PV of Income Path: Y1=100, Y2=125 & r=0.5

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Homework Statement


What is the permanent income that corresponds to present value of the two period income path Y 1 =100, Y 2 =125 for the real interest rate r=.5? (Note: 50% not ½%!)



Homework Equations



PV = Y1 + Y2/(1+r)^t

The Attempt at a Solution




Correct Answer:

a) 110

I did Pv = 100 + 125/1,5 = 183, but the answer is 110!?
 
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i found the anser, it s the definition

1+r/2+r x y1 + y2/1+r !

its 109,8
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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