APY Interest #8-10

Question

Given an APR of 3.00%, calculate the APY for each of the following.
(Round all answers to the nearest thousandth of a percent.)

Annually %=
Quarterly %=
Monthly %=
Daily %=

Answer 1

The forumula for APY is:

 

APY =  100 * ((1 + r/f)^f - 1)

 

r is the annual interest rate (as a decimal)
f is the frequency of compounding per year

In this case, r = 3% = .03

So with annual compounding, APY = 100 * ((1 + .03)¹ - 1)= 3.000 %

 

Quarterly:  Since there are 4 quarters per year, APY =  100 * ((1 + .03/4)⁴ - 1) = 3.034 %. 

 

Monthly:  Since there are 12 months per year, APY = 100 * ((1 + .03/12)¹² - 1) = 3.042 %

 

Daily:  Since there are 365 days per year, APY = 100 * ((1 + .03/365)³⁶⁵ - 1) = 3.045 %