f[x_] := (((x/12)*87750)/(1-(1+x/12)^(-180)))-980.96

a = 0.1025

b = 0.2

fa = f[a]

fb = f[b]

c = a+.5(b-a)

While[a<b && b<c,
fc = f[c];
If[Sign[fc] == Sign[fa], a=c; fa=fc, b=c; fb=fc];
c = a+.5(b-a);]

c

f2[x_] := x*Exp[-x] - 0.16064

a2 = .1

b2 = 0.4

.3

f2a2 = f2[a2]

f2b2 = f2[b2]

c2 = a2+.5(b2-a2)

While[a2<b2 && b2<c2,
f2c2 = f2[c2];
If[Sign[f2c2] == Sign[f2a2], a2=c2; f2a2=f2c2, b2=c2; f2b2=f2c2];
c2 = a2+.5(b2-a2);]

c2