Author 
Comment/Response 
Bill Simpson

02/05/13 5:03pm
You seem to have several different errors in what you showed.
You had Sum{} instead of Sum[].
You were subscripting beyond the end of TauxZC.
And there were other problems.
See if this perhaps does what you need.
In[1]:= TauxCA={0.58`,0.71`,1.1`,1.38`,2.04`,2.47`,2.94`,3.26`,3.49`,3.68`,3.85`,3.99`};
TauxZC={0.5583333333333332`,0.58`};
Do[
TauxZC=Sort[
Join[
TauxZC,
Cases[x/.Solve[100==Sum[TauxCA[[i]]*100/(1+TauxZC[[i]])^i+(100+100*TauxCA[[Length[TauxZC]+1]])/(1+x)^(Length[TauxZC]+1),{i,1,Min[Length[TauxCA],Length[TauxZC]]}],x],v_/;v∈Reals&&v>0]]],{i,1,Min[Length[TauxCA]2,Length[TauxZC]]}];
TauxZC
Out[4]= {0.558333,0.58,1.30381,1.30401}
URL: , 
