The annual percentage rate (APR) and effective annual rate (EAR) are both annualized representations of the cost of borrowing. They differ, however, in the way they handle the compounding of interest. The EAR assumes that interest earned by investors is reinvested at the same interest rate. Converting the EAR into an APR involves removing this compounding effect.
APR = n x ((EAR+1)1/n-1)
where n = number of compounding periods
Suppose you have an effective annual rate of 5.5% with monthly compounding. You can convert it to the APR using the following formula:
APR = 12 x ((1.055)1/12 - 1)
APR = 12 x (1.044717 -1)
APR = 0.05366
The APR equals 5.366%.