 12.68% EAR.

Solve for

Compounding

EAR from APR (Annual Compounding)

When compounding is annual, the effective annual rate equals the stated APR.

When to use: Use as a baseline — with annual compounding, nominal and effective rates are the same.

Calculator

Formula

EAR = APR

Variables

Symbol	Name	Description	Unit
EAR	Effective Annual Rate	True annual return	%
k	APR	Stated annual percentage rate	%

Real-Life Examples

Example 1: Annual Compounding

A savings account states 5% APR with annual compounding. What is the EAR?

Given

k = 5.0000%

Step-by-Step

1.Use the nominal/effective conversion shown above with the stated compounding frequency

2.Keep the rate in decimal form until converting the final answer to percent

3.EAR ≈ 5.000000%

Result:5.0000%

For these inputs, Effective Annual Rate is 5.000000% under the stated payment, compounding and accounting assumptions.

Example 2: Annual Bond Yield

A bond yields 8% with annual compounding.

Given

k = 8.0000%

Step-by-Step

1.Use the nominal/effective conversion shown above with the stated compounding frequency

2.Keep the rate in decimal form until converting the final answer to percent

3.EAR ≈ 8.000000%

Result:8.0000%

For these inputs, Effective Annual Rate is 8.000000% under the stated payment, compounding and accounting assumptions.

Frequently Asked Questions

This formula serves as a baseline reference. Use it to confirm that with annual compounding, no adjustment is needed. For other compounding frequencies, use the m-times or continuous EAR formulas to find the true annual rate.

These equations convert nominal interest rates and effective annual rates for the specified compounding convention. Regulatory APR may also reflect fees, cash-flow timing and product-specific rules; this conversion alone does not calculate every disclosed loan APR.