Solving Present Value Question: Finding (1+i)^2n | Actuary Class

[Jrb599]

[SOLVED] Present Value question

I didn't really know where to post this. It's for an actuary class which eventually gets to applied statitistics, so I put it here. Anyways here it goes

The sum of the present value of 1 paid at the end of n periods and 1 paid at the end of 2n periods is 1. Find (1 +i)^2n.

The back of the book says the answer is 3/2 + sqrt(5)/2


I start with

1/(1+i)^n + 1/(1+i)^2n = 1


There are no given values for i and n. Anyone able to help?

 

[EnumaElish]

Let x = 1/(1+i)^n and y = 1/(1+i)^2n

(Eq.1) x/y = (1 + r)^n
(Eq.2) x + y = 1
(Eq.3) 1/(1 + r)^n + 1/(1 + r)^(2 n) = 1

Solve for x, y, r.