My Math Forum Finding Effective Annual Rate (Financial Management Class)

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 April 3rd, 2016, 01:23 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 semi-annually $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........ Thanks from manus April 3rd, 2016, 05:30 PM #2 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,477 Thanks: 693 Quote:  Originally Posted by samkb8 Interest rate: 6 % compounded semi-annually$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)
The EAR calculation has nothing to do with the frequency of the payment:
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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