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April 3rd, 2016, 02:23 AM  #1 
Newbie Joined: Apr 2016 From: Korea Posts: 1 Thanks: 1  Finding Effective Annual Rate (Financial Management Class)
This is a Perpetuity question and I'm having a hard time finding the EAR(Effective Annual Rate) It states the following: Interest rate: 6 % compounded semiannually $100 payed every three months per year So how would you calculate the EAR in this situation? The amount of cash flows per year is greater than the number of compounding per year (PP>CP) Please help........ 
April 3rd, 2016, 06:30 PM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,900 Thanks: 716  Quote:
r = .06 (annual rate/100) n = 2 (compounding periods) EAR = (1 + r/n)^n  1 = (1 + .06/2)^2  1 = 1.0609  1 = .0609 which means 6.09% If the payment frequency does not match the compounding frequency, then the rate used in order to pay interest on payment dates needs to be calculated, and must result such that it equals the EAR: EAR = .0609 p = 4 (payment frequency) k = required rate (1 + k)^p = 1 + EAR 1 + k = (1 + EAR)^(1/p) k = (1 + EAR)^(1/p)  1 k = 1.0609^(1/4)  1 k = 1.014889...  1 k = .014889... which means ~1.4889% In other words, crediting the interest every 3 months using rate of ~1.4889 results in effective annual rate of 6.09 %  

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