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
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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