Effective Annual Rate

EAR is the actual rate paid (or received) after accounting for compounding that occurs during a year. EAR gives the amount of compound interest earned in one year.

EAR and APR are only different if interest is compounded non-annually.

Suppose:

• Bank 1 offers 3% per quarter:

$$EA{R}_1=(1+0.03{)}^4-1=12.55\%$$

• Bank 2 offers 1% per month:

$$EA{R}_2=(1+0.01{)}^{12}-1=12.68\%$$

EAR increases with frequency of compounding.

Where the interest rate per compounding period is:

$$i_m=\frac{\text{APR}}{m}$$

Given APR:

$$\text{EAR}={\left[1+\frac{\text{APR}}{m}\right]}^m-1$$

where APR is the quoted rate and $m$ is the number of compounding per year.

Period interest rate from EAR:

$$i_m=(1+\text{EAR}{)}^{1/m}-1$$

where $m$ is the number of compounding periods.

Equivalent $n$-period discount rate:

$$(1+r{)}^n-1$$