f[r_]:=(((r/12)(87750))/(1-(((1+r/12))^(-180))))-980.96

a=.1025

b=.2

fa=f[a]; fb=f[b];

fa

fb

c=a+.5*(b-a)

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

c