#### Definition:

Annual Percentage Yield is a standardized illustration of annual interest rate in finance, depending on the compounding time of one year.

#### Formula:

APY = (1 + r/n)^{n} - 1
###### Where,

APY = Annual Percentage Yield
r = stated annual interest rate
n = number of compounding periods per year
#### Example :

A man got loan from the bank with a 5% stated annual interest rate. The bank compounds the interest for 8 months. Calculate the annual percentage yield.

##### Given,

Interest rate (r) = 5% = 0.05
Number of compounding periods (n) = 8

##### To Find,

APY

##### Solution:

APY = (1 + r/n)^{n} - 1
= (1 + (0.05 / 8))^{8} - 1
= (1 + 0.00625)^{8} - 1
= 1.00625^{8} - 1
= 1.0511 - 1
= 0.0511
= 5.11 %