Solving for n: 5000=200(1-(1.01)^-n/.01

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Homework Statement


5000=200(1-(1.01)to the -n power, divided by .01


Homework Equations





The Attempt at a Solution

 
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Take logs of both sides.
 
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Thread 'Finding the nth roots of a complex number'

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 . 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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