My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance


Thanks Tree3Thanks
  • 1 Post By samkb8
  • 2 Post By Denis
Reply
 
LinkBack Thread Tools Display Modes
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
samkb8 is offline  
 
April 3rd, 2016, 05:30 PM   #2
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 7,893
Thanks: 536

Quote:
Originally Posted by samkb8 View Post
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 %
Thanks from jonah and manus
Denis is offline  
Reply

  My Math Forum > Science Forums > Economics

Tags
annual, class, effective, financial, finding, management, rate



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Effective rate of interest jenjenjen Economics 2 May 6th, 2013 01:10 PM
Financial and Management Accounting almazz Algebra 3 February 15th, 2012 04:52 AM
Financial and Management Accounting almazz Algebra 1 February 12th, 2012 06:29 PM
Need help using my financial calculator for finance class courvy Economics 0 November 5th, 2011 09:13 PM
effective interest rate. can you help me? gusty Economics 0 October 25th, 2008 06:17 AM





Copyright © 2017 My Math Forum. All rights reserved.