Question 275098: How do you find the effective yield of 8(1 + r)^4 = 200?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! In order to find the effective yield, you have to find the interest rate per time period and then use the formula for effective yield as given by the following reference:
http://investinganswers.com/term/effective-yield-1013
your equation is:
8*(1 + r)^4 = 200
divide both sides of that equation by 8 to get:
(1+r)^4 = 25
take the 4th root of both sides of the equation to get:
(1+r) = root(4,25)
substract 1 from both sides of the equation to get:
r = root(4,25) - 1
root(4,25) means take the 4th root of 25.
you get:
r = 1.236067978
the formula for effective yield from the reference is:
effective yield = (1 + (i/n))^n - 1
In your equation, n = 4 and r = i/4
this makes that equation equal to:
effective yield = 1 + 1.236067978)^4 - 1 which becomes:
effective yield = 2.236067978^4 - 1 which becomes:
effective yield = 25 - 1 which becomes:
effective yield = 24.
that's your answer.
they really threw you a curve with this one.
normally they give you the nominal rate and then ask you to solve for the effective yield.
see the reference to see what they normally ask.
in this problem, they did not give you the nominal rate.
that, by the way, is 4 * 1.236067978 = 4.94427191
they also made the problem a lot harder by giving you interest rates that are out of this world in comparison to normal interest rates.
despite that, if you use the method for finding effective rate, given the nominal rate I calculated for you, you will see that the method works despite the very large interest rates.
following the referenced method, you would divide 4.94427191 by 4 to get 1.1236067978.
you would then take:
(1 + 1.1236067978)^4 - 1 which becomes:
2.1236067978^4 - 1 which becomes:
25 - 1 which becomes:
effective yield = 24.
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