Point III is about <em>real interest rate</em>
point I doesn't apply since both nominal and effective ir are calculated by year
let alone the fact that if you look close to those numbers it would probably mean that the loan had 1year and 1 day duration :)
the II answer is the correct one
if the loan is compounded at 6 months you have to add the interest of the first 6 months interest to the total interest to find out the effective interest rate
Ie 32^2 - 4ac=0 so ac=256 and a+c=130
So, that means:2 equations ac=256 a+c=130 ie c=130-a
So,a(130-a)=256 so 130a -a^2=256 ie a^2-130a +256=0 (a-2)(a-128)=0
Finally,giving a= 2 or a=128 so, a=2 c=128 or a=128 c=2
Since, a>c , a=128 and c=2 ie (128,2)